Tracking and Decision Making for Automotive

Link¨ oping Studies in Science and Technology Thesis No. 965

Tracking and Decision Making for Automotive Collision Avoidance Jonas Jansson

REGL

AU

ERTEKNIK

OL TOM ATIC CONTR

LINKÖPING

Division of Automatic Control Department of Electrical Engineering Link¨opings universitet, SE–581 83 Link¨oping, Sweden WWW: http://www.control.isy.liu.se Email: [email protected] Link¨oping 2002

Tracking and Decision Making for Automotive Collision Avoidance c 2002 Jonas Jansson

Department of Electrical Engineering, Link¨ opings universitet, SE–581 83 Link¨ oping, Sweden.

ISBN 91-7373-387-3 ISSN 0280-7971 LiU-TEK-LIC-2002:38 Printed by UniTryck, Link¨ oping, Sweden 2002

To Eva and Alexander

Abstract Active safety and collision avoidance (CA) is a growing field within the automotive industry. The aim of CA systems is to prevent or mitigate collisions by active interventions, i.e., warning, braking and steering. For many reasons, such as driver acceptance of the system and the legal requirement that the system itself must not cause hazards, the decision making is a crucial part of the system. This thesis presents a method for risk estimation on which the decision-making can be based. In particular a system that performs autonomous braking actuation when a collision is imminent is studied. The approach is to form a criterion for decision-making in terms of probability of collision. This criterion handles the noisy sensor data and process noise (driver behavior) in a natural way, using existing tracking theory. The method is illustrated by simulation results as well as test results from a prototype vehicle. To evaluate false alarm rates test drives have been performed in real traffic and performance in collision scenarios has been tested with an inflatable car.

i

Acknowledgments The work presented in this thesis would not have been possible without a number of people. First of all I would like to thank my supervisor Jonas Ekmark at Volvo Car. He has always found time for discussions, and has been an inexhaustible source of good advice and experience. I would also like to thank my academic supervisor Professor Fredrik Gustafsson for support and inspiring advice during the work. Other people who have contributed significantly to the work in this thesis are Lars Nilsson at Volvo TU and Fredrik Lundholm at Volvo Car. This work has been carried out within the Volvo Ph.D. program to which I am very grateful. I would also like to thank Robert Hansson at Volvo Car for guidance and assistance of my Ph.D. project. Several people have read and commented this thesis. Special thanks to: Richard Karlsson, Niclas Persson and Claes Ohlsson. Your reviews significantly improved the quality of this thesis. I also greatfully acknowledge Professor Lennart Ljung, Ph.D. Ahmed El-Bahrawy and Raymond Johansson who together with Robert Hansson recruited me for this project. I would also like to acknowledge all my colleagues at the Chassi & Vehicle Dynamic department at Volvo and at the Control & Communication group at LiTH, who have all contributed with a positive attitude and many interesting discussions. Finally I would like to thank my family. You have always supported me in my work “playing with cars”. A special thank to my son Alexander for helping me in getting the right perspective on life.

Jonas Jansson Link¨ oping, September 2002

iii

Contents

1 Introduction 1.1 Car Safety . . . . . . . . . . . . . . . 1.1.1 Passive Safety . . . . . . . . . 1.1.2 Active Safety . . . . . . . . . 1.1.3 Forward Collision Mitigation 1.1.4 Automotive Safety History . 1.2 Accident Statistics . . . . . . . . . . 1.2.1 Accident Types . . . . . . . . 1.2.2 Speed versus Severity . . . . 1.2.3 Weather Conditions . . . . . 1.3 System Overview . . . . . . . . . . . 1.4 Outline and Contributions . . . . . .

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1.A Safety systems introduced on Volvo cars . . . . . . . . . . . . . . . . 14 2 Sensors 2.1 The Radar Sensor . . . . . 2.2 Laser Radar . . . . . . . . . 2.3 Vision Systems for Obstacle 2.4 Infrared Vision Sensors . . .

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Contents

2.5 2.6

Inter-Vehicle Communication . . . . . . . . . . . . . . . . . . . . . . 22 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 Tracking for Collision Avoidance Applications 3.1 State Estimation . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Kalman Filter . . . . . . . . . . . . . . . . . . . . . . 3.2.1 The Stationary Kalman Filter . . . . . . . . . . . . 3.2.2 The Time-Varying Kalman Filter . . . . . . . . . . 3.2.3 The Extended Kalman Filter . . . . . . . . . . . . 3.3 Point Mass Filtering . . . . . . . . . . . . . . . . . . . . . 3.4 Particle Filtering . . . . . . . . . . . . . . . . . . . . . . . 3.5 Measurement Association . . . . . . . . . . . . . . . . . . 3.5.1 Gating . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 Association Methods and Techniques . . . . . . . 3.6 Pre-Filtering of Measurements . . . . . . . . . . . . . . . 3.6.1 Pre-filtering measurements using range only . . . . 3.6.2 Pre-filtering by Range Rate and Time-to-Collision 3.6.3 Pre-filtering Objects by their Azimuth Angle . . . 3.6.4 Summary of Pre-filtering Strategies . . . . . . . . . 3.7 Sensor Fusion . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Models for tracking and navigation . . . . . . . . . . . . . 3.8.1 The Constant Velocity Model . . . . . . . . . . . . 3.8.2 The Constant Acceleration Model . . . . . . . . . 3.8.3 The Coordinated Turn Model . . . . . . . . . . . . 3.8.4 Bicycle Model . . . . . . . . . . . . . . . . . . . . . 3.8.5 Navigation . . . . . . . . . . . . . . . . . . . . . .

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25 26 28 28 29 29 31 33 33 34 35 38 39 40 40 41 42 45 46 46 46 49 50

4 Decision Making 4.1 Collision Mitigation Countermeasures . . . . . . . . . . . 4.2 Risk Estimation . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Probability of Collision . . . . . . . . . . . . . . . . . . . . 4.4 Decision Strategy - Choices of Thresholds for Intervention 4.5 Behavior Modeling and Situation Assessment . . . . . . .

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5 System design and Testing 5.1 Simulation environment . . . . . . . . . . . . . . . . 5.2 The Prototype Vehicle . . . . . . . . . . . . . . . . . 5.2.1 Prototype Vehicle Tracking Sensors . . . . . . 5.2.2 The Braking System of the Prototype vehicle 5.3 Ideal CMbB System Performance . . . . . . . . . . . 5.4 Test Scenarios . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Collision Scenarios . . . . . . . . . . . . . . . 5.4.2 Scenarios to Provoke Faulty Interventions . . 5.5 Discussion of Test Results . . . . . . . . . . . . . . .

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Contents

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6 Conclusions 97 6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Bibliography

101

Notation

Symbols A Dhead Dbrake Dsteer et eˆ  f (·) ϕ G(i) φ Φ(·) h(·)

Linearized state matrix Headway distance to vehicle in-front Distance needed to avoid a stationary obstacle by means of braking Distance needed to avoid a stationary obstacle by means of steering Measurement noise Estimate of e Residual vector, innovations State equation transition mapping (discrete-time) Azimuth angle Gate belonging to track i Host vehicle heading angle Gaussian probability distribution function Measurement relation

ix

x

H Kt lhost J M mi N N P r{·} p(·) p et pvt px0 px , py p P R R Π σ Q T u vt ω ∆V i v01 v1 vhost vPOV whost w ˆPOV xt (i) xt x1 , . . . , xn x = (x1 · · · xn )T xt−1,i

Notation

Linearized measurement relation Kalman gain matrix at time t Length of the host vehicle Maximum number of tracks in the tracking system maximum number of measured objects from one tracking sensor Mass of vehicle i Number of particles, samples or models Number of grid points in a PMF or particles in a PF Probability Probability density function Measurement noise probability density Process noise probability density Initial state probability density x and y position Position vector (px py )T Covariance matrix Measurement noise covariance matrix The set of real numbers Covariance matrix for p Standard deviation Process noise covariance matrix Sample period Control input Process noise Turn rate Speed change of vehicle i during a collision Speed of vehicle 1 before collision Speed of vehicle 1 after collision Speed of the host vehicle POV speed Width of the host vehicle Estimated width of an obstacle State vector at time t States of the ith object in a MTT system State variables State vector Sample state variable drawn from a known prior distribution

Notation

xdes 1 xref 1 yt

xi

Desired value of x1 Reference value of x1 Measurement at time t

Acronyms ABS CA CM CMbB CPU DOF EKF FARS FCA FCM FCW FM-CW FM-Pulse FOV FSK GES GPS i.i.d. IMM IR KF LMS LS MAP MC MHT ML MLE MMSE MTT NCAP NN PDF

Anti Blockier Systeme/Anti lock Braking System Collision Avoidance Collision Mitigation Collision Mitigation by Braking Central processing unit Degrees of freedom Extended Kalman Filter Fatality Analysis Reporting System Forward Collision Avoidance Forward Collision Mitigation Forward Collision Warning Frequency modulated continuous wave Frequency modulated pulsed wave Field of View Frequency shift keying General Estimation System Global Position System Independent Identically Distributed Interacting Multiple Model Infrared Kalman Filter Least Mean Square Least Square Maximum a Posteriori Monte Carlo Multiple Hypotheses Tracking Maximum Likelihood Maximum Likelihood Estimate Minimum Mean Square Error Multiple target tracking New Car Assessment Program Nearest Neighbor Probability Density Function

xii

PF PMF POV RADAR RCS RMSE TTC THW

Notation

Particle filter Point Mass Filter Principal Other Vehicle Radio Detection and Ranging Radar Cross Section Root Mean Square Error Time-to-collision Time-Headway

1 Introduction

Passenger car safety is an issue that has received increasing attention over the last few decades. In the last 10 years, the crashworthiness of automobiles has improved drastically. Evidence of improvements in crash performance can be found from the results of crash tests carried out by organizations all over the world (see Section 1.1.1). Despite this progress, many people are still killed or injured in traffic accidents. In the USA, there were 37409 accidents reported in FARS (a database recording all fatal car crashes reported in the USA [16]) for year 2000. In the reported accidents a total of 41821 people were killed. The number of non-fatal crashes and non-fatal injuries the same year is of course much greater. Despite the improved crashworthiness of modern cars it is clear that there is still a need to significantly reduce traffic related injuries. Having evolved rapidly, existing passive safety technologies have become quite mature. Therefore a significant reduction of injuries becomes technically infeasible as well as too costly using these technologies. In recent years, people in the automotive industry have increased their efforts in trying to find other ways of reducing the number of people injured in traffic. One alternative way to avoid dangers is to try to prevent accidents from happening by means of driver support systems. One of the first such systems was the Anti Blockier System (ABS) braking system (see [2] for a description), which helps the driver maintain steerability during hard braking maneuvers. This thesis will discuss 1

2

Introduction

Figure 1.1 Example of a FCM system. The system warns the driver of danger, in this case that the vehicle ahead is braking hard

issues relating to the design of Forward Collision Mitigation (FCM) systems, which is a specific type of driver support system. An FCM system uses sensors to observe the environment directly in front of the host vehicle. Based on information from the forward-looking sensors, a decision can be made to deploy countermeasures to avoid imminent frontal collisions. Typical interventions are warning signals (audible, visible or haptic/tactile), braking and steering. Figure 1.1 shows an example of a FCM system that warns the driver of an imminent threat by a visible display. There are three main tasks that a FCM system must complete in order to perform correct interventions. The tasks are: 1. Object classification: Classifying the observed objects. 2. Tracking, navigation and prediction: Estimating and predicting the current and future kinematic states of both the host vehicle and the observed objects. 3. Decision-making: Based on the prediction, deciding whether or not a countermeasure should be deployed. The focus of this thesis will be on tracking, prediction and decision-making. Ex-

1.1 Car Safety

3

isting tracking theory will be examined and the tracking performance that can be achieved using commercially available sensors will be investigated. Furthermore, we will show how to form metrics for collision risk that can deal with general traffic scenarios. Object classification will only be discussed briefly in Chapter 2, where an overview of the capabilities of existing sensors is given.

1.1

Car Safety

When vehicle safety is discussed most people normally think of what we will refer to as passive safety. However, in modern cars, several other aspects have to be considered. Systems such as ABS brakes, yaw control etc. are introduced to enhance passenger safety. These systems are sometimes called active safety systems. Conversely, a car with good handling capability is sometimes also said to have good active safety. In Section 1.1.1 and 1.1.2 we will give an account for different aspects of vehicle safety. In broad terms the safety properties of a car can be divided into three groups: • Passive safety • Active safety • Security Security deals with the car’s capacity to protect against theft and vandalism and possibly also attacks on the owner. This will not be discussed further in this thesis. The definition of passive and active safety will be discussed in more detail in the following sections.

1.1.1

Passive Safety

When we discuss a vehicle’s passive safety properties, we mean the ability of the car to protect passengers from injuries in a collision. The ability of the car to protect its passengers is sometimes called crashworthiness. We thus define a car’s crashworthiness or passive safety properties as its abilities to protect passengers from injury from the instant that the collision occurs and afterwards. One way to achieve good passive safety is to optimize the structure of the car’s body in such a way that it absorbs crash energy whilst keeping the crash pulse (momentaneous acceleration) experienced by the passengers as low as possible. Some systems that help to protect the passengers in a collision are seat belts, airbags, belt pretensioners and belt load limiters. The interior of the car should also be designed in such a

4

Introduction

way that panels, switches, etc. cause minimal injury. To achieve good passive safety properties, quite a few areas of the car’s design must be considered. The crashworthiness of automobiles is tested in collision tests. Some organizations that perform such tests are EuroNCAP [41], ANCAP [40] JNCAP [30] and NHTSA [42]). In the tests performed by these organizations, passive safety properties are measured in terms of accelerations and forces experienced by a crash test dummy in some specific collisions. The crashworthiness of cars is also evaluated by insurance institutes (for example, Folksam [17] and IIHS [18]) which rate the performance for different vehicles in real accidents.

1.1.2

Active Safety

Active safety also comprises several different aspects of the car. We will divide active safety properties and functions into three groups: preventive, dynamic and collision mitigation. Here we present a brief account for these groups: 1. Preventive - The preventive part of active safety is about the driver seeing threats and being seen himself. If threats are detected early the driver can take precautionary action before the situation becomes dangerous. Several factors play a role in this: • Detecting threats: To improve the driver’s perceptive ability one traditionally works with headlight performance, headlight cleaning, windshield cleaning, minimizing glare in the windows etc. Some examples of new innovations that improve driver perception are night vision systems and see-through A-pillars. A night vision system uses an IR camera and a driver display unit to present the IR image to the driver. This enables the driver to detect warm objects further away than what is possible when using conventional headlights ([35], [52] and [38] discuses night vision system in automotive applications). The see-through A pillar, which was displayed on the Volvo Safety Concept Car, improves the driver’s perception by allowing him to see through the A-pillar, see Figure 1.2. • Visibility: Visibility of the driver’s own vehicle is another important issue in preventive active safety. In short this means that the car should be designed in such a way that it is easily observed by other road-users. Examples of features to improve visibility are daytime running lights and high positioned brake lights. • Driver information: Driver information also plays an important role in the driver’s ability to detect dangers. Through GPS technology and digital maps, the driver can be provided with geographically dependent information. Other systems that could provide the driver with essential information to avoid collisions are, for example, road friction monitoring

1.1 Car Safety

5

Figure 1.2 See-through A-pillar systems ([24]) and tire pressure monitoring systems ([45] and [46]). It is important to remember that the driver’s cognitive ability is limited, and information overload can cause the driver to fail to detect or react erroneously to imminent threats. In the future we might see systems that prioritize what information to display to the driver depending upon the situation. • The driver: To ensure that the driver’s perception of the traffic environment is adequate, it might be sensible to monitor the driver himself. A driver monitoring system can, for instance be used to warn the driver if he falls asleep behind the steering wheel. 2. Dynamic - From a safety perspective, a car should be designed to have safe handling and ride characteristics. By this we mean that it should be easy for the driver to keep control of the vehicle in all road conditions, in any traffic situation and during all types of maneuvers. Examples: • It should be easy to perform avoidance maneuvers without losing control of the vehicle. • The car should be minimally influenced by side wind. In short, it should be easy for the driver to make the car follow his intended path. To achieve these properties, quite a few areas of the vehicle’s design come into play. Important factors are steering and brake system characteristics. There are already several active systems in existence today that improve

6

Introduction

a vehicle’s dynamic properties. In this thesis, “active systems” refers to the use of sensors and actuators to perform some kind of closed loop control to help the driver. Some common systems are listed below: • ABS brake systems prevent the wheels from locking during hard braking. This enables the driver to achieve fair deceleration whilst maintaining steerability of the vehicle. • Yaw control systems monitor steering angle, yaw rate and lateral acceleration. Brake force is applied to individual wheels to aid the driver in keeping control of the vehicle in situations where the lateral traction limit is reached. • Traction control systems help maintain traction and stability by reducing engine torque and applying brakes if the wheels are spinning. • Roll stability systems apply individual brakes to decrease the risk of rolling over when the car experiences high roll angle rates and roll angles. 3. Collision Mitigation - Collision mitigation (CM) systems are given some perception of the environment surrounding the vehicle. Based on this perception the system takes steps to avoid or mitigate imminent collisions. The main scope of this thesis falls in this field. It must be pointed out that these systems are often called Collision Avoidance (CA) systems. To some people, the term “avoidance” might imply that accidents should be completely avoided by these systems. For several reasons, systems that avoid all collisions are infeasible. This thesis will therefore talk about CM systems. Generally a CM system will try to reduce the severity of the accident as much as possible under some constraints. In the best case, accidents might be avoided altogether whilst in the worst cases the systems have no positive effect at all. The perception of a CM system can come from several sources. The environment may be perceived with radar sensors, laser radar, vision sensors, ultrasonic sensors, GPS sensors and inter-vehicle communication. Properties of individual sensors will be discussed in Chapter 2. Based on the information acquired from the sensors, the vehicle itself acts to prevent or mitigate collisions. Typical actions the systems can take to mitigate a collision are issuing a warning to the driver, applying the brake and changing the course of the vehicle by applying torque to the steering wheel. Other possible countermeasures might be activating the brake lights to avoid being hit from behind, early airbag inflation or adjusting the vehicle’s height to increase crash compatibility. Several systems exist or have been proposed with CM functionality: • Lane-keeping aid systems [37], [33] monitor the lane markings. Using the observations of the lane markings an estimate of the vehicle’s position in the lane can be obtained. Should the vehicle swerve out of the lane a warning can be issued or a steering intervention executed. • Lane change aid systems monitor the blind spot and some distance behind the car. The system can then warn or intervene by adding steering wheel torque to avoid a collision when switching lane.

1.1 Car Safety

7

• Forward collision mitigation systems [53], [47], [15], [12] monitor what is in front of the host vehicle and intervene to prevent or mitigate a frontal collision. A more detailed introduction to FCM systems is given in Section 1.1.3. • Adaptive cruise control (ACC) works like normal cruise control, but adapts the speed to the vehicle in front; if the driver is closing in on a vehicle in the same lane. ACC is really an FCM system. The reason that it is dealt with separately here is that it is marketed (Mercedes, BMW, Jaguar, Nissan etc.) as a comfort system that is switched on and off by the driver.

1.1.3

Forward Collision Mitigation

FCM systems mainly try to avoid or mitigate frontal collisions. The countermeasure that we will mainly focus on in this thesis is braking, and to some extent warning. Hereafter, forward collision warning systems will be referred to as FCW systems and forward collision mitigation by braking systems as CMbB systems. Although FCW and CMbB systems are similar in many ways, they also present different challenges. In a FCW system, we rely on the driver to react quickly and correctly to the warning. However, this might not always be the case. A warning might actually startle the driver and cause his performance to worsen. A great deal of work is going on to determine how to warn the driver in the best way (see e.g. [58]). The timing in FCW and CMbB systems is also quite different. In a FCW system, driver reaction time must be taken into account. In [36] it is stated that 85 % of all drivers are able to react to a warning within 1.18 seconds. Apart from reaction time, one must also take into account that the driver might not perform the optimal avoidance maneuver. Taking this into consideration means that a FCW system has to predict future states several seconds in advance. For CMbB systems we assume that braking will be initiated at the last second, i.e., when a collision is becoming unavoidable or close to this point. The reason for this is that a driver may in some cases drive in such a way that a collision is “spatially close” without the situation being critical. A FCW system therefore presents the problem of making correct predictions over a longer time horizon. In CMbB system on the other hand the tolerance for faulty decisions is lower. In a FCW system some faulty interventions are tolerated, whilst in CMbB systems practically no faulty interventions are allowed.

1.1.4

Automotive Safety History

Ever since automobiles were introduced to the mass market in the beginning of the century, safety has been an issue. During the first half of the decade, focus

8

Introduction

was mainly on energy-absorbing structures, reinforced steel passenger cages and visibility issues. In 1959 Volvo introduced the first three-point seat belt. In the 1980s the first driver support system was introduced on a large scale. This was the well-known ABS system. In the 1990s more driver support systems became common. Examples of such systems are traction control systems, yaw-control systems etc. The first ACC system was introduced in 1999 by Mercedes. Year 2002 Nissan introduced the first lane-keeping assist system and also the first CMbB system. Another major trend during the last two decades is the increased use of airbag systems. This is one of the major reasons for the improved crashworthiness of modern cars. In appendix 1.4 a list of different safety designs introduced in Volvo cars is given. Volvo was not first with all of these designs.

1.2

Accident Statistics

To investigate the possible effects of FCM systems, some accident statistics will be examined. A thorough investigation of potential effects of FCW and CMbB systems is presented in [59], other works discussing the potential effects of FCM systems are [11], [34].

1.2.1

Accident Types

Given that the field of view (FOV) of FCM systems is often limited, it is clear that not all accident types can be mitigated. Typical accidents where FCM systems are ineffective are those where the principal other vehicle (POV) approaches the host vehicle at a wide angle, so that the POV appears in the sensors’ FOV late or not at all. Figure 1.3 shows how common different types of accidents were in the USA in the year 1998. The statistics displayed in Figure 1.3 come from the GES database [19]. Categories which are very likely to be affected by a FCM system are rear-end (26 percent) and single vehicle hit fixed (16 percent) and non fixed object (11 percent) collisions. The reason for this is that in many of these accidents the struck object has been in the sensor’s FOV for a long time (several seconds). The statistics indicate that potentially more than 50 percent of all accidents might be affected by a FCM system (assuming that all rear end and single vehicle accidents can be affected). For this to hold, the FOV of the FCM system needs to be large, at least 180 degrees.

1.2 Accident Statistics

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5%

4%

11%

Other Single vehicle hitting nonfixed object Single vehicle hitting fixed object Sideswipe opposite direction Rear end Head on Angle Sideswipe same direction

35% 16%

1%

2% 26%

Figure 1.3 Accident Types

1.2.2

Speed versus Severity

It is clear that there is a connection between collision speed and the severity of passenger injury. The kinetic energy of a vehicle is given by Ekinetic =

mv 2 , 2

(1.1)

where m is the mass of the vehicle and v is the speed. In a (completely non elastic) collision with a fixed barrier, halving the speed thus means decreasing the collision energy by a factor of 4. Clearly, reducing the impact speed has a large potential in injury reduction. Accident research has found that the speed change at impact (∆V ) and the probability of being injured is strongly correlated. In [31] and [44] the relationship between fatality risk and ∆V is investigated. The relationship found is displayed in Figure 1.4. In real life accidents the speed change of a vehicle in a collision between two vehicles can be calculated by the equation for conservation of momentum m1 v0,1 + m2 v0,2 = m1 v1 + m2 v2 .

(1.2)

10

Introduction

Fatality risk 1 Joksch,1993 O‘Day and Flora, 1982

0.9

Probability of fatality

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

20

40 60 80 Change in speed ∆ V [km/h]

100

120

Figure 1.4 Fatality risk versus collision-induced speed change The speed change for vehicle 1 is given by ∆V1 = v0,1 − v1 .

(1.3)

Example 1.1 Consider a collision where one car hits another stationary car, assume that both vehicles have equal mass. Furthermore we assume that the speed of the striking vehicle is 100 km/h. If the collision is completely non elastic we can calculate ∆V for the two vehicles using (1.2) and (1.3). In this case ∆V for both the vehicles will be ∆V =

v0,1 . 2

(1.4)

The speed change in the above example will thus be 50 km/h. Using Joksch relationship (in Figure 1.4) we find that the probability of a fatal injury for passengers in both vehicles will be 0.037. Now assume that the initial speed is reduced 15 km/h (giving an initial speed of 85 km/h for the striking vehicle) we find that the probability for a fatal injury is 0.019. At 100 km/h a 15 km/h

1.2 Accident Statistics

11

reduction of the speed will thus almost halve the risk of being mortally injured in this particular scenario. Performing the same calculations but assuming that the striking vehicle hits a fixed barrier instead, ∆V will be 100 km/h and 85 km/h. The probabilities in this case will be 0.59 and 0.31. In the fixed barrier scenario (assuming the same collision speeds) we thus also see approximately a halving of the probability of being fatally wounded.

The example shows that for some scenarios a moderate reduction of the collision speed can have a significant effect on the injury severity to the people involved in an accident. This is one of the reasons why CMbB systems are of particular interest.

1.2.3

Weather Conditions

Different sensors are not affected in the same way by the weather condition and light conditions. Some sensors are more robust to bad weather conditions while other sensors might be more sensitive. However those sensors that do not cope with bad weather or poor light conditions well, might have other advantages. When designing a CM system it becomes interesting to examine in what conditions accidents occur. The statistics in tables 1.1 and 1.2 come from the GES (a sample database of all types of accidents in the USA) and the FARS (all car accidents with fatal outcome in the USA) database (year 1998) and were presented in [59]. It is worth noting Weather Condition No Adverse Weather Condition Rain Sleet (Hail) Snow Fog Rain and Fog Sleet and Fog Other (Smog, Smoke, Dust) Unknown

FARS [%] 87.26 8.80 0.39 1.26 1.50 0.16 0.02 0.19 0.44

GES [%] 82.72 13.22 0.24 1.71 0.42 0.03 0.01 0.29 1.35

Table 1.1 Accident frequency for different weather conditions that most accidents occur at day time (68.6 percent) and under no adverse weather conditions (82.7 percent). It is also clear that for fatal accidents a much larger share occur during dark light conditions.

12

Introduction

Light Condition Day time Dark Dark but Light Dawn Dusk Unknown

FARS [%] 50.55 30.00 14.92 1.96 2.30 0.28

GES [%] 68.55 11.49 11.76 1.41 2.29 1.49

Table 1.2 Accident frequency for different light conditions

1.3

System Overview

The main problem to be solved when designing a FCM system is deciding when to intervene. This is complicated by the two desired system properties contradicting each other: • Avoid all collisions • No faulty interventions are allowed Different people might have different opinions on what should be considered a faulty intervention. In this thesis we make the following definitions. Definition 1.1 A faulty intervention is an intervention that occurs in a situation where the driver would have avoided the collision without a CM system intervention. The task of deciding when and how to perform an intervention will here be called decision making. The decision is based on predictions of kinematic quantities from the tracking system. We will thus use the following definition for decision making in this thesis. Definition 1.2 Given information of the other objects and the own vehicle’s kinematic states, decision making is defined as the task of determining when and how to perform an intervention. Determining if the object considered is relevant or not is not part of the decision making. This task will be called object classification. As already stated, deciding when to intervene consists of several tasks. This thesis will focus on target tracking and decision making. The task of target tracking is to estimate kinematic states of objects in the environment of the tracking platform. In our case we are interested in estimating position, speed, acceleration and yaw rate of vehicles and other objects.

1.4 Outline and Contributions

13

In an FCM system several objects are normally tracked. The tracking platform (the host vehicle) might be equipped with several sensors to detect and track objects, and it should of course be possible to track objects whilst driving. In this thesis we will therefore mainly look at multiple target tracking (MTT) systems using multiple sensors and a moving tracking platform. To be able to deal with the movement of the tracking platform an accurate navigation system is required. Navigation (i.e., tracking the own vehicles kinematic states) will also be discussed briefly.

1.4

Outline and Contributions

The main contributions of this thesis are: • The introduction of probability of collision as a decision parameter in Section 4.3. • A comparison of tracking performance for different motion models when tracking a maneuvering vehicle in a specific traffic scenario (Section 3.8). • Performance results of a prototype CMbB system using commercially available sensors: – Simulation results Section 5.4 – Field test results Section 5.4 The idea of using the collision metric - probability of collision was presented in [28] [29].

Appendix

1.A

Safety systems introduced on Volvo cars

1920-1960 1927 1944 1944 1954 1956 1956 1957 1958 1959

-

Safety glass Full safety cage Laminated windshield Front defroster Windshield washers Padded dashboard Front seat safety belt anchorage points Padded door handles Three point front safety belts

1960-1970 1965 1966 1966 1966 1967 1968 1969 1969

-

Power brakes with pressure limiting valves Dual circuit triangular split brake system Front and rear crumple zones Roll over roof protection bar Two point rear safety belts Front seat head restraints Three point inertia reel front seat belts Heated rear window

1970-1980 1972 1972 1972 1972

-

Three point inertia reel rear seat belts Child safety seat Child proof rear door locks Audio visual seat belt reminder 14

1.A Safety systems introduced on Volvo cars

1972 1972 1973 1973 1974 1974 1974 1978 1979

-

Hazard warning lamps Rear head restraints Energy absorbing bumpers Headlamp wiper washers Isolated fuel tank Multi stage impact absorbing steering column Stepped bore master cylinder braking system Front and rear fog lights Wide angle rear view mirrors

1980-1990 1982 1982 1984 1985 1986 1987 1987

-

Anti submarining seat protection Door warning lamps ABS anti lock brakes ETC electronic traction control High level brake lamp Automatic safety belt tensioner SRS driver side airbag

1990-2000 1990 1990 1991 1991 1992 1994 1998 1998 1998 1998 1998 1999 1999 1999

-

Three point inertia reel rear center seat belt Integrated rear child seat SIPS side impact protection system Automatic height adjusting seat belts SRS passenger side airbag SIPS front seat side impact airbags ROPS roll over protection system Boron steel windshield A-Pillars SIPS II front seat side impact airbags WHIPS whiplash protection system EBD electronic brake force distribution DSTC dynamic stability and traction control IC inflatable curtain airbags HID xenon headlights

2000-Beyond 2001 2002 2002 2002

-

EBA electronic brake assist RSC roll stability control Boron steel reinforced roof structure Lower compatibility cross-member

15

16

Introduction

2 Sensors

In order to track objects and predict collisions we need to monitor both the movement of the host vehicle and the movement of the surrounding objects. Wheel speed sensors (mounted on all cars with ABS), accelerometers, rate-gyro (often called yaw rate sensor) and GPS can be used to measure kinematic states of the host vehicle. This chapter will discuss sensors observing other objects in the surrounding environment of the host vehicle. These are referred to as “tracking sensors”. There are many requirements for tracking sensors. For automotive purposes, one very important requirement is the price of the sensor. When we discuss sensor performance this will be for sensors that are commercially available, or at least seen as feasible for use in automotive applications. In general, there may exist sensors with both better performance and more capabilities than the ones discussed below.

2.1

The Radar Sensor

Radar, which stands for radio detection and ranging, is traditionally the most common tracking sensor. Radar has been used in military applications for several decades. Today radar is common in aircraft and missile tracking, air traffic control, naval applications, etc. In recent years, radar has been introduced in automotive 17

18

Sensors

Figure 2.1 Measurement example ACC systems. The most important measurements provided by the radar sensor are range (r), range rate (r), ˙ azimuth angle (ϕ), and elevation angle. In Figure 2.1 the range and azimuth angle measurements are displayed. The radar sensor is an active sensor in the sense that it emits electro-magnetic radiation to illuminate targets. The emitted energy has a particular waveform. By listening to the echo from the transmitted signal, information on the environment is gathered. Most automotive radars use frequencies in the region 76-77 GHz. By their wavelength they are often called millimeter-wavelength radars (hereafter referred to as mm-radars). In [51] the basic theory of radar systems is described. The shape of the radiation pattern is determined by the antenna design. In automotive radars, the antenna is designed so that the main lobe has a conical shape. The beam width is normally 1-4 degrees both in the azimuth and the elevation direction. To provide azimuth angle information, the sensor either mechanically sweeps the antenna over a range or electronically switches between different emission angles. The total field of view (FOV) (see Figure 2.1 for an example) is normally 10-15 degrees for available ACC sensors. The techniques that are used to provide azimuth resolution can of course also be used to provide elevation angle information. However, most existing automotive radars do not provide elevation measurements (scanning is only one dimensional). The radar sensor has both advantages and disadvantages. Advantages: • Bad-weather performance: Frequencies at 30-300 GHz are generally lineof-sight and experience attenuation due to absorption in atmospheric gases (0.3-0.5 dB/km [1]). The sensor does, however, have the ability to detect objects in darkness, haze, rain and snow for the short distances required for automotive applications (where the range is normally less than 200 m). Automotive radar sensors are also insensitive to dirt deposits (i.e., mud and dirt from the road). • Range and range rate: Automotive radars provide accurate range measurements, in contrast to passive sensors. Some radars also measures the range

2.1 The Radar Sensor

19

rate using the Doppler effect.

Disadvantages:

• Clutter and spurious reflections: A number of objects in the environment reflect emitted radar signals. Unwanted reflections (often called clutter) from the asphalt for instance, might give “ghost” obstacles (i.e., obstacles that do not exist). Multipath propagation might also cause such phenomena. • Resolution: Because of the relatively wide lobe, the spatial resolution of the radar is poor. Its ability to measure spatial properties of the observed object is therefore limited. • Elevation: Since automotive radars have no resolution in elevation and a wide beam, it might be hard to discriminate obstacles from low overhead objects (road signs above the road etc.).

Most available sensors have an update frequency of 10 Hz, i.e., one sweep is completed in 100 ms. In Table 2.1 some basic sensor properties from different suppliers are displayed. Range accuracy is often better than 1 m and angular resolution is normally better than 1 degree (for radars with scanning antennas). In [1], [22], [56] and [50] mm-radars for automotive purposes are discussed. A thorough description of radar sensors is given in [51]. Radar Supplier Fujitsu Ten Mitsubishi Denso Nec Hitachi A.D.C. Bosch Autocruise Delphi Eaton Visteon

Waveform FM-CW FM-Pulse ? FM-CW FSK FM-CW FM-CW FSK FM-CW FSK FSK

Range >120 m 150 m 150 m 120 m 120 m 150 m 150 m 150 m 150 m 150 m 150 m

FOV 16◦ 12-16◦ 20◦ 16◦ 16◦ 10◦ 8◦ 12◦ 16◦ 12◦ 12◦

Scanning Mechanical 8 beams Mechanical 8 beams ? Synchronized 9 beams Monopulse switched 3 beams synchronized 3 beams Monopulse Mechanical Monopulse Monopulse

Table 2.1 Properties of Radar Sensors

20

Sensors

2.2

Laser Radar

A laser radar (lidar) is similar in its basic function to a mm-radar. Lidars provide range, range rate, azimuth and elevation measurements. While most automotive radar sensors provide no elevation measurements, there are some lidars that do. The lidar sensor is also an active sensor, i.e., it uses a laser diode to illuminate obstacles. The frequency region in which lidars operate is the infrared region. Wavelengths are around 850 nm (just above visible light). The wave propagation properties of lidars are similar to visible light. Lidars often consist of a one dimensional (distance) measurement device combined with a mechanical beam deflection system (e.g. a rotating mirror) to provide spatial measurements. Distance is measured by observing time of flight between received and transmitted signals. Lidar systems for automotive purposes are discussed in [54], [50] and [48]. In [56] a comparison between mm-radar and lidar for ACC purposes is presented. Compared to mm-radars, lidars have advantages and disadvantages: Advantages: • Resolution: The beam of the lidars is normally quite narrow. There are lidars that measure at several hundred azimuth angles and for several angles of elevation in one sweep (normally 100 ms). It thus provides a pixel map which could potentially provide much more detailed information of objects than an mm-radar. • Clutter: Due to the narrow beam and detection, the lidar does not experience clutter and spurious reflections to the same extent as a mm-radar. • Gray scale: The photo detector can easily detect reflected intensity, thus providing a gray scale “picture”. This could be used to monitor lane markings, etc. • Light conditions: Lidars are relatively insensitive to light conditions • Cost: Lidars are less expensive compared to mm-radars. Disadvantages: • Bad weather: In hard rain, fog or snow, the lidars experience performance degradation. • Dirt deposit: Lidars are sensitive to dirt deposits on the lens.

2.3 Vision Systems for Obstacle Recognition

Radar Supplier Mitsubishi Denso Denso (gen.II) Nec Omron Omron (gen II) Kansei A.D.C.

Range [m] 130 120 120 100 150 150 120 150

Vertical range 4◦ 4.4 ◦ 4.4 ◦ 3◦ 3.3 ◦ 6.5 ◦ 3.5 ◦ ?

21

FOV 12 ◦ 16 ◦ 40 ◦ 20 ◦ 10.5 ◦ 20-30 ◦ 12 ◦ 17 ◦

scanning 1-D 2-D 2-D 1-D ? 2-D 1-D ?

Table 2.2 Properties of Lidar Sensors

2.3

Vision Systems for Obstacle Recognition

Vision systems use one or several cameras together with a microprocessor to perform image processing. Since they operate in the visible light region, their capabilities are similar to that of our own eyes. The two main type of systems are: • Single camera systems - using either a monochrome or a color camera. One use in automotive applications for single camera systems is to monitor the lane markings in lane keeping aid systems ([37], [33]). • Stereo camera systems - A stereo camera system provides a 3D image by combining the images from two (or more) cameras. In such a system, range can be measured through triangulation. Because of the 3D information obstacle detection is easier. Generally, shape or pattern recognition is not needed to the same extent as for a single camera system. Stereo vision systems for automotive applications are discussed in [8] and [27] The performance of a vision system depends on the optics, the size of the ccd array, number of pixels, dynamic range, etc. The update frequency of many vision sensors is 25 Hz. However, image processing can be computationally demanding. Vision system performance in automotive systems is discussed in [13], [9] and [26]. In the VITA II project [55] extensive tests were performed using several vision systems to perform automated driving. Advantages: • High resolution: A pixel array with 640 × 480 pixels is common. This resolution makes it possible to measure spatial properties of the obstacle with good accuracy. Advanced target classification is also possible from the detailed images. Disadvantages:

22

Sensors

• Sensitivity to light conditions: A vision system can suffer severe performance degradation in certain light conditions (for example wet roadway combined with backlight or thick fog). • Sensitivity to dirt: Dirt deposits on/in front of the lens can cause problems to a vision system. • Computational demands: The image processing algorithms are computationally intensive.

2.4

Infrared Vision Sensors

Infrared (IR), or thermal cameras, basically give the same information as any normal camera. In many ways an IR vision system thus has the same properties as normal vision systems discussed in the previous chapter. The difference is that the IR camera is sensitive to wavelengths typical to heat radiation (the same region that lidars normally operate in). In automotive systems, IR cameras have been introduced with night vision systems. Night vision systems are used to enhance the driver’s perceptive abilities (Figure 2.2). These sensors are most sensitive to wavelengths corresponding to the normal body temperature of humans and large animals. So far, IR cameras have not been used in CM systems. The ability to measure the temperature of objects is unique to the IR sensor. IR cameras could potentially be quite useful in classifying objects and providing accurate angle measurements. For example, on some cars the exhaust system is visible and easily observed in a heat sensitive camera. Humans and animals are also often easily detected in an IR-image.

2.5

Inter-Vehicle Communication

Today, vehicles are more frequently being equipped with navigation systems consisting of GPS receivers and digital maps. If cars were equipped with communication systems it would be possible to transmit the navigation data to other vehicles. This data could the be used by the tracking system of the other vehicle. Potentially, this could yield very accurate measurements of kinematic properties as well as an accurate object classification (for example make, model and performance specification can be transmitted to tracking vehicles).

2.6 Summary

23

Figure 2.2 Image displayed by a night vision system

2.6

Summary

The two main tasks for tracking sensors are: 1. To detect obstacles and provide measurements for the tracking system. 2. To provide data for object classification. In a CM system, objects must be classified into at least one of the following groups: • Obstacles which the system should react to (for example cars or humans) • Obstacle which the system should ignore (for example a pot hole, a small tin can or an overhead road sign). Today, there exist commercial radars, lidars and mono-camera sensors for automotive use. These sensors have different strengths and weaknesses. To be able to provide both accurate measurements and correct object classification for a CM system, one sensor might not be sufficient. This is due to the fact that a sensor might report a target that does not really exist (a false positive). A sensor might also

24

Sensors

miss detecting an object (false negative). By using more than one sensor the risk for erroneous decision can be made smaller. Furthermore, to be able to monitor the function of the sensors themselves (i.e., diagnosis) it might also be necessary to include more than one tracking sensor. How to merge data from several sensors will be discussed further in section 3.7.

3 Tracking for Collision Avoidance Applications

The task of a target tracking system is to detect objects and estimate kinematic quantities of these objects. Estimating kinematic quantities (states) of an object is often called filtering. The quantities that we are interested in estimating are position, speed, acceleration and turn rate. For CM system applications it is sufficient to look at motion in the ground plane (i.e., motion in two dimensions only will be considered). In this thesis a ground fixed Cartesian coordinate system will be used. This chapter will present some of the most common filters that appear in the tracking literature. One reason for estimating the current kinematic states of an object with a tracking system is to be able to make a prediction of future kinematic states. This is the case for CM systems (i.e. to be able to predict if a collision will occur). In a CM system, several objects usually have to be tracked simultaneously. We will refer to one tracked object as a track or a trace. In a multi-target system one must determine which measurement belongs to which trace. This task is called data association and will be discussed in Section 3.5. For observing the targets, a CM system can have several tracking sensors. The task of merging the measurement from the different sensors will be addressed in Section 3.7. An example of the architecture of a tracking system is shown in Figure 3.1. For a thorough treatment of basic tracking techniques see [10] and [6]. 25

26

Tracking for Collision Avoidance Applications

Figure 3.1 Schematic picture of a tracking system providing state estimates to a decision and control system

3.1

State Estimation

In general, the states x that we are interested in estimating cannot be measured directly. Instead, they have to be estimated from some measurements y normally corrupted by noise. Estimating states that cannot be directly measured is a wellstudied problem. In control theory literature, an algorithm that estimates or reconstructs the non-measurable states from the measurements is called an observer. All state estimation is model-based. The model describes the dynamics of the system to be estimated. A general model for a dynamic system is given by (3.1). Since the sensors and processing units in an FCM system work with discrete time we will use discrete time models throughout this thesis. xt+1 = f (xt , vt ).

(3.1)

In (3.1), xt is the state vector at time t and vt is the process noise (also called system disturbance). In our vehicle tracking examples, the main contributions to vt come from the driver’s acceleration, deceleration, and steering commands. The measurement equation is given by (3.2). yt = h(xt , et ).

(3.2)

Here yt is the measurement vector and et is the measurement noise. It is assumed that the process noise distribution pv (.) and the measurement noise distribution pe (.) are known. There are two main approaches that can be taken to state estimation: 1. The deterministic (Fisher) approach: In this approach, we assume that there exists a true value of the states x. The connection between the stochastic observation vector y and the states x is given by the probability density function p(y|x). A popular choice of state estimate x ˆ, is to take x ˆ as the value that maximizes the likelihood of the observation (3.3). x ˆt = arg max p(yt |xt ) xt

(3.3)

3.1 State Estimation

27

Another common approach is to choose x ˆ so that the square of the expected prediction error is minimized: xt|t−1 , et ))2 x ˆt = arg min(yt − h(ˆ x ˆ

(3.4)

2. The Bayesian Approach: As in the Fisherian case, the observations are treated as random variables. The observation vector yt is assumed to have a known probability density function p(yt |xt ) which can depend on the states. In the Bayesian approach we also consider the state vector xt to be a stochastic variable. We assume that the random vector xt has some known prior density function p(xt ). The prior distribution encompasses the knowledge of xt before any observation has been made. When a measurement is made, this observation alters our knowledge of xt . The distribution after an observation has been made is called the posterior density function p(xt |yt ). The posterior density function can be expressed using Bayes’ rule: p(xt |yt ) =

p(yt |xt )p(xt ) p(yt )

(3.5)

In (3.5), p(yt ) is a scalar constant that can be found through marginalization: Z p(y|x)p(x)dx.

p(y) =

(3.6)

Rn

The posterior density p(x|y) is the most general solution to the tracking problem. It can be used to calculate the probability of any characteristics of states. As we will see in Chapter 4 this approach is very suitable for the kind of decision making we are interested in for CM purposes. A vague motivation for favoring the Bayesian approach is that when you make a decision in a CM system, all possible scenarios should be considered. Therefore, a point estimate of x is not sufficient. The general Bayesian solution (p(x|y)), on the other hand, contains all information. In many applications, however, one is interested in finding a point estimate of state vector x ˆ. Some popular choices are the least mean square estimate given by (3.7) or the maximum a posteriori estimate given by (3.8) Z x ˆM M S =

xp(x|y)dx

(3.7)

x ˆM AP = arg max p(x|y)

(3.8)

Rn

x

In the following Sections 3.2 – 3.4 we examine some filtering methods that provide a solution to the Bayesian state estimation problem.

28

3.2

Tracking for Collision Avoidance Applications

The Kalman Filter

The well known Kalman filter is widely used in tracking applications, and there are numerous examples of its implementations.

3.2.1

The Stationary Kalman Filter

We will start with looking at the stationary Kalman filter. Assume we have a linear time discrete dynamic model given by (3.9) and that the measurement equation can be written as in (3.10). Thus, in (3.9) and (3.10), A, B and C are constant matrices. The sampling time of the system is T . The subscript t denotes the sample time at sample number n, thus t = nT and t + 1 = (n + 1)T . xt+1 yt

= Axt + Bvt , cov(vt ) = Q = Cxt + et , cov(et ) = R

(3.9) (3.10)

A straightforward estimation of xt is given by (3.11). xt|t−1 + Kεt x ˆt|t = Aˆ

(3.11)

ˆt|t−1 . ε t = yt − C x

(3.12)

where

In (3.11) the choice of K will of course affect the filter. If K is chosen as in (3.13) we get the time invariant Kalman filter. In Kalman filtering, K is often referred to as the Kalman gain, K = P C T (CP C T + R)−1 .

(3.13)

In (3.13) the covariance matrix P is given by the solution to the stationary Riccati Equation (3.14) according to P = AP AT − AP C T (CP C T + R)−1 CP AT + BQB T .

(3.14)

We are interested in finding the Bayesian solution p(xt |yt ). Under the assumption that vt ∈ N (0, Q) and et ∈ N (0, R), then x ∈ N (0, P ). The solution is thus given by (3.15). 1

p(xt |yt ) = p

(2π)p (det P )

e

−(x−ˆ xt )T P −1 (x−ˆ xt ) 2

(3.15)

ˆt )(xt − x ˆt )T is obThe covariance of the state estimate P = cov(xt ) = E(xt − x tained by solving (3.14). Notice that in the stationary case the Kalman gain K and state covariance matrix can be calculated off line (i.e., they do not depend on the measurements).

3.2 The Kalman Filter

3.2.2

29

The Time-Varying Kalman Filter

We now consider a linear time varying model given by (3.16) and (3.17). xt+1 yt

= At xt + Bt vt , cov(vt ) = Qt = Ct xt + et , cov(et ) = Rt .

(3.16) (3.17)

The subscript t of the system matrices A, B and C indicates that the dynamics of the system, and also the measurement equation, vary over time. We also allow the process noise covariance Qt and measurement noise covariance Rt to vary with time. Due to the time variability of the system the state covariance P will now vary with time. The Kalman gain thus needs to be calculated at each time instant. The time-varying Kalman filter is given by (3.18) – (3.21). Normally (3.18) – (3.19) are called the measurement update and (3.20) – (3.21) are called the time update. In the measurement update, the state and covariance estimate is revised according to the latest measurement. In the time update step a prediction is made. In a CM system, predictions for several future time instances might be required. Prediction for time t+2, t+3, t+4... are easily obtained by iterating the time update equations. x ˆt|t

= x ˆt|t−1 + Pt|t−1 CtT (Ct Pt|t−1 CtT + Rt )−1 (yt − Ct x ˆt|t−1 ) Pt|t−1 CtT (Ct Pt|t−1 CtT

x ˆt+1|t

= Pt|t−1 + = At x ˆt|t

Pt+1|t

= At Pt ATt + Bt Qt BtT .

Pt|t

−1

+ Rt )

Ct Pt|t−1

(3.18) (3.19) (3.20) (3.21)

As in the stationary case, the a posteriori density is known if vt ∈ N (0, σvt ) and ˆt+1|t et ∈ N (0, σet ). Then p(xt+1 |yt ) is given by (3.15), where the state estimate x and the cov(xt+1|t ) = Pt+1|t are given by the time update (3.20) and (3.21). For a deeper study of Kalman filtering, [32] and [4] are recommended.

3.2.3

The Extended Kalman Filter

In many cases the dynamic model and the measurement equations are non-linear. This is, for example, the case for most tracking models. The assumption of Gaussian noise might not be fulfilled either. In this case it is normally hard to find an analytical solution to the estimation problem, i.e., finding p(x|y). We will look at a system that can be written as in (3.22) and (3.23). xt+1 = f (xt ) + vt , cov(vt ) = Qt yt = h(xt ) + et , cov(et ) = Rt

(3.22) (3.23)

The idea of extended Kalman filtering (EKF) is to solve an approximation of the original problem by linearizing the equations and approximating the noise distributions with Gaussian distributions. There are some different approaches that can

30

Tracking for Collision Avoidance Applications

be taken; we start with discussing how to deal with a non-linear measurement equation. Linearizing (3.23) by Taylor expansion and neglecting higher order terms we get (3.24) dh(x) xt|t−1 ) + (xt − x ˆt|t−1 ) + et , (3.24) h(xt ) = h(ˆ dx x=ˆxt|t−1

where

dh(x) dx

x=ˆ xt|t−1

= Ht . A new measurement equation (3.25) is formed using

the expansion (3.24), xt|t−1 ) + Ht x ˆt|t−1 ≈ Ht x ˆt|t−1 + et . y¯t = yt − h(ˆ

(3.25)

The right hand side of (3.25) looks as in the linear case (3.17), and the Kalman filter measurement update (3.18),(3.19) can be applied. Another approach to treat a non-linear measurement equation is to make a nonlinear transformation of the measurements. The aim of the transformation is for the transformed measurements to yield a linear measurement equation. One such transformation is to take y¯ = h−1 (y). In example 3.1, a transformation of nonlinear measurements from a radar sensor is shown.

Example 3.1 A radar sensor measuring range and azimuth angle has the following measurement equation   r y= . (3.26) ϕ In a tracking system using a Cartesian coordinate system, position measurements in Cartesian coordinates (px and py ) would yield a linear measurement equation. To obtain this we perform a non-linear transformation of the range and angle measurement, the measurement equation is given by     r cos(ϕ) px (3.27) = y¯ = py r sin(ϕ)

The problem with this approach is that the measurement covariance R must also be transformed. This can only be done approximately, and Gaussianity is in general not preserved. To be able to use the Kalman filter time update equations (3.20) and (3.21), f (xt ) must also be linearized. Starting with a non-linear continuous time model, there

3.3 Point Mass Filtering

31

are two choices for how to do this. Either by using discretized linearization or linearized discretization. Both these methods are described in [23]. If a discrete time non-linear function exists as in (3.22), a Taylor expansion for each component (i) of the state vector yields the estimate 1 (i) xt ) + (f (i) )0 (ˆ xt )(xt − x ˆt ) + (xt − x ˆt )T (f (i) )00 (ˆ xt )(xt − x ˆt ) + vi,t , xt+1 = f (i) (ˆ 2 (3.28) where (f (i) )0 denotes a row vector consisting of partial derivatives with respect to all states. Using this expression the time update of the EKF will be x ˆt+1|t Pt+1|t

= f (ˆ xt|t ) 0

(3.29) 0

T

= f (ˆ xt|t )Pt|t f (ˆ xt|t ) + Qt ,

(3.30) (3.31)

where 

 (f (1) )0   .. f0 =   . (n) 0 (f )

(3.32)

The EKF will give a suboptimal solution since the dynamics and measurement equations of the system are an approximation of the true system. The true process and measurement noise might also not be Gaussian, in which case the posteriori distribution given by the EKF is only an approximation of the true density. For highly non-linear systems or when the pdfs are not well approximated with Gaussian distributions, the EKF is not sufficient. To improve tracking performance several techniques using multiple models have been proposed.

3.3

Point Mass Filtering

All the filters discussed so far use linearized models and Gaussian noise processes to deal with non-linear and non-Gaussian systems. We will now look at methods where we do not linearize the system, but instead we try to solve the estimation problem for the “true” system. The systems are non-linear with additive noise as described by (3.22) and (3.23). The process and measurement noise distributions (pv (.) and pe (.)) are assumed to be known, but they are not necessarily Gaussian. As already stated, it is often not possible to find an analytical solution to the Bayesian tracking problem. The idea here is to solve the problems by numerical approximation. Defining Yt = [y1 , y2 , ..., yt ], a recursive solution to the Bayesian

32

Tracking for Collision Avoidance Applications

estimation problem is given by (3.33) – (3.35). p(yt |xt )p(xt |Yt−1 ) p(yt |Yt−1 ) Z p(xt+1 |xt )p(xt |Yt )dxt , p(xt+1 |Yt ) = p(xt |Yt ) =

(3.33) (3.34)

Rn

where

Z p(yt |Yt−1 ) =

Rn

p(yt |xt )p(xt |Yt−1 )dxt ,

(3.35)

and the recursion is initiated by p(x0 |Y−1 ) = p(x0 ). Inserting the measurement equation (3.23) into (3.33) we get p(xt |Yt ) = αt−1 pet (yt − h(xt ))p(xt |Yt−1 ), where

(3.36)

Z p(yt |Yt−1 ) = αt =

The time update is given by

Rn

pet (yt − h(xt ))p(xt |Yt−1 )dxt .

(3.37)

Z

p(xt+1 |Yt ) =

Rn

pvt (xt+1 − f (xt ))p(xt |Yt )dxt

(3.38)

One approach to approximately solve the recursive estimation problem is to evaluate the recursion (3.36) - (3.38) for several points around the working point (i.e., the current value of xt ). These points are then updated at each time step through the recursion. We thus have a quantization of the state space. Each point is assigned some weight or mass corresponding to the probability that the states assume that particular value. This approach has sometimes been called the point mass filter (PMF). Assume that a grid consisting of N points is chosen to approximate the density function p(xt |Yt ). These N points in the state space will be denoted xt (k), k = 1, 2, ..., N . The associated probability mass for each point is denoted p(xt (k)|Yt ), k = 1, 2, ..., N . Assuming that the grid is uniform with the distance δ between the points, an integral over some region in the state space can be approximated by a sum (3.39) Z Rn

p(xt )dxt ≈

N X

p(xt (k))δ n

(3.39)

k=1

Applying the PMF approximation yields the recursion: p(xt (k)|Yt ) = αt−1 pet (yt − h(xt (k)))p(xt (k)|Yt−1 ) xt+1 (k) = f (xt (k)), k = 1, 2, ..., N p(xt+1 (k)|Yt ) =

N X n=1

pvt (xt+1 (k) − f (xt (n))p(xt (n)|Yt−1 ))δ n .

(3.40) (3.41) (3.42)

3.4 Particle Filtering

33

In order for the PMF to work, the grid or points must be adapted to the support of the conditional density. One way to do this is to remove points with low mass. Doing this will of course decrease the number of points, so when the number of grid points falls below some lower bound one should increase the number of points. A thorough account for the point mass filter with tracking and navigation examples is given in [7].

3.4

Particle Filtering

One of the main problems with the PMF approach is the computational complexity. The relative error of brute force techniques for approximating the integral (3.34) is shown in [7] to be of the complexity order O(L−1/n ) (where L depends on the distance between grid points and n is the state dimension). For large dimensional problems, the PMF approach thus becomes intractable. The particle filter (PF) approach bears many similarities to the PMF. Again we are interested in finding a numerical approximation of the recursive Bayesian solution to the tracking problem in (3.33) – (3.35). The PF approach also uses a set of points to represent the posteriori distribution of the states. Instead of discretizing the state space, the PF depends on the assumption that it is possible to draw N >> 1 samples from the a priori distribution p(xt−1 |Yt−1 ). The samples are then simulated according to the dynamic model. The resulting swarm of particles represents the posterior density, which is given by: p(xt |Yt−1 ) ≈

N X

p(xt |xt−1,i ).

(3.43)

i=1

xt−1,i denotes the i:th sample drawn from p(xt−1 |Yt−1 ). This approach is often referred to as simulation based, because of the fact that it uses Monte Carlo simulations to approximate the solution.

3.5

Measurement Association

A MTT system’s task is to track several objects simultaneously. The system thus (i) normally tracks several targets (represented by their estimated state vector xt , i = 1, 2, .., J where J is the maximum number of tracks) at any given time. The tracking sensors will then generally provide measurements originating from several objects, (i) yt , i = 1, 2, .., M . Before updating the state estimates of current traces with new measurement, the system needs to determine which measurement belongs to which trace. The task of assigning measurements to traces is called measurement

34

Tracking for Collision Avoidance Applications

Gating 5 4.5 y

5

4

h(ˆ x(3) )

y−coordinate [m]

3.5 3 2.5 y3

2 y2

1.5 y1

1

h(ˆ x(2) ) y4

h(ˆ x(1) )

0.5 0

−1

0

1 2 x−coordinate [m]

3

4

Figure 3.2 Gating example in a Cartesian coordinate system association. Given a dense target environment, noisy measurements and the fact that the sensors might erroneously detect object caused by multi path propagation or spurious reflections, this is not always an easy task.

3.5.1

Gating

The first step in assigning measurements to traces is called gating. Gating is used to eliminate unlikely observation-to-track pairings, and if no conflicts exist, to assign the measurement. For each track, a subspace G(i) is defined in the measured coordinate space, G(i) ⊂ Rm . If a measurement falls within the gate of a track (j) yt ∈ G(p) , then that measurement is considered a candidate for updating that track. Figure 3.2 shows an example of a gating procedure in a 2-D Cartesian space. We clearly see that there are conflicts: There are several measurements falling within the same gate (i.e., y1 , y2 ∈ G(1) and (y2 , y3 , y4 ∈ G(2) ) and there are also measurements falling within more than one gate (y2 ∈ G(1) , G(2) ). If a measurement falls in one gate only and there are no other measurements that can be associated to that gate, then that measurement can be directly associated with the track to which the gate belongs. If there are conflicts, on the other hand, further correlation logic is needed. If a measurement does not fall into any gate

3.5 Measurement Association

35

this measurement is considered a candidate to initiate a new track.

3.5.2

Association Methods and Techniques

In the previous chapter it was shown that after the gating procedure there might still be conflicts regarding which measure to assign to which track. In this section we will look at some common techniques on how to resolve these conflicts. In tracking literature, the process of solving conflicting assignments is normally referred to as data or measurement association.

The Nearest Neighbor Approach The Nearest Neighbor (NN) approach looks for a unique pairing (i.e. one observation can only be used to update one track). To decide which observation to associate with which track, a distance measure gij is formed. gij denotes the distance from observation i to track j. The idea is then to choose the assignments in such a way that the total distance is minimized. One popular choice of distance measure is the likelihood function associated with the assignment of observation j to track i. In this case the idea is to maximize the total likelihood of all assignments.

The Multiple Hypothesis Approach In the multiple hypothesis tracking (MHT) approaches, a track is only updated with one measurement, as in the NN approach. If there are conflicts, however, the tracks are divided into several tracks and all possible associations are made. That is, one measurement can now be used to update several tracks.

Example 3.2 x(2) ,ˆ x(3) ) before the measurement In Figure 3.2, there are three tracks (ˆ x(1) ,ˆ (1) ˆ(1) association. In the association step track x ˆ is updated with y1 and y2 . x (11) (12) (2) is thus divided into two tracks x ˆ and x ˆ . Similarly x ˆ splits into three tracks and x ˆ(3) is not split.

In the MHT approach it is of course possible that the number of tracks becomes large. This has to be dealt with in order for the solution to be tractable. One way to handle the problem is calculating the probability of the different tracks, and terminating tracks with low probability.

36

Tracking for Collision Avoidance Applications

Clustering 5 4.5

y−coordinate [m]

4 A

3.5 3

C

2.5 2

B

1.5 0

0.5

1

1.5 2 2.5 x−coordinate [m]

3

3.5

Figure 3.3 Example of measurement clustering in a Cartesian coordinate system

Clustering Techniques In some applications it is common to receive multiple measurement from the same obstacle. In this case, it is possible to initiate and maintain several tracks that correspond to the same entity. Having several tracks for the same entity might cause confusion in further analysis and waste computational effort. Possibly, the erroneous allocation of tracks could lead to discrimination of interesting targets. One way to handle this is to cluster tracks or merge tracks that are likely to represent the same target. Figure 3.3 shows an example where several tracks (denoted by x) in a Cartesian coordinate system are clustered into three groups A, B and C. How to cluster objects is not clear and will differ for different applications. In CM applications one will typical try to estimate the physical size of the object, this estimate can be used to determine if several tracks actually represent the same

3.5 Measurement Association

37

Figure 3.4 Traffic scenario where the vehicle ahead of the host vehicle (POV2) has come to a stop. Depending on what maneuver the driver of the host vehicle decides on, POV 1 – 3 and the stationary obstacle can all constitute a threat.

object. Clustering is sometimes used to track troop movements in military applications. An introduction and further references to clustering techniques are given in [25]. Another approach to deal with the problem of multiple measurement from the same object is to allow tracks to be updated with several measurements, i.e., several measurements are associated with the same track. One reason for using clustering is to save computational power; in example 3.3 we discuss why this might be desirable for CM applications.

Example 3.3 The computational power of a commercial CM system will of course be limited. This means that the maximum number of live tracks at any one time will be limited. We assume that we have a system that is able to track four different objects simultaneously. In Figure 3.4 there are four objects that can become a threat depending on how the host vehicle driver choses to avoid the stopped vehicle ahead (POV 2). Figure 3.5 shows measurements from a commercial radar sensor. The measurement was performed on a large open tarmac area with only one stationary target present (see Figure 3.6). Clearly, in Figure 3.5 the radar detects two targets which are coming from the same physical object. In this case it is certainly possible to initiate two tracks from the two measurements. If this would happen in the scenario from Figure 3.4 two tracks would be used for the stopped vehicle (POV 2), and since the maximum number of tracked objects is four, one of the other potential threats will not be tracked.

Tracking for Collision Avoidance Applications

Range [m]

38

Multiple Detection of a Stationary Target − Range and Azimuth Angle 40 Target 1 Target 2 30 20 10

Azimuth Angle [degrees]

0 −0.5

0

0.5

1

1.5 Time [s]

2

2.5

3

5 Target 1 Target 2

0 −5 −10 −15 −0.5

0

0.5

1

1.5 Time [s]

2

2.5

3

Figure 3.5 Range and azimuth angle measurements from a commercial radar sensor. The host vehicle is approaching one lone stationary obstacle at 40 km/h. Two obstacles at the same range and an angular spacing of 3-4 degrees are detected (between time 0.5 and 1.75), however, only one physical object is present. This is a clear case of multiple reflections from one object.

3.6

Pre-Filtering of Measurements

It has already been stated that there normally is an upper limit to the number of objects that can be tracked simultaneously (because of limited computational power). The sensor, however, might possibly detect more objects than can be dealt with by the tracking system. To make the total system as effective as possible, it is desirable to use the most relevant measurements and to remove irrelevant measurements. The process of selecting relevant measurements will in this thesis be called pre-filtering. This section will discuss how pre-filtering can be done in a CM system. Assume that the sensor on which we want to perform pre-filtering measures a maximum of M different obstacles. The measurements are given in a vector Y = (y (1) , y (2) , ..., y (M ) ). Because of computational limits we only allow

3.6 Pre-Filtering of Measurements

39

Figure 3.6 The test area where the measurement of Figure 3.5 was performed, there are no other objects close to the stationary obstacle

i ≤ M measurements to be passed on to the tracking system. The idea is now to reorder the measurements of Y to get Y˜ = (˜ y (1) , y˜(2) , ..., y˜(M ) ), where y˜(1) is the most relevant measurement and so on. How to perform the pre-filtering in general will of course depend on the type of application considered. Here we give some considerations, when ranking the importance of a measurement for different CM systems. Since the aim of the pre-filtering process is to decrease the computational burden, it must not be computationally demanding itself. The sensors normally measure range, range rate and azimuth angle, so pre-filtering will be based on these quantities.

3.6.1

Pre-filtering measurements using range only

For CM systems, it might be wise to prioritize the measurements according to range, since objects close to the host vehicle in many cases constitute the greatest threat. For some systems, it is at least possible to say that measurements with a range above a certain value are irrelevant (see example 3.4).

40

Tracking for Collision Avoidance Applications

Example 3.4 Assume that we have a CMbB system which performs braking when a collision becomes unavoidable. The collision unavoidable point is closer than 30 m for stationary targets and speeds up to 150 km/h. Assuming that other vehicles have similar handling characteristics, one can say that measurements where the range is much larger than 60 m are irrelevant. For such a system it would be wise to rank measurements below 60 m as more relevant than those above 60m.

The danger in ranking measurements on range alone is that one might miss objects that are serious threats because of a high relative speed.

3.6.2

Pre-filtering by Range Rate and Time-to-Collision

Some sensors measure range rate directly. For such sensors it is possible to prioritize objects according to their oncoming speed, which is approximated by the measured ˙ An estimate using both range and range rate is time-to-collision (TTC) given R. by TTC ≈

R . R˙

(3.44)

˙ reasoning that they We now prioritize measurements with a short TTC or large R, present a large threat because of their high closing speed. The danger here is of possible discrimination of objects with a short range that are traveling at the same speed or faster then the host vehicle. Such an object can very quickly become a threat if the driver of that vehicle hits the brakes hard. The tracking sensors often pick up a lot of stationary road side objects which make such discriminations likely. The T T C for road side objects is often short but normally they constitute no threat.

3.6.3

Pre-filtering Objects by their Azimuth Angle

Finally azimuth angle is considered. A simple approach would be to consider objects straight ahead as more dangerous. This approach, of course, also has the risk of missing some threats. For example, an object that is dead ahead but far away and has low oncoming speed will be considered more dangerous than an object near by with a high relative speed but azimuth angle not equal to zero. In general one should also consider the own vehicle’s turn rate when one uses the azimuth angle to prioritize threats. If the vehicle is turning, objects with an azimuth angle

3.6 Pre-Filtering of Measurements

41

in that direction are probably a greater threat than those with azimuth angle equal to zero.

3.6.4

Summary of Pre-filtering Strategies

It is clear that real threats will sometimes be missed if one chooses to prioritize objects only after range, T T C or azimuth angle. A more appropriate and general approach is to use all of the quantities to rank the relevance of each measurement. One suggestion on how this could be done is given in [21]. Of course when designing the pre-filtering algorithm one should always keep in mind that this step is used to decrease computational load. It is therefore desirable to keep the algorithm as computationally simple as possible. We have now presented all theory needed to build a tracking system. Algorithm 3.1 summarizes the tracking algorithm that will be used hereafter. Algorithm 3.1 (Tracking algorithm) 1.For each tracking sensor (in this case one mm-radar and one lidar) perform the following: (a)Cluster measurements. Measurements from the same sensor that are very close to each other are clustered. (b)Pre-filter measurements. Measurements are reordered (here range, TTC and azimuth angle is used to determine the importance of each meassurement). The ordered measurements are denoted Y = (y (1) , y (2) , ..., y (M ) ). (c)Select the most relevant measurements. Y is divided into two parts. The first part is used for further processing (in the measurement association step). The second part is thrown away. (d)Gating. The measurements Y are compared with h(ˆ x(j) ) to check if they fall (i) in any of the gates G . The gate is defined by a rectangular gate: (i)
T (j) y − h(ˆ x ) = r(i) r˙ (i) ϕ(i) − h(ˆ x(j) )
T < rgate r˙gate ϕgate (e)Measurement association. If there exist conflicts after the gating procedure these are resolved using a NN approach. Here a geometric distance measure is used. The measurement k that is associated with track j is denoted y kj . (f)Update state estimates for track j ∈ {1, 2, 3, 4} with associated measurement y kj .

42

Tracking for Collision Avoidance Applications

(j)

= x ˆt|t−1 + Pt|t−1 CtT (Ct Pt|t−1 CtT + Rt )−1 (yt

(j)

= Pt|t−1 + Pt|t−1 CtT (Ct Pt|t−1 CtT + Rt )−1 Ct Pt|t−1

x ˆt|t Pt|t

(j)

(j)

(j)

(j)

(j)

(k)

(j)

(j)

− Ct x ˆt|t−1 )

(j)

2.Predict future states. (j)

= At x ˆt|t

(j)

= At Pt ATt + Bt Qt BtT .

x ˆt+1|t Pt+1|t

(j) (j)

3.Iterate the previous step to obtain predictions for as many time instants as desired.

3.7

Sensor Fusion

In tracking systems, it is often the case that there are several tracking sensors. For example, in a CMbB system it is desirable to have more than one tracking sensor to increase the reliability of the system, i.e., to avoid making faulty interventions caused by invalid obstacles or spurious target observations at one sensor. Now the question arises how to fuse the data from the different sensors. This task is often called sensor or data fusion. A thorough treatment of sensor fusion problems is given in [25]. It is straightforward how to fuse independent measurements of the same quantity. If X 1 and X 2 are two independent measurements of the same quantity with covariance matrices P 1 and P 2 , the Equation (3.45) will yield the optimal fused estimate, in the sense that the covariance of X f used is minimized. X f used P

= P ((P 1 )−1 X 1 + (P 2 )−1 X 2 ) =

1 −1

((P )

2 −1 −1

+ (P )

)

.

(3.45) (3.46)

The problem of fusing sensor information in tracking systems is that the sensors measure widely different quantities. For example, a mm-radar measures reflected radar energy at the antenna, a vision sensor measures light intensity at each pixel, and a GPS receiver measures the flight time of coded transmissions from satellites. In many applications one is not only interested in tracking kinetic quantity of detected objects; one might also be interested in inferring a number of different features of the object. These features as well as the kinetic quantities can then be used to classify the object. When designing a system one must decide on what level fusion of sensor data should be performed. Figures 3.7 and 3.8 schematically display two extreme approaches to fusion of sensor information. In the pixel level fusion displayed in Figure 3.7, one tries to fuse the data at the lowest level, i.e., fusing the raw sensor output. This approach is the most general and promises the best

3.7 Sensor Fusion

43

Figure 3.7 Pixel/data level fusion. In this approach the information from each sensor is associated with current tracks and then jointly fused to extract features of the measured object.

Figure 3.8 Declaration level fusion. Here each sensor extracts features and maintains its own objects. The tracked objects from each sensor are then fused in the last stage.

results. Normally, it is also the computationally most demanding approach. For large systems, pixel level fusion is often infeasible both because of computational cost and system complexity issues. The other extreme is the approach displayed in Figure 3.8. Here the data from each sensor is treated separately and has its own tracking and feature extraction. The estimated states and features are then fused at the top level. This approach has the advantage that it is robust against failure of one sensor node. Should one sensor fail there will still be a state estimate from the other sensors. From a system engineering point of view such a system is also easier to understand and maintain. For example, switching to another sensor will not require a total redesign of the entire system. These two examples are, of course, extremes and any set-up between these two is of course possible. It is also possible to have feedback in the system for sensor management and diagnosis. For example to decrease the computational load in one sensor information from other sensors

44

Tracking for Collision Avoidance Applications

Figure 3.9 Fusion of a radar and a camera sensor. The radar is used to detect obstacles and measure kinematic quantities. The detected obstacles (indicated by the points in the sensor image) are fed back to the camera sensor that performs template matching in the pixel image. After a positive matching spatial properties such as width and height can then be measured in the pixel image.

can be used. An example of such a system is given in the example below.

Example 3.5 In a CM system it is desirable not only to determine the speed and distance of objects close to the host vehicle. One also want to determine its size and type. Figure 3.9 shows a picture of a system that fuses data from a mmradar and a camera sensor to achieve this. In this system the radar is used to detect obstacles and determine the range, range rate and azimuth angle. This information is then fed back to the camera sensor which performs template matching to determine if the object is a car or not. It also provides a width measurement and a more accurate azimuth angle measurement of the obstacle.

3.8 Models for tracking and navigation

45

In CM systems, faulty interventions are not allowed. Since available tracking sensors all have their weaknesses that cause them to sometimes report false targets, the sensor fusion is a crucial part of the system. In CM systems, sensor information should be fused in such a way that the risk of passing on false targets as valid ones to the decision making algorithm is minimized.

3.8

Models for tracking and navigation

It has already been stated that all tracking is model based. In this section we will discuss consideration of model choices for tracking systems. In particular some different models that can be used to describe the dynamics of the car will be reviewed. The performance of a tracking system will, to a large extent, depend upon how well the dynamics of the true system is described by the model. Generally speaking, a better model yields a better tracking performance. In our case we are interested in finding the Bayesian solution p(xt+1 |Yt ), so the better the model, the closer the posterior distribution will be to the true distribution of the vehicle’s future states. However, it is also desirable to use as simple a model as possible, both for computational issues and for understanding the system. The modeling of vehicle dynamics is a well explored area. Most car manufacturers today have very detailed models for simulating vehicle dynamics. These models use a complex model of each subsystem (suspension, tires, engine, etc.), and give very accurate descriptions of the dynamics. Such models are too complex for tracking purposes. Instead, a model which captures the major characteristics of the vehicle’s dynamics is sufficient. A good introduction to the fundamentals of vehicle dynamics is given in [20] and [57]. Apart from which tracking model to choose, it is also necessary to think about which coordinate system to track in. In [3], it is stated that modified polar coordinates are better for angle-only tracking. Throughout this thesis, an earth-fixed Cartesian coordinate system will be used. We will use the following notation: px – Position in the x direction py – Position in the y direction vx – Velocity in the x direction vy – Velocity in the y direction ax – Acceleration in the x direction ay – Acceleration in the y direction ω – Vehicle turn/yaw rate In aircraft and tracking literature, several tracking models exist that are also suitable for tracking ground vehicles.

46

3.8.1

Tracking for Collision Avoidance Applications

The Constant Velocity Model

One of the simplest models for tracking is given in (3.47). In this model the motion of the vehicle is modeled as having piecewise constant velocity in the x and y direction. The transitions between different velocity are modeled by white random noise, and there is no correlation between motion in the x and y directions. x = xt+1



py

px

1 0  0 1 =   0 0 0 0

vx T 0 1 0

vy 


T 

0  T   xt +   0  1

0 0 1 0

(3.47)



0 0  v 0  t 1

(3.48)

We assume that the noise is Gaussian distributed and that the covariance matrix is given by (3.49)  2  σ vx 0 (3.49) Qv = 0 σv2y

3.8.2

The Constant Acceleration Model

A model that assumes that tracked objects have constant velocity, is of course, a very simple one. For tracking of maneuvering targets one often wants to model the dynamics better. A simple extension of the model is to add the acceleration as a state. We then get the constant acceleration model (3.50)−(3.52) x =

xt+1



   =     

Qv

3.8.3

=

px 1 0 0 0 0 0 σa2x 0

py

vx

0 T 1 0 0 1 0 0 0 0 0 0 0 σa2y

0 T 0 1 0 0 

vy

ax 2

T 2

0 T 0 1 0

0


T ay 



     0 x +   t  T      0 1

T2 2

0 0 0 0 1 0

0 0 0 0 0 1

     vt   

(3.50)

(3.51)

(3.52)

The Coordinated Turn Model

The constant velocity and constant acceleration models are very nice to use in the sense that they are both linear. When modeling the motion of a car, there are more aspects that could be considered. One fundamental property of the motion of a car

3.8 Models for tracking and navigation

47

is that lateral and longitudinal motion are coupled. For example, when standing still, a car cannot start traveling sideways. The lateral friction forces generated at the tires normally cause the body of the vehicle to rotate as it turns. Somewhat simplified this type of motion can be described by straight lines and circle segments. Such a model was proposed in [39], and is often called the coordinated turn model. In this model it is assumed that the yaw rate is known and piecewise constant. In reality, the turn rate is often not known and has to be estimated. The model which assumes piecewise constant turn rate and includes ω as a part of the state estimation process is called the nearly coordinated turn model. The discrete-time nearly coordinated turn model is given by (3.53) – (3.54). x =

xt+1

Qv



px

py

vx

vy




ω

sin(ω)T ω −( 1−cos(ω)T ω

1 0  0 1 )  =  cos(ω)T  0 0  0 0 −cos(ω)T 0 0 0   σv 0 0 =  0 σv 0  0 0 σω

1−cos(ω)T ω − sin(ω)T ω

sin(ω)T sin(ω)T 0

0 0 0 0 1





0  0     xt +  1    0  0

0 0 0 1 0

0 0 0 0 1



(3.53)

   v(3.54)  t 

(3.55)

To get an intuitive feeling for how the constant acceleration model differs from the (nearly) coordinated turn model, we can think of the motion of a hovercraft compared to the motion of a car. Tracked vehicle path 30

Global position [m]

20 10 0

T1

T3

T2

T4

T5

T6 T7

−10 −20 −30 −40 0

20

40

60 80 Global position [m]

100

120

Figure 3.10 Trajectory of a tracked vehicle performing: acceleration–lane change–deceleration–right turn. Acceleration starts at point T1, lane change at point T3, deceleration at T5 and right turn starts at T6.

48

Tracking for Collision Avoidance Applications

Tracked path for 3 tracking models (average path from 1000 MC simulations) 4 2

global y coordinate [m]

0 −2 −4 −6 −8

True Path Constant Acceleration Constant Velocity Coordinated Turn

−10 −12 −14 −16 0

50 100 global x coordinate [m]

150

Figure 3.11 Tracked trajectory for the constant velocity model, the constant acceleration model and the nearly coordinated turn model. The figure displays the average path from 1000 MC simulations for each model.

Example 3.6 In Figure 3.11 a comparison between the constant velocity, the constant acceleration model and the nearly coordinated turn model is displayed. In the comparison the maneuver described in Figure 3.10 is used. For each model 1000 Monte Carlo simulations are performed (the same measurement noise realizations are used for each model). The KF parameters were tuned to give the best possible tracking performance in this particular maneuver and with the sensor noise given below. The measurements are given by       r er r (3.56) y =  r˙  + et =  r˙  +  er˙  , eϕ ϕ ϕ where all the ei :s are independent Gaussian random variables, with σr =0.5, σr˙ =1 and σϕ = 0.5 · π/180. The measurement rate and tracking system update frequency in this example is 10 Hz. By looking at the figure, it appears that the constant acceleration model and the nearly coordinated turn model have similar performance. Looking at the mean square predicted error and the maximum predicted error in table 3.6, we see that the coordinated turn model performs better in both aspects. For all the models an EKF was used since the measure-

3.8 Models for tracking and navigation

Tracking model Constant velocity Constant acceleration Nearly coordinated turn

RMSE [m] 0.88 0.65 0.56

49

Maximum error [m] 5.2 4.7 3.5

Table 3.1 Results from a comparison of three tracking models. Each model was run 1000 Monte Carlo simulation, were the same noise realizations were used for all models. Both the average error in column two and the maximum error in column three is a measure of the spatial distance between the true position and the prediction position.

ment equations are non-linear. The nearly coordinated turn model is non-linear and thus the model needs to be linearized at each time. This is not the case for the constant velocity and the constant acceleration model. The filter for the nearly coordinated turn model will thus be slightly more computationally demanding. In the Monte Carlo simulations performed here, the required CPU time for the nearly coordinated turn model was 2.8 times more than for the constant velocity model. The constant acceleration model required 1.2 times more CPU time than the constant velocity model.

3.8.4

Bicycle Model

A more accurate model for modeling handling properties of a car is the well known bicycle model. In this model the front and rear wheels are lumped together as one wheel (thus we have a bicycle). The motion of the vehicle is then approximated by calculating the forces generated at the front and rear wheel. Figure 3.12 shows a schematic image of this model. In the figure only the lateral wheel forces are indicated. The longitudinal and lateral forces on the wheels are given as a function of the longitudinal and lateral slip, respectively. The relationship between slip and force is a non-linear function; an example of this function using Pacejkas’ magic formula ( [5] ) is plotted in Figure 3.13. This kind of model can explain phenomena such as skidding. Therefore it is often used, for example, as a reference model in yaw control systems. For tracking other vehicles, this model is probably too detailed. For tracking the own vehicle (navigation) this model might be appropriate. In fact, in vehicles equipped with a yaw control system, a bicycle model is probably used as a reference model to detect when the vehicle is skidding. A derivation of the dynamic equations for the bicycle model is given in [43], where it is referred to as the single track model.

50

Tracking for Collision Avoidance Applications

Figure 3.12 A schematic image of the bicycle model, here only the lateral forces on each tire are indicated. The longitudinal forces work along the wheel direction normal to the lateral forces.

3.8.5

Navigation

This chapter has mainly discussed the tracking of other vehicles’ dynamic states. The tracking of the own vehicle’s states is often called navigation. Basically the same filtering techniques and vehicle models that are used for tracking other vehicles can be used for this purpose. The only difference is that other sensors are used to provide information of the kinematic properties of the vehicle. One example of sensors that already exists on most cars are the wheel speed sensors of the ABS system. On cars equipped with a yaw control system there is a rate gyro and a lateral accelerometer, and sometimes also longitudinal accelerometers. Other possible sensors installed in cars are GPS receivers. The kinematics of the own vehicle can often be measured more accurately. For example, a yaw rate sensor is sometimes available to measure yaw rate directly, and the wheel speed sensors give wheel speed measurements with a low noise level. Therefore, it often makes sense to use a more accurate model for navigation than for tracking other vehicles.

3.8 Models for tracking and navigation

51

Force as a function of slip 1 0.8

Normalized force µ (F/N)

0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1 −1

−0.5

0 Slip

0.5

1

Figure 3.13 Relationship between slip and force between tire and road surface, in the longitudinal direction for dry asphalt. Here the value is normalized with the normal force on the wheel.

Example 3.7 Sometimes cars are equipped with, steering wheel position sensor and a brake pedal force and position sensor. These sensors can be used to increase the tracking and prediction performance of the host vehicle. Figure 3.14 shows the relationship between steering wheel angle and yaw-rate of a vehicle traveling at 50 km/h. We see that there is a delay in the order of several hundred milliseconds. Compared with the use of yaw rate measurements, only the use of steering wheel measurements will tell you much earlier when the vehicle will turn. In this case it will clearly make sense to model the dynamics between steering wheel and yaw rate in the navigation system. The performance of a CM system using this information would be significantly improved by the “preview” offered by the use of the steering wheel sensor.

52

Tracking for Collision Avoidance Applications

Yaw rate and steering wheel angle for a lane change maneuver 150 Yaw rate Steering wheel angle

Yaw rate [deg/s]

100

50

0

−50

−100

−150 0

1

2

3

4 Time [s]

5

6

7

8

Figure 3.14 The yaw rate and steering wheel angle for a vehicle traveling at 50 km/h performing a lane change maneuver. The steering wheel angle has been scaled to be of the same size as the yaw rate. The time constant between steering wheel angle and yaw rate is approximately 500 milli-seconds.

4 Decision Making

The ultimate goal of a CM system is to avoid or mitigate collisions by taking some kind of autonomous action. The task of deciding when to take action is here called decision making. The problem of deciding when a system should “interfere” is complicated by several factors. Among these factors are measurement and process noise, but it should also be borne in mind that different people have different preferences and will perceive an intervention differently. Drivers might also have quite individual driving styles.

4.1

Collision Mitigation Countermeasures

The decision of when to intervene will of course depend upon what type of intervention or countermeasure is being considered. In this thesis, the main focus is on braking interventions. Other possible intervention are: • Warning: Warnings can be issued in several ways: audible signal, visible signals and haptic signals, i.e., signals that are felt (for example, vibrations in the seat or steering wheel). 53

54

Decision Making

• Steering: Steering can be used both to try to avoid the collision completely or just to align the vehicle so that the collision occurs where energy absorption is best. • Switch-on brake lights: To give following vehicles some extra time to avoid hitting the host vehicle from behind. • Vehicle height alignment: This aims at making it compatible with the struck vehicle’s energy absorbing structure. So that the utilization of both vehicles deformation zones is optimized during the collision. • Belt pretentioning: Makes sure that the passengers are correctly seated prior to the crash. • Early airbag inflation: Maximizes the effect of the airbag by early deployment.

4.2

Risk Estimation

The input for the decision-making algorithm normally comes from the tracking system. To be able to make a decision, we first have to form one or more metrics that measure the risk of collision. A simple form of decision-making will then simply be thresholding the risk metric. More complex decision-making algorithms are probably needed in systems that have different degrees of intervention and simultaneously use different types of intervention. Many existing systems only consider 1-D movement. The assumption in such a system is that the tracked vehicle/POV is in the same lane. Some systems using the in-lane assumption and 1-D reasoning are presented in [53], [49] and [14]. To determine if the POV is in the lane, a forward prediction based on the yaw rate is normally made. Assuming that the POV is in the same lane, the velocity of the two vehicles and head distances are used to form a metric. Typical examples of interesting metrics are time to collision (TTC), headway time (THW) and deceleration required to avoid collision. In (4.1) the deceleration required to avoid the vehicle in front is given. adec =

2 2 − vPOV vhost , 2Dhead

where:

vhost = Host vehicle speed vPOV = POV speed Dhead = Headway distance

(4.1)

4.3 Probability of Collision

55

Figure 4.1 In a tracking system the host vehicle and the POV are normally represented by a point. The area D corresponds to all-possibleconfigurations between the two vehicle so that their bodies intersect, i.e., they collide. The area D is not actually an area since it not only depends on the relative distance between the two points, but also on their heading angles. So the indicated area is actually a 3 dimensional volume of the vehicle’s relative position and orientation. It is over this volume the PDF should be integrated to obtain the collision probability.

With this metric, a critical deceleration is then chosen as the decision boundary. For example, if a deceleration larger than 6 m/s2 is required to avoid the vehicle in front of the host vehicle, the system will perform autonomous braking. The main advantage with metrics of this kind is that they are both intuitive and computationally cheap. It is easy to account for driver reaction time (in a CW system) and system delay time. As long as the in-lane assumption holds, the performance is very predictable. The disadvantage, however, is that in real life the in-lane assumption is not as easily determined. One car may switch lane at any time, and sometimes a driver will not necessarily drive in the lane. With the in lane assumption, a number of difficulties that come from 2-D movement are “brushed under the carpet”. Another weakness is that these metrics do not consider measurement and process uncertainty.

4.3

Probability of Collision

Here we propose to use the probability of collision (Pr(collision)) as a metric for decision making. The probability of collision can be calculated according to (4.2).

56

Decision Making

Pr(collision at time t + 1) = Pr(˜ px , p˜y , ψ˜ ∈ D) ZZZ ˜ t )dxdydψ pt+1 (˜ px , p˜y , ψ|Y =

(4.2)

˜ p˜x ,p˜y ,ψ∈D

Here:

D =The area which corresponds to a collision, i.e., the area that corresponds to physical overlap of the two vehicles, see Figure 4.1. p˜x =Relative position of the x coordinate p˜y =Relative position of the y coordinate ψ˜ =Relative heading angle

˜ t ) of the vehicles’ relative position is obpx , p˜y , ψ|Y The probability density pt+1 (˜ tained directly from the Bayesian solution to the tracking problem, if relative coordinates are chosen. If ground fixed coordinates are used, the density of the relative position has to be calculated before the collision probability can be calculated. As˜ = xhost − xP OV is given suming xhost and xP OV are independent, the density of x by the convolution (4.3). Z ∞ x) = pxP OV (x)pxhost (x − x ˜)dx (4.3) pX˜ (˜ −∞

ˆhost − x ˆP OV ∈ In the case where xhost and xP OV are Gaussian and independent, x x, P˜ ). Such estimates typically come from N (xhost − xP OV , Phost + PP OV ) = N (˜ a Kalman filter, which also provides the desired covariance matrices. An example of how the probability density can look like for a Kalman filter estimate is shown in Figure 4.2 Generally no analytical solution can be found to (4.2). Now we ˆPOV and length is approximate the area D with a square who’s width is whost + w lhost . Here w denotes the width of the object and lhost denotes the host vehicle’s length. In this approximation of the area D we don’t account for the vehicles’ relative heading. Furthermore we make the assumption that movement in the x and y direction is independent. We can now derive the following expression for the probability of collision. ZZ pt+i (px , py |Yt )dxdy Pr(collision at time t + i) = p ˜ ∈D ZZ T ˜ −1 1 1 q e− 2 (p−˜p) Π (p−˜p) dxdy = p ˜ ∈D ˜ (2π)2 det(Π) Z =

whost +w ˆ POV 2 −(whost +w ˆ POV ) 2

Z

0

−lhost

1

q

˜ (2π)2 det(Π)

1

e− 2 (p−˜p)

T

˜ −1 (p−˜ Π p)

dxdy

4.3 Probability of Collision

57

PDF for a vehicle traveling at 60 km/h 6

5

4

3

2

1

0 4 2 0 −2 −4

global y coordinate [m]

92

90

98

96

94

100

102

104

global x coordinate [m]

Figure 4.2 Probability density of a car traveling at 60 km/h. The plot shows the pdf at time t+0.7, t+0.8, t+0.9 and t+1.0 seconds respectively. Z =

−(whost +w ˆ POV ) 2

Z ×

whost +w ˆ POV 2

0 −lhost

= (Φ(

q

q

1

1

e− 2 (y−p˜y )

T

˜ −1 (y−p˜y ) Π

dy

˜ (2π)2 det(Π)

1

1

e− 2 (x−p˜x )

T

˜ −1 (x−p˜x ) Π

dx

˜ (2π)2 det(Π)

whost +w ˆPOV 2

σy

− py

) − Φ(−

whost +w ˆPOV 2

− py

σy

))(Φ(

0 − py lhost − px ) − Φ(− )) σx σx (4.4)

In the above equations p ˜=

p˜x

p˜y


T

˜ is the covariance matrix of p and Π ˜.

If the point mass or particle filter methods as described in Sections 3.3 and 3.4 are used, the posteriori density is given by a particle cloud or a grid with assigned weights. The probability of collision in (4.2) is, in this case, approximated by the sum in (4.5). X pi pj . (4.5) Prt+1 (collision) = (i)

(j)

i,j:xP OV −xhost ∈D

58

Decision Making

In (4.5) pi and pj denotes the probability weight of a particular grid-point or a particle. The strength in using the probability of collision as a collision risk metric is that it incorporates both process and measurement uncertainties. This makes it easy to deal with “missed” measurements and time varying sensor performance. The main disadvantages are that it requires more computational resources and that it might not be intuitive for design. In the next section we will discuss strategies for intervention and how we can design thresholds that fulfill these strategies. The Algorithm 4.1 summarizes decision making using probability of collision to determine if the system should activate. In the algorithm we make the assumption that movement in the x and y direction is independent. We also approximate the area D with a rectangular area. Algorithm 4.1 (Decision making) (j) (j) 1.Given x ˆhost x ˆP OV Pˆhost and PˆP OV j = 1,2,3,4 from Algorithm 3.1. Transform the position and its covariance matrix to a host vehicle fixed coordinate system (if relative coordinates are used  this step is not needed).  sin(φ) − cos(φ) ˆ host ); T = p ˜ = T (ˆ pP OV − p cos(φ) sin(φ) ˜ = T (ΠPOV + Πhost )T T Π 2.Calculate the collision probability for each time and each obstacle Prt+i,obstaclej (collision) =

= (Φ(

whost +w ˆ POV 2

σy

−py

) − Φ(−

whost +w ˆ POV 2

σy

−py

))(Φ(

0−py σx )

x − Φ(− lhostσ−p )) x

3.Calculate maximum probability for all objects and prediction times. Pr(collision) = maxi,j (Prt+i,obstaclej (collision)) 4.Threshold the probability to determine if the system should activate. If(Pr(collision) > Threshold) Activate system

4.4

Decision Strategy - Choices of Thresholds for Intervention

The two main desired properties of a CM system are that it should avoid all collisions and that no faulty interventions should occur. The problem of choosing an intervention strategy is that these properties are contradictory. To help analyzing possible strategies, driving will be divided into five different states. In Figure 4.3, these states are visualized for a scenario in which a vehicle is approaching a stationary obstacle. Here is a short description for each state:

4.4 Decision Strategy - Choices of Thresholds for Intervention

59

Figure 4.3 Driving is divided into five different states. The figure shows an example of these states for a vehicle approaching a stationary obstacle. At first the obstacle is far away and presents no imminent threat, this is called normal driving. As the vehicle comes closer to the obstacle it enters the collision avoidable state, here the obstacle is a threat that can still be avoided by a braking or steering maneuver. At some point it becomes impossible to avoid the collision; this state is called the collision unavoidable state. The collision state is the state in which the vehicle collides. The state after the collision is called the post crash state.

1. Normal Driving: In this state there is no imminent threat or risk for collision. Forward control might be exerted by an ACC system in this state. 2. Collision Avoidable: Here there is some threat to the vehicle. A non-negligible risk exists that a collision will occur. In this state it is still possible to avoid the imminent collision by an appropriate avoidance maneuver. From a drivers’ perspective this will be perceived as a threatening or dangerous traffic situation. Whether a situation is perceived as dangerous varies between different drivers. What is perceived by a CM system as a dangerous situation will of course also vary depending upon the collision risk metric chosen. It is normally in this state that FCW systems are activated. Any system intended to entirely avoid collision has to launch its countermeasure in this state. 3. Collision Unavoidable: In this state a collision is imminent, and cannot be avoided by any maneuver (steering and braking) performed by both vehicles jointly. Although the accident cannot be avoided, it might still be possible to significantly reduce it’s severity (i.e., the collision speed). 4. Collision: This is the state where a collision occurs.

60

Decision Making

(a) Overtaking situation, here two vehicles are on collision course. The appropriate maneuver for the overtaking vehicle is to accelerate and then turn back into the lane to avoid a collision.

(b) Meeting on a narrow road, the two vehicles might be on collision course. Normally both driver will steer their vehicle to the right side of the road just before they pass each other.

Figure 4.4 Two examples of traffic situation where the two involved vehicles are on a collision course. Even though the situation is threatening in some sense, there is no danger except if the driver has misjudged the situation (e.g. there is not enough time to finish the overtaking, or the road is to narrow for the two vehicles to pass.)

5. Post Collision: The state after a collision has occurred. It should be noted that it is possible to go directly from the normal driving state to the collision unavoidable state. One example of such an event is a wild animal accident. In many such accidents the animal suddenly jumps up in front of the vehicle. If the distance between the car and the animal is too short, there is simply no maneuver that can avoid the accident from taking place. An FCM system that avoids all collisions will therefore never be feasible. In general, the collision avoidable state is very hard to define. Despite there being many situations in normal driving where a collision is close, these situations are not always perceived as threatening (or at least not as situations where a CM system should intervene). Two examples of such situations are overtaking situations or two cars meeting on a narrow road, as displayed in Figure 4.4. The strategy of

4.4 Decision Strategy - Choices of Thresholds for Intervention

61

when to perform an intervention will inevitably be a trade-off between a system’s effectiveness in avoiding collisions and faulty intervention frequency. The tolerance for faulty intervention will, of course, depend on the type of intervention. For example, an erroneous warning is not as bad as an erroneous braking maneuver. Some faulty warnings can be accepted in an FCW system. Due to this, and the fact that driver reaction time and non-ideal performance must be accounted for, the decision boundary for an FCW systems must be in the collision avoidable state quite a distance from the collision unavoidable state. For an inattentive driver to be able to avoid an imminent collision, the warning normally has to come more than one second before the collision unavoidable state is entered (see [36]). The tolerance for faulty interventions is expected to be very low for steering and hard braking maneuvers. For these countermeasures, the decision boundary must lie close to, or even within the collision unavoidable state. In the coming sections we will specifically look at systems that only use brake intervention. We have to be aware that for such a system, performance will vary greatly depending on the situation even if the same decision boundary is used. We will give two examples to illustrate this fact:

Example 4.1 •Two vehicles going head to head at 200 km/h: In this scenario, a CMbB vehicle would have to start braking 5.5 seconds before the collision (assuming 10 m/s2 deceleration) to come to a full stop. Having come to a stop, it would still be hit by the other vehicle traveling at 200 km/h, unless the driver in this vehicle also took some action. A steering maneuver could be executed much later and would completely avoid the accident. •Two vehicles traveling at high speed in the same direction with only a few meters’ distance. Suddenly the lead vehicle brakes hard. In this case, no steering maneuver will avoid the collision, but hard braking will if it is executed quickly enough.

These two example were chosen to point out that braking and steering are effective in different situations. Looking at a system that uses only braking interventions, there will be situations where the system is effective, and situations where there is little or no effect at all. Since there is no tolerance for faulty interventions, a straightforward approach on how to avoid this is to design a system that is only allowed to intervene when the collision unavoidable state has been entered. The probability of collision metric is well suited to determine when an accident becomes unavoidable. Assuming a perfect dynamic model, no measurement noise and no system delays, one can set the threshold value to one, and this will correspond exactly to the point where collision becomes unavoidable for any driving situation.

62

Decision Making

In reality, there are of course measurement errors and modeling errors, etc. Since faulty interventions are undesired we design our system model so that the handling capabilities of the vehicles are overestimated. This means that when the “true” probability of collision is equal to one, the estimated/calculated collision probability is less than one. This means that the Pr(collision) = 1 threshold will actually lie a bit into the collision unavoidable region. To get a feeling of the potential of such a system, we will look at the ideal performance (i.e., no measurement and modeling errors) for a specific scenario. The scenario that we will look at is the head on against a stationary obstacle as displayed in Figure 4.3. It is assumed that both the vehicle and the obstacle have a width of 2 meters. Furthermore, it is assumed that maximum deceleration and centripetal force can be achieved instantaneously. The braking distance and the distance needed to avoid the obstacle by a steering maneuver are plotted in Figure 4.5. The radius rcp of a body traveling with a constant centripetal force alat (typically the best possible lateral acceleration is around alat ≈ 9.82m/s2 ) is given by (4.6). rcp =

v2 alat

(4.6)

The longitudinal and lateral distance traveled under centripetal motion can be calculated by Pythagoras theorem 4.7. 2 = x2 + y 2 rcp

(4.7)

To calculate the distance to clear an obstacle with width wobstacle , assuming that the own vehicles width is wown we modify 4.7. (rcp + wown /2)2 = x2 + (y − rcp )2

(4.8)

Setting y equal to wobst /2 and solving for x (the longitudinal distance) yields r w2 w2 (4.9) x = rcp wown + own + rcp wobstacle − obstacle 4 4 s =

(

2 (w2 − wobstacle ) v2 )(wown + wobstacle ) + own alat 4

(4.10)

The braking distance can be calculated from v 2 − v02 = 2along Dbrake

(4.11)

Equations (4.12) and (4.13) thus give the braking distance and steering avoidance distance. Dbrake Dsteer

v02 2along s 2 (w2 − wobstacle ) v2 , = ( )(wown + wobstacle ) + own alat 4 =

(4.12) (4.13)

4.4 Decision Strategy - Choices of Thresholds for Intervention

63

Distance needed to avoid collision (intersect at ~33 km/h) 90 brakedist steerdist

80 70

Distance [m]

60 50 40 30 20 10 0 0

50

100

150

Speed [km/h]

Figure 4.5 Distance required to avoid a collision by braking and by steering. The assumption here is that the vehicle can instantaneously achieve 10 m/s2 deceleration or 10 m/s2 lateral acceleration. The width of the own vehicle is here set to 2 meters and the width of the obstacle is 0 meters

As can be seen from both the equations and the graph, the braking distance is proportional to the square of the velocity, whilst the steering distance is basically linearly proportional to the velocity. Furthermore, for low speeds (below 45 km/h), braking is a more efficient countermeasure and for high speeds (above 45 km/h), steering is a more efficient way of avoiding the accident. If braking could be applied exactly at the collision unavoidable boundary, the collision speed for this scenario would be as displayed in Figure 4.6. Collisions below 45 km/h are completely avoided. For collisions where the initial speed is above 45 km/h, the impact speed is reduced by 25 km/h. Chapter 5 will look more closely at system performance using results from more accurate motion models, as well as physical testing with a prototype vehicle.

64

Decision Making

Collision speed 160 With braking No braking

140

Collision speed [km/h]

120 100 80 60 40 20 0 −20 0

50

100 Initial speed [km/h]

150

Figure 4.6 Here the collision speed as shown for the head on scenario is displayed. The assumption is that a deceleration of 10 m/s2 can be applied instantaneously when the collision unavoidable state is entered. For this scenario the distance when this occurs is given as the minimum distance of the braking and steering avoidance distance plotted in Figure 4.5.

4.5

Behavior Modeling and Situation Assessment

When the probability of collision is used as a metric for collision risk, it is assumed that an accurate description of the posterior probability density function is available. Finding the pdf is the task of the tracking system. In Section 3.8, some models for describing the dynamics of the vehicle were presented. To estimate the pdf correctly, an accurate description of the process noise (vt ) distribution is essential. The main source of process noise is the driver’s steering, brake and accelerator commands. This section will discuss some considerations of how to form the process noise (i.e., model the driver’s behavior). By using measurement of the steering wheel angle from normal driving, a histogram can be plotted that shows an empirical steering wheel angle distribution (Figure 4.7). It might now be tempting to use an approximation of this distribution for

4.5 Behavior Modeling and Situation Assessment

65

Empirical distribution of steering wheel angels 1000 900 800 700 600 500 400 300 200 100 0 −200

−150

−100 −50 0 50 Steering wheel angle [deg]

100

150

Figure 4.7 Empirical distribution of steering wheel angle at normal driving. In this example the data was collected during urban area driving at speeds ranging from 0 to 60 km/h.

the process noise. This might be appropriate for CW systems. For CMbB systems, however, behavior in critical situations is more relevant. Thus we are interested in finding the collision unavoidable boundary when the vehicle is operated close to the limits of its handling capability. In normal driving, the full handling capability’s of the vehicle is very rarely used. If the empirical distribution (as given in Figure 4.7) from normal driving is used, the resulting estimate of the posterior distribution will be an underestimation of the vehicle’s handling capability. In a CMbB system the focus is on avoiding faulty interventions. To achieve this the handling capabilities of the vehicle should always be overestimated. So instead of looking at normal driving, the vehicles maximum acceleration, maximum deceleration and maximum lateral acceleration should be considered. The tire-road friction, engine strength, brakes and how fast the driver is capable of turning the steering wheel, etc, determines these properties. The maximum acceleration that can be achieved by a passenger car is normally approximately 1 g (= 9.82 m/s2 ) in the longitudinal direction. The maximum rate at which a driver can turn the steering wheel is approximately 700 deg/s.

66

Decision Making

In the above discussion, we again stumble into the difference in decision making for CW systems and CMbB systems. With the added insight of different driving states and threshold choices, we can generally say, that for CMbB systems we are mainly interested in capturing the physical limits of the car’s dynamics and estimating collision risk close to the collision unavoidable boundary. For CW systems on the other hand, we are interested in extending the prediction far out in the collision avoidable state. In order to do this and still be accurate, we need to consider driver intention and road/lane geometry. CW systems with low false alarm rate require sensors able to detect lane markings and logic to interpret these measurements. To determine when to perform braking actuation in general requires some additional logic to the probability of collision metric. This is because braking is not always an appropriate action in a collision situation. For example, suppose a CMbB vehicle is equipped with sensors that can monitor the entire surrounding of the vehicle. In the case that this vehicle was hit from behind the probability of collision would be one, but braking might worsen the accident. Clearly braking can only mitigate collisions with objects in front of the striking vehicle (if it is traveling forwards). Therefore, CMbB systems should perform braking only for objects in front of the vehicle. The reasons that this is pointed out is that during testing we found that it was possible to get interventions with a CMbB system in scenarios when performing late avoidance maneuvers. An example of such a maneuver is displayed in Figure 4.8. In these scenarios because of modeling and sensor errors, the tracking system would predict a collision when the CMbB vehicle is next to the obstacle as in Figure 4.8(c). By requiring the obstacle to be in front of the CMbB vehicle such faulty interventions can be avoided.

4.5 Behavior Modeling and Situation Assessment

(a) Initially, the vehicle approaches the stationary obstacle head on.

(b) At the last moment the driver makes an evasive steering maneuver.

(c) The maneuver is sufficient to avoid the obstacle with the smallest possible margin.

(d) During the maneuver the driver turned the steering wheel as fast as possible. The entire maneuver is executed at the limits of this vehicle’s handling capabilities.

Figure 4.8 Example of a late avoidance maneuver. The driver steers away from the obstacle at the last moment and manages to avoid a collision.

67

68

Decision Making

5 System design and Testing

In this chapter we will consider a specific CMbB system. This system uses the probability of collision as a metric to decide when to perform braking interventions. The strategy is to reduce collision speed as much as possible under the constraint that no faulty interventions are allowed. This means that we want the system to engage the brakes as soon as the collision unavoidable driving state is entered. Performance of the system has been evaluated both by simulations and by field tests with a prototype vehicle. An overview of the simulation environment is presented in Figure 5.1. The simulation environment has been designed to bear as much resemblance as possible to the prototype vehicle and its sensors. This enables the

[Obstacles]

Environment

Driver_Command

Driver_in

Obstacles

Traking Sensor Measurements

Obstacles Predictions

Driver Inputs Collision Requested Brake Vehicle state

Virtual Driver/Chassi control

Vehicle Kinematic States

Virtual_in

Host Vehicle

Navigation Sensor Measurements

Sensor Model

In

Collision Probability

Host Vehicle

Tracking System

Decision Making

Host Vehicle Model

Figure 5.1 Simulation model of CMbB system 69

70

System design and Testing

use of the same code (for the tracking system and decision making system) in both the simulation environment and in the prototype vehicle.

5.1

Simulation environment

The Simulation environment in Figure 5.1 has been implemented using Matlab and Simulink. From the simulink code it is possible to auto generate real time code. Thus the tracking system and decision making blocks can be directly implemented in the prototype vehicle, using real time workshop to produce the real time code. It is possible in the simulation to have at most ten different obstacles at the same time, and the tracking and decision making system will handle a maximum of 4 tracks at any given time. All the maneuvers of the host vehicle and the obstacles are specified before the simulation starts. The main purpose of the simulation environment is to test performance of the algorithm in different scenarios and to see whether or not it is possible to provoke a faulty intervention. Especially for high speed collisions where physical testing with the prototype vehicle might be too dangerous or too costly. Here is a short description of the blocks that the model consists of (corresponding to the blocks of Figure 5.1): Driver Inputs: The driver inputs are described by work space variables that specify the driver’s steering wheel, brake and accelerator commands. These are all specified before the simulation starts, and are not affected by the CMbB system’s brake intervention. The driver will thus continue the same maneuver as he was attempting before the system was activated. The CMbB system will of course override the drivers accelerator and braking commands. Environment: The environment describes the traffic environment of the CMbB vehicle. It is specified by workspace variables describing the objects surrounding the host vehicle. These are also specified before the simulation starts and are not affected by eachother or by the host vehicle movement. Together with the driver inputs, the environment variables describe how a specific scenario will look. Typical objects are other vehicles and stationary objects. There is currently no information about lane geometries or changes in road conditions. Host Vehicle Model: The host vehicle model is a dynamic handling model that describes the physical limitations of the handling performance of the host vehicle. It takes driver commands such as steering wheel angle, brake and accelerator commands as input. The outputs are position, velocity, acceleration and turn rate (yaw rate) of the host vehicle. For most simulations, a bicycle model (as described in section 3.8.4) was used. This model has no actuator dynamics except for the pressure build-up in the braking system. The pressure build-up is modeled as a ramp which has a rise time of 300 milli-seconds to achieve maximum brake force. To model tire to road

5.1 Simulation environment

71

friction, Pacejkas magic formula (see [5]) was used. For the simulations in Section 5.3, a more detailed model was used. This model has 15 degrees of freedom and has been verified against a Volvo S80. Sensor model: The sensor model simulates the host vehicle’s tracking and navigation sensors. It takes inputs from the environment block and from the host vehicle. It calculates range, range rate and azimuth angle to the surrounding objects. To these “ideal” measurements, noise is added according to   r (5.1) y =  r˙  + et . ϕ The additive sensor noise et is assumed to be Gaussian and independent. The form of the sensor output is the same as in that from the sensors in the prototype vehicle. Currently this vehicle is equipped with one mm-radar and one lidar. Therefore, the sensor model outputs measurements corresponding to the output of these sensors. The field of view of the sensor model has been set to ± 60 degrees, which is much larger than the FOV of the sensors in the prototype vehicle. The reason for this is that it is interesting to evaluate performance for other sensors than those now available, since they have been designed for use in ACC systems where a large FOV is not required. This block also adds noise to the navigation sensor measurement (yaw rate and speed of the host vehicle) Tracking system: The tracking system (Figure 5.2) which is also described in Algorithm 3.1, performs measurement association and finds the Bayesian solution to the tracking problem. It also makes predictions on future states, which is used by the decision making system to calculate collision probability. Measurement association is performed by the nearest neighbor approach. The maximum number of live tracks are four at any given time instant. Since the mm-radar provides a maximum of 10 targets, the measurements have to be chosen so that the most “dangerous” measurements are used to initiate new tracks; this is done in the pre-filtering block. Tracks are killed when the covariance of the estimated position becomes too large. The Bayesian solution to the tracking problem is obtained by an EKF. The tracking model that is used is the nearly coordinated turn model from Section 3.8.3. The system predicts positions for 20 future time instants. The spacing between each prediction is 100 milli seconds, thus the vehicles future motion is predicted two seconds forward in time. Fusion of the laser and radar measurement is done in the EKF measurement update. The measurement update equation will thus change over time. There are four possible updates: • Measurements from both sensors are associated with the track. • Only measurements from the mm-radar is associated with the track. • Only measurements from the laser radar is associated with the track.

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Associated measurements

Tracking sensor measurement

Predictions Predicted Association Quanteties

1

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Predicted Posistions and Covariances

Candidate tracks

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Track status

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Tracking sensor measurement Pre−Filtering

Candidates

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Predicted Posistions and Covariance

2

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Navigation sensor Measurements

1 Predicted Posistions and Covariances

Filtering

Figure 5.2 Overview of the tracking system implementation • No measurements are associated with the track. When tuning the tracking filter parameters, one normally has to make a tradeoff between noise attenuation and tracking performance. In our case there is a further consideration. Since the covariance matrix is used for decision making on when to perform braking, it is important that the true handling capabilities of the vehicle are reflected by the a posterior distribution. The handling capabilities typically vary with the state of the vehicle and also by changes in the environment. Therefore the process noise will, in general, vary over time. In our model the process noise varies with the speed of the vehicle. The tracking system used in the simulation environment also run in real-time in the prototype vehicle. Decision Making: The decision making algorithm takes as input the posterior distribution of both the host vehicle and the observed obstacles for several future time instants. The system is also described by Algorithm 4.1.In this system posterior distributions for 20 time instants is calculated. In this case the posterior distribution is described by the state estimate together with the covariance matrix. From the posterior distributions the probability of collision between the host and each obstacle is calculated for each predicted time instant (according to section 4.3). The maximum probability in (5.2) of all obstacles and all time instants is then thresholded to determine if there is an unavoidable accident or not. P rM ax (collision) = max P rti ,obstaclej (collision). i,j

(5.2)

Note that if we have an accurate model the threshold value should be one. Here we use linearized models and Gaussian noise to model the process. Since emphasis is on avoiding faulty intervention, the model should overestimate the handling capabilities of the vehicle. This will always be the case when we use a Gaussian noise distribution that extends to infinity. This means that the calculated probability of collision will be lower than one when the actual probability of collision is one, i.e., when the collision unavoidable state is entered. To find the appropriate setting for the threshold, simulation of near-miss scenarios have been used. The scenarios were run for speeds ranging from 0-200 km/h and the threshold was set sufficiently high not to give false interventions. The threshold that is used varies with the speed of the host

5.2 The Prototype Vehicle

73

vehicle. There are several reasons for this: first of all the model of the varying process noise is not very accurate, secondly for low speeds and short ranges the sensors of the prototype vehicle has proved to have bad performance, thirdly it might be desirable to have different intervention levels for different host speed intervals. In this algorithm, the threshold is set very high for speeds below 20 km/h. For speeds above 20 km/h, the threshold has been set as low as possible (without having faulty interventions). Apart from the probability metric the decision making algorithm uses some additional logic to determine when to intervene. The algorithm requires the object to have been observed in both tracking sensors for it to be classified as a valid target. This means that at least one measurement from each sensor must have been associated with the track.

Virtual Driver/Chassis Control: This block performs braking when the probability of collision is above the threshold value. In the prototype system discussed in this chapter, maximum braking is always performed when the intervention threshold is reached. The rise time of the brake system is normally 300 milli-seconds, and the maximum deceleration is 8 m/s2 . There is also a system delay of 100 milli-seconds from the time that the threshold value is exceeded and brake actuation is performed. This performance is similar to the performance of the prototype vehicle. However, for some simulation a model with better braking performance has been used. This is mainly to display the full potential of the CMbB system. In those cases we have used a system that should correspond to the new generation of electro hydraulic braking systems (EHB systems). These systems claim a pressure rise time of 100 milli-seconds and a higher maximum braking force than conventional systems. Our model of such a system is that a maximum deceleration of 9.82 m/s2 is reached within 100 milli-seconds. There is still a 100 milli-seconds delay before the brakes are actuated. In Table 5.1 the most important features of the simulation environment is summarized.

5.2

The Prototype Vehicle

The prototype vehicle is a standard Volvo V70. It has been equipped with two tracking sensors and one dSPACE Auto-box. The Autobox (Figure 5.3) is used to performed necessary computations for the tracking and decision making system and it is also used to actuate the brakes. The processor of the Auto-box is a 400 Mhz power PC. To evaluate the system’s performance in collisions, an inflatable car (Figure 5.4) is used. For safety and cost reasons, collision tests have been made at speeds up to 70 km/h only.

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Feature/property Maximum number of live tracking filters Number of future predictions in the tracking system Temporal spacing between predictions Maximum Deceleration Brake system rise time Delay from decision making to brake actuation FOV of the mm-radar Std. on range measurements in mm-radar model Std. on range rate measurements in mm-radar model Std. on azimuth angle measurements in lidar model FOV of the lidar Std. on range measurements in lidar model Std. on range rate measurements in lidar model Std. on azimuth angle measurements in lidar model Tracking and decision making system update rate

Value 4 20 100 [ms] 8 [m/s2 ] 300 [ms] 100 [ms] 60 [degrees] 1 [m] 0.5 [m/s] 1 [degrees] 60 [degrees] 1 [m] 1 [m/s] 1 [degrees] 10 [Hz]

Table 5.1 Summary of important characteristics of the simulation environment

5.2.1

Prototype Vehicle Tracking Sensors

The two tracking sensors used are a mm-radar installed in the front bumper (see Figure 5.5) and a laser radar installed behind the windshield close to the rearview mirror (Figure 5.6). Both of these sensors are production units that are used for ACC systems. The measurement vector (for one obstacle) from the sensors are given by   r     r˙ r     , r˙ (5.3) ymm-radar =   ϕleft  , ylaser radar =  ϕcenter  ϕcenter ϕright where ϕleft = azimuth angle to the left edge of the detected object, ϕcenter = azimuth angle to the center of the detected object, ϕright = azimuth angle to the right edge of the detected object. Thus the mm-radar provides some information that can be used to determine the object’s width. Both sensors also provide additional measurement on reflected energy etc. This information, is however, not used. Both sensors can detect obstacles at ranges beyond 150 m and have an update frequency of 10 Hz. The FOV is 13.6 degrees for the mm-radar and 14 degrees for the laser radar. The narrow FOV is often sufficient for ACC systems. We will later see that performance of the CMbB system will degrade because of the narrow FOV. To check the range accuracy of the sensors, stationary measurements were performed. In these tests, the distance to a parked vehicle was measured when the host vehicle itself was standing still. Both the laser and the radar measured

5.2 The Prototype Vehicle

75

Figure 5.3 The dSPACE unit is installed under the floor of the luggage compartment

the true distance to an accuracy within 0.1 m. However this is not the case when the host vehicle is moving. Figure 5.7 shows the range measurements from the laser and the mm-radar as a stationary target is approached head-on at 40 km/h. There is a clear discrepancy between the range measurements from the laser and the mm-radar (the difference is approximately two meters). In dynamic scenarios, the measurements for each sensor is consistent but the discrepancy between the sensors will cause problems when we want to fuse the sensor data (in the tracking algorithm this is solved by using large gates in the measurement association step). This problem is believed to be caused by an unknown and varying delay in the sensors. Currently there is no time stamp of a measurement or any way to synchronize the sensors. Another problem with the two sensors used here is that none of them provides accurate measurements over short distances. In most cases the sensor “loses” sight of objects when the range is shorter than 10 meters (see e.g. Figure 5.7 at time 28). Furthermore, as the measured object moves out of the FOV of the mm-radar the azimuth angle measurement deteriorates. This means that in many cases the azimuth angle measurement is erroneous when the entire object is not in the FOV of the sensor. Figure 5.8 shows typical performance for the sensor in a head-on scenario. At time 3 the range is approximately 10 m and the entire object is not within the sensors FOV; the azimuth angle grows larger until the time when the object is lost by the sensor (at time 3.8). In this scenario it looks as if the measured object moves out of the path of the host vehicle, even though it really was stationary and was hit head-on by the host vehicle. The behavior displayed in Figure 5.8 causes problems in head-on collisions at low speed (less than 30 km/h) where the distance for intervention is much shorter than 10 m. There is thus a lower limit at which collision test can be performed with reliable results.

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Figure 5.4 Inflatable car used for collision test, maximum collision speeds 70 km/h

This limit lies around 30 km/h. In many of the tests with the prototype vehicle, an inflatable car was used as an obstacle. It is therefore interesting to examine if its radar cross section differs from that of ordinary vehicles. To investigate this, stationary tests were performed. The measurements were performed as displayed in Figure 5.9 (picture taken from the viewpoint of the host vehicle). Here both the host vehicle and the measured objects are stationary. From these measurements we found that both obstacles were detected with the same accuracy and that the reflected signal strength was very similar from the rear end of a Volvo V70 and from the rear end of the inflatable car.

5.2.2

The Braking System of the Prototype vehicle

The brake system is of great importance for the kind of CMbB system that is considered here (intervention only when the collision unavoidable state has been entered). This is due to the fact that an intervention is issued very late. In many cases less than 1 second before collision. Because of this short time, it is crucial that the brake system quickly reaches maximum deceleration. The prototype vehicle is equipped with a production ABS system. Brake actuation (when CMbB system initiated) is achieved by opening a solenoid valve in the brake booster. There is also a vacuum pump that can be manually switched on and off to ensure vacuum in the brake booster at intervention. Performance of the brake system is plotted in Figure 5.10. The plot shows a CMbB system induced brake maneuver, i.e., the driver does not touch the pedal. The notch in the acceleration curve between time

5.2 The Prototype Vehicle

77

Figure 5.5 The mm-radar installed in the front bumper of the vehicle

Figure 5.6 The laser radar is installed behind the windshield of the prototype vehicle

15 s and time 16s comes from activation of the ABS system. Both the speed and accelerations are derived from the wheel speed sensor. The rise time for the CMbB system actuated braking maneuver is typically larger than 500 milli-seconds. The maximum deceleration achieved in the test displayed in Figure 5.10 is approximately 6.3 m/s2 . The condition when this test was performed was wet asphalt, the temperature was between 0 and 5 degrees and the vehicle was equipped with non-studded winter tires. This explains the low maximum deceleration reached. We stress here that brake actuation through the opening of a solenoid valve in the brake booster is specific to this prototype vehicle, and that better alternatives ex-

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Range measurements 45 Lidar mm−radar

40 35

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Figure 5.7 In dynamic scenarios there is often a discrepancy between range measurements from the lidar and the mm-radar. In this scenario an inflatable car is approached head-on at 40 km/h. The collision occurs at time 33. At time 28 the laser radar loses track of the obstacle. The difference in the range measurements is approximately 2 meters. For other test runs under the same conditions the difference is different.

ist. The important characteristics of the prototype vehicle is summarized in Table 5.2.2

5.3

Ideal CMbB System Performance

Before looking further into results from simulations and field tests with the system described in the previous sections, we will examine what performance to expect from the best possible CMbB system for a head-on collision scenario. The assumption is that obstacles can be measured with a high accuracy (in the order of 0.01 m and speed with 0.1 km/h) and a high sensor sample rate (not less than 10 Hz). The computational power is sufficient to find the Bayesian solution to the tracking problem for an accurate vehicle model (the system cycle time should be the same as the sensor update rate). With such a system the probability of collision will become one on the border between the collision avoidable and collision unavoidable state. The distance needed to avoid collision (by means of either steering or braking) for the head-on scenario in 4.3 was plotted in Figure 4.5. Assuming that there exists no better maneuver than pure steering or braking, the distance

5.3 Ideal CMbB System Performance

79

Degeneration of Azimuth Angle Measurement 50

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Figure 5.8 Range and azimuth angle measurements provided by the mm-radar, from a stationary obstacle straight ahead. The obstacle is approached head-on without any steering maneuvers before the collision occurs, at time 3.9 s. At time 3 the range to the obstacle is approximately 10 meters. After this point the azimuth measurement clearly deteriorates.

at which a collision becomes unavoidable is given by the minimum of the plotted braking distance and the steering avoidance distance of Figure 4.5. For low speeds, braking is more efficient and for high speeds steering is more efficient at avoiding the collision. If the decision boundary coincides with the border of the collision unavoidable state the collision speed is given by Figure 4.6. In Figures 4.5 and 4.6 a very simple motion model is used, i.e., straight line motion with constant deceleration and circular motion with a constant centripetal force. In Figure 5.11 we again plot the distances needed to avoid an obstacle by means of braking and steering; here we have used a 15 degree of freedom handling model that has been verified against measured data to simulate the maneuvers. Comparing Figures 4.5 and 5.11, it can be noted that both the steering and braking distances are longer for the simulated data (in Figure 5.11). The intersection is now at approximately 65 km/h; the simulated data thus tells us that braking might be a more efficient countermeasure than our original guess (from the simple reasoning in Section 4.4). If it would be possible to start braking at the minimum avoidance distance displayed in Figure 5.11, the collision speed would be as plotted in Figure 5.12. However, it should be stated that the maneuver that has been simulated here is a simple one where the driver quickly turns the steering wheel either to the left or to the right. It has not been studied if this actually is the most efficient avoidance maneuver (by steering); possibly it could be more effective to first turn left and then right to

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Figure 5.9 Measuring the radar response from the back of a Volvo V70 and from the inflatable car it was found that the radar echo was as strong from the inflatable car as from the Volvo in this particular set up

Feature/property Maximum number of active tracking filters Number of future predictions in the tracking system Temporal spacing between predictions Brake system rise time Delay from decision making to brake actuation FOV of the mm-radar FOV of the lidar Tracking and decision making system update rate

Value 4 20 100 [ms] > 300 [ms] ? 13.6 [degrees] 14 [degrees] 10 [Hz]

Table 5.2 Summary of important characteristics of the prototype vehicle avoid the car hitting the obstacle with its side. Also no studies have been made to investigate if it is possible to achieve a shorter avoidance distance by a combined steering and braking maneuver.

5.4

Test Scenarios

In this section we will look at the performance of the CMbB system (described above) in different traffic scenarios. The tests have been performed using the simulation environment, and for those scenarios where it has been possible also by physical testing (with the prototype vehicle and inflatable car). The test scenarios can be divided into two groups. • The first group consists of scenarios where there is a collision. For these scenarios we are interested in finding the mitigation performance of the system,

5.4 Test Scenarios

81

Velocity [km/h]

Velocity and acceleration under a CMBB system induced brake manouver 60 40 20 0 13

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Figure 5.10 The speed and acceleration of the CMbB vehicle when the system intervenes (initial speed 50 km/h). The brakes are applied by opening a solenoid valve in the brake booster, maximum deceleration achieved is 6.3m/s2

i.e., how much the speed of the host vehicle was reduced at collision, distance between colliding objects when the system activates, etc. • The second group consists of scenarios where there is no collision. These scenarios are used for design and to check if it is possible to provoke a faulty intervention. The system should only react when a collision is unavoidable, so any intervention occurring without being followed by a collision will by definition be a faulty intervention. Totally, 20 collision scenarios and 10 near-miss scenarios have been studied. For space reasons we only present a selection here.

5.4.1

Collision Scenarios

In all the simulated scenarios, we use the same settings for the sensors. It should be noted however that the FOV of the sensors in the simulated scenarios are larger than the FOV of the sensors in the prototype vehicle. The measurement noises in the simulation environment are assumed to be Gaussian. In the simulation environment, the standard deviation of the range measurement is 0.5 m, the standard deviation of range rate is 0.5 m/s2 and the standard deviation of azimuth angle is 1 degree. These settings are used both for the mm-radar and the lidar. The

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Distance needed to avoid collision by braking and steering 100 Brakedist Steerdist

90 80

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70 60 50 40 30 20 10 0 0

50

100

150

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Figure 5.11 Distance required to avoid a stationary object collision by braking and by steering. This plot shows the result from simulation with a 15 dof handling model. Both the object and the host vehicle have a width of 2 meters, in Figure 4.5 the obstacle width was zero. Comparing the result from 4.5 and the results displayed here, it seems that braking might be a more efficient countermeasure than the initial guess.

scenarios that are studied in this section are mainly those where a CMbB has a large potential of significantly reducing the collision speed. Examples of scenarios where CMbB has low potential for reducing the collision speed are angle accidents (where the angle between colliding vehicles is large e.g. intersection collisions), rear end collisions with a large lateral offset between the colliding vehicles, and frontal collisions where the relative speed between the colliding vehicles is large.

Head-on to stationary Obstacle The first scenario that we will look at is the head-on against a stationary object described by Figure 4.3. This scenario has already been discussed in Sections 4.4 and 5.3. This type of scenario corresponds well to many real life accidents where the driver of the striking vehicle is inattentive, or even falls asleep, and hits a stationary object. One will also observe this performance for accidents where the host vehicle follows another vehicle that suddenly stops (rear end collisions). This holds when the leading vehicle comes to a stop at a distance greater than the intervention distance. This is of course not true for all rear end accidents. Another reason for

5.4 Test Scenarios

83

Collision Speed 120

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100 80 60 40 20 0 −20 0

50

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Figure 5.12 Speed at which the CMbB equipped vehicle would hit the stationary obstacle for different initial speeds. The distance at which braking starts is given by the minimum distance for avoidance in Figure 5.11. The width of both the obstacle and the vehicle is assumed to be 2 meters

studying this scenario is its simplicity, meaning that it is easy to perform both simulations and physical testing. The intervention distance will of course depend on the lateral offset between the host vehicle and the obstacle. Figure 5.13 shows the range between the vehicles versus the host vehicle longitudinal speed from simulation results of the head-on scenario with zero lateral offset. Figure 5.14 shows the same results from testing with the prototype vehicle. In Figure 5.15 the speed reduction is shown for simulation results for the head-on scenario when there is an 0.5 m offset between the host vehicle and the stationary obstacle. As we mentioned previously, the performance of the braking system is crucial to a CMbB system. To evaluate the effect of a more efficient braking system, the headon scenario with zero lateral offset was simulated again and the braking system performance was changed to mirror the specified performance of some recent EHB braking systems. These systems claim a pressure rise time of 100 milli-seconds and they also reached a higher maximum pressure, thus providing a higher maximum deceleration (here we assume 1 g (= 9.8 m/s2 )). Simulated performance of the CMbB system when the EHB system is used is shown in Figure 5.16.

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Range versus Rangerate − No Lateral Offset 40 35 30

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Figure 5.13 Head-on to stationary object scenario, average results from 20 Monte Carlo simulations. The width of the host vehicle is set to 1.8 meters and the width of the obstacle is 1.5 m

Rear End Collision, Lead Vehicle Brakes Hard

Rear end collision is one of the most common types of accident. Approximately 30 % of all accidents are of this type. A rear end collision is defined as a collision between two vehicles traveling in the same direction, where the trailing vehicle hits the leading vehicles’ rear end with its front end (Figure 5.4.1). Even though the injuries from rear end collisions are not life-threatening most of the time, this type of accident is one of the most costly to society. This is partly because the accident type is so common and partly because the whiplash injuries that are often caused by rear end collision are hard to treat and cause victims pain over long periods of time. The performance of the CMbB system for this type of accidents will vary with many factors such as relative speed of the vehicles, head distance, braking force applied by the lead vehicle, lateral offset, etc. If the head distance is long enough, performance will be the same as in the previous scenario (head-on against a stationary obstacle). In Figure 5.4.1 simulation results are displayed for a scenario where the lead vehicle and the following vehicle initially travel at the same speed with a head distance of 1 second. Suddenly the lead vehicle brakes hard (8 m/s2 ). There is no lateral offset between the vehicles.

5.4 Test Scenarios

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Head on scenario no lateral offset − Test result with protype vehicle 60

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Figure 5.14 Head-on to stationary obstacle. Results from testing with the prototype vehicle against an inflatable car

Cut-in Behind a Stationary Object In this scenario the CMbB vehicle travels straight ahead, and then makes a sudden lane change. In the lane that is entered there is a stationary obstacle. The lane change maneuver is executed as a sinusoid input to the steering wheel. The duration of the maneuver is 3.14 seconds for speeds below 40 km/h and 1.57 seconds for speeds above 40km/h. The amplitude of the input maneuver is tuned to give a 2 m lateral displacement. The scenario is displayed in Figure 5.4.1. In the simulated scenario, an average speed reduction of approximately 5 km/h for most speeds is attained. For low speeds the reduction is greater and as the speed becomes greater than 100 km/h there is no speed reduction. This type of scenario was also tested with the prototype vehicle. However the result was poor. For low speeds (below 50 km/h) the obstacle will move out of the sensors’ FOV before turning in towards the obstacle. In such cases the tracking system often fails to re-acquire the target and react in time before the collision. The sensors also have problems detecting the stationary target under hard maneuvers. This causes problems even for speeds where the obstacle does not move out of the FOV.

Cut-in, in Front of the Host Vehicle This scenario is the opposite of the previous example. Here the host vehicle drives straight ahead and another vehicle traveling at a lower speed enters the host vehicles

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Range versus Rangerate − Head on, 0.5 m Lateral Offset 25

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Figure 5.15 Head-on to stationary object scenario, average results from 20 Monte Carlo simulations. In these simulations there was a 0.5 m lateral offset between the two vehicles.

lane. Figure 5.4.1 displays an overview of the scenario. This scenario tests the ability of the tracking system to track a sudden maneuver of a tracked object. The efficiency of the CMbB system will of course depend on many factors such as relative speed between the two vehicles, how close the lead vehicle cuts in in front of the host vehicle, etc. This scenario has only been evaluated through simulations. We will look at two scenarios. The first scenario is displayed in Figure 5.4.1. Here the relative speed is low. The POV is traveling 20 km/h slower than the CMbB vehicle, the cut-in occurs late when the time to collision is one second. As Figure 5.4.1 shows for initial host speeds up to 60 km/h, the collision speed is reduced almost 10 km/h at an average. For higher speed the tracking system loses track of the lead vehicle as the sudden lane change is performed. In these cases there is no intervention. In the second scenario displayed in Figure 5.4.1 the relative speed is much greater, 50 km/h, and when the cut-in occurs, the TTC is 3 seconds.

5.4.2

Scenarios to Provoke Faulty Interventions

The scenarios to provoke faulty interventions are those where the host vehicle is close to a collision. Since no collision occurs in these scenarios, any CMbB system intervention is considered a faulty intervention. These scenarios are used for design, i.e., for choosing the intervention threshold. The threshold for CMbB intervention is set as low as possible without giving faulty interventions in any of these near-

5.4 Test Scenarios

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Range versus Rangerate − No Lateral Offset 30

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Figure 5.16 Head-on stationary object scenario, both vehicles have a width of 2 m. Here an EHB braking system is used. The thick line shows the average speed from 20 Monte Carlo simulations, and the thinner lines show the performance in single simulations.

Figure 5.17 Rear end collision scenario. Initially both vehicles travel with the same velocity. Suddenly the leading vehicles brakes hard, achieving a deceleration of 8 m/s2 .

miss scenarios. Testing with the prototype vehicle is also performed to verify that the thresholds are correct. During this work, it has not been possible to make test runs with the prototype vehicle against moving obstacles. So here we will look at some scenarios where the obstacle is stationary.

Drive-By Scenario The first scenario to be studied is a drive-by scenario. This can be viewed as a special case of the head-on collision scenario that was presented in section 5.4.1.

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Range versus Hostvehicle speed − No Lateral Offset 25

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Figure 5.18 Rear end collision scenario described in Figure 5.4.1 The plot shows the average speed from 20 Monte Carlo simulations.

Figure 5.19 Cut-in scenario - the host vehicle makes a sudden lane change, in the lane that it enters there is a stationary obstacle.

Here the offset between the host vehicle and the obstacle is just large enough for the host vehicle to pass the stationary object without colliding (see Figure 5.4.2). From the simulation results in Figure 5.4.2, we see that this particular scenario does not generate high collision probabilities. The threshold is 0.7 for all the plotted speeds. However, when this test was performed with the prototype vehicle and the inflatable car much larger probabilities were observed. Figure 5.4.2 shows the probabilities for four drive-by tests at 50 km/h with the prototype vehicle and the inflatable car. The reason for the high probabilities in this scenario was found to be deterioration of the sensor measurements for short ranges. This problem was already displayed in Figure 5.8. When examining the sensor input from these tests one find that in many cases the measurements (from the mm-radar) appear to be

5.4 Test Scenarios

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Range versus Hostvehicle speed 30

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Figure 5.20 The driver makes a lane change maneuver (a sinusoid input that cause a 2 m lateral offset of the CMbB vehicle). The stationary obstacle is situated exactly at the point where the maneuver ends in the middle of the lane. The plot shows the average performance from 20 Monte Carlo simulations.

coming from an obstacle that is moving into the path of the host vehicle. Even though this causes much higher probabilities than from the simulations none of the drive-by tests caused a faulty intervention.

Head-on to Stationary Object Late Avoidance The late avoidance maneuver examined in this section is a maneuver where the host vehicle travels towards a stationary obstacle and avoids the obstacle by steering away as late as possible. Pictures from such a maneuver were displayed in Figure 4.8. In Figure 5.4.2 simulation results from this maneuver are displayed. In this Figure the estimated probability of collision during the maneuver is plotted (for speeds 30, 40 and 50 km/h). The first peak corresponds to simulations at 50 km/h, and the second peak corresponds to speeds of 40 km/h. The peak for simulations at 30 km/h lies exactly between the 40 and 50 km/h peaks, reaching a maximum value of approximately 0.2. The intervention threshold was 0.7 for all these speeds. There is no intervention for the simulated late avoidance scenarios. This should, of course, also be the case since there is no collision. The test results displayed in Figure 5.4.2 show probabilities below 0.5 for the late avoidance scenario. However during trials performing this scenario it has been possible to get faulty interventions.

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Figure 5.21 Cut-in scenario, the POV, that is traveling at a lower speed, enters the lane of the CMbB vehicle.

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Figure 5.22 The TTC when the lead vehicle cuts in when the head distance is 1 second. The relative speed is 20 km/h , i.e., the lead vehicle travels at 20 km/h slower than the CMbB vehicle.

Unfortunately these tests have not yet been logged and examined thoroughly. A possible reason for the faulty intervention is the deteriorated performance of the sensors at short range. It is however worth noting that there were little complaint about these faulty intervention from different test drivers. One possible explanation for this is that the steering avoidance maneuver is so violent that the hard braking is not felt or possibly considered to be appropriate because of the extreme maneuver.

5.4 Test Scenarios

91

Range versus Hostvehicle speed 30

25

Range [m]

20

15

10

5

0 50

60

70 80 Hostvehicle speed [km/h]

90

100

Figure 5.23 The TTC when the lead vehicle cuts in when the head distance is 3 seconds. The relative speed is 50 km/h , i.e., the lead vehicle travels at 50 km/h slower than the CMbB vehicle.

Figure 5.24 Drive-by scenario, the offset between the host vehicle is just large enough for the two vehicles not to collide

Driving on Public Roads Apart from testing the system in specific scenarios on a test track, the prototype vehicle has also been driven on public roads in normal traffic situations. In these tests the braking actuation of the CMbB system is shut off. Any intervention (indicated by a LED head up display) is considered a faulty intervention as long as an accident does not actually occur. During driving in normal traffic it was found that some faulty interventions do occur. Analyzing these interventions, none has been found to depend primarily on the decision making, but rather they are

92

System design and Testing

Probability of Collision − Drive by scenario 60 Km/h, Threshold at 0.7 1 0.9

Probability of Collisioon

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.5

1

1.5

2 Time [s]

2.5

3

3.5

4

Figure 5.25 Probability of collision in a drive-by scenario; the plotted probabilities are from 20 Monte Carlo simulations at 30, 40, 50 and 60 km/h.

caused by sensors deficiencies, the sensor fusion and the tracking system. Below, we will discuss some typical situations that have been identified to cause faulty intervention. We will also discuss causes and possible solutions to avoid these faulty interventions. • Low speed driving: When driving at low speed (below 20) in target-rich environments faulty interventions sometimes occur for no apparent reason. Looking closer at the sensor performance and the tracking algorithm, this is not very strange. When traveling at low speeds there are often objects close to the vehicle. At short distances the sensor measurements are often deteriorated. There is also an increased risk for spurious reflections, i.e., false targets, with a lot of reflecting surfaces close to the sensors. In the current algorithm the gates for measurements association are large (several meters). New obstacles are also very “easily” initialized (it requires three consecutively associated samples). Due to this, the risk that the algorithm should detect faulty targets is large. The current system could be improved in several ways to attempt to correct this particular problem. By synchronizing the sensors, the gates for measurement association could be kept smaller. Initialization of new objects should possibly be made more “carefully”, i.e., require more than three consecutive measurements to initialize new obstacles. The bad performance at short range is specific to the sensors used here. Using other sensors might alleviate the problems with bad measurement at short range; again it is stressed that both sensors of the current system were designed

5.4 Test Scenarios

93

Probability of collision for close drive by manuvers at 50 km/h 0.7 0.6

Probability

0.5 0.4 0.3 0.2 0.1 0 0

2

4

6

8

10

Time [s]

Figure 5.26 Probability of collision from tests with the prototype vehicle and inflatable car at 50 km/h.

mainly for use in ACC systems. • Spatial sampling: Driving close to structures that have a spatially periodic appearance (for example fences and roadside reflector markers) sometimes cause faulty interventions. This happens due to the sensor sampling rate and the equidistant spacing of the reflecting objects. For example a fence might appear to be a target moving at the same speed as the host vehicle for certain speeds. Even worse, it might also look like an object moving slower and into the path of the host vehicle. Example 5.1 The sensor sampling frequency is 10 Hz. If the host vehicle is traveling at 30 m/s it will travel 3 m between two consecutive samples. If a structure on the side of the road has a spatial periodicity of 3 meters it will appear as a object moving along with the host vehicle at the same speed. The problem of spatial sampling might be tough to solve using radar sensors only. Of course, by the measured range rate (via Doppler shift) the targets can be determined to be stationary and thus be filtered out. This would remove all stationary targets, which is not desirable because it decreases the effectiveness of the system. Using another sensor, e.g. a vision sensor, could possibly be used to classify this type of target as invalid. Possibly this problem will also be diminished if the gates can be made smaller.

94

System design and Testing

Probability of Collision − Drive by scenario 60 Km/h, Threshold at 0.7 1 0.9

Probability of Collisioon

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

2

4

6

8

10

Time [s]

Figure 5.27 Calculated probability of collision for a late avoidance maneuver scenario. The plotted probabilities are from closing speeds of 30, 40 and 50 km/h, 20 Monte Carlo simulations for each speed is plotted. The peak lateral acceleration during the avoidance maneuver is 4 m/s2 . The intervention threshold is set to 0.7 for all speeds.

• Multiple Reflections on Large vehicles: The radar sensor’s image of an object is clearly not the same as our visual image. The strongest point of reflection from an object might vary quite a lot between two samples. For large vehicles the risk for receiving measurements from different points on the vehicle is particularly great. A typical scenario where this kind of phenomenon has caused faulty interventions is when meeting a large vehicle in a right hand curve. This problem might require sensors that have a better capability of classifying the object than the ones currently used. • Spurious reflections: There is always a chance that the sensor reports a ghost target due to spurious reflections. This has mainly been a problem with the mm-wavelength radar. An example of how spurious reflection might cause a faulty intervention is when driving behind a vehicle. A faulty measurement from the space between the host vehicle and the lead vehicle would look like a hard braking maneuver from the lead vehicle. From the driving on public roads so far no such faulty interventions have been observed. However, for an ACC system using the same radar sensor, speed control has been observed when there is clearly no obstacle ahead on which to perform control. Again by using smaller gates the probability of faulty associations decreases. By the use of two sensors (operating at different wavelengths) this problem is alleviated to a great extent.

5.5 Discussion of Test Results

95

Probability of collision for late avoidance manuvers 0.5 0.45 0.4

Probability

0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0

2

4

6 Time [s]

8

10

12

Figure 5.28 Calculated probability of collision for a late avoidance maneuver scenario. The plotted probabilities are from tests with the prototype vehicle and the inflatable car. The closing speeds range from 30 - 70 km/h.

5.5

Discussion of Test Results

In this chapter we have looked at a specific CM system that uses the probability of collision as a metric for determining when to perform braking actuation. The question is if this metric provides correct decisions for any type of traffic situation. This has been tested by simulation and testing with a prototype vehicle. In all the simulations and test drives, no faulty intervention was found to be caused by an erroneous decision. However some faulty interventions did occur during tests with the prototype vehicle. These interventions were found to be caused by sensor and tracking system inadequacies. It should be mentioned that the tracking system was not designed primarily to suppress spurious reflections and faulty measurements; rather it was designed for fast detection of suddenly appearing targets. The design strategy to ascertain that the CMbB system avoids making faulty decisions was to use a model of the vehicle that overestimates the handling capabilities of the vehicle. The probability threshold is then set high enough not to make faulty decisions. Using this design method it becomes interesting to study the effect of the system in collision scenarios, i.e., will there be any significant reduction of the collision speed. The simulation and testing in this chapter shows that significant speed reduction is possible for certain type of accident, e.g. rear-end collisions and head-on collisions with stationary obstacles. In many cases the speed is reduced by around 10 km/h. This reduction is achieved with a brake system that is far

96

System design and Testing

from optimal (both in the simulation environment and in the prototype vehicle). Also most of the prototype vehicle testing was performed in late December with temperatures between 0-5 degrees Celsius, and on wet asphalt. There are several obvious improvements that could be made to achieve better performance than the system that has been tested here. Some important ones are to use a state of the art braking system, incorporation of steering wheel and brake pedal sensors in the navigation system, synchronization of the tracking sensors and reducing the system delay from decision to brake actuation. In simulations with a high performance braking system (Figure 5.16) average speed reductions of almost 20 km/h were achieved in some scenarios. Reducing the collision speed is particularly effective for low relative speeds. For high relative speeds (above 100 km/h) the probability of serious injuries and death will still be very high even if the collision speed is reduced by 20 km/h. Looking at the distance at which interventions occur for relative speeds below 100 km/h one finds that the range is less than 20 m. For a CMbB system like the one studied in this chapter, a maximum sensor range of 50 m is therefore probably sufficient. The current sensors detect obstacle at ranges beyond 150 meters, which is much more than needed. The sensors’ narrow FOV, however, creates problems as measurements deteriorate at short ranges. This causes bad performance (especially at low relative speeds) and also possible faulty interventions. In some of the scenarios that try to provoke faulty interventions, much higher collision probabilities are calculated in tests with the prototype vehicle than from simulations. This phenomenon has been found mainly to be caused by inconsistent sensor performance at short ranges.

6 Conclusions

FCM systems have a large potential of positively affecting accident statistic by helping the driver to avoid collisions or decreasing accident severity. Even systems that only perform braking as a collision becomes unavoidable show potential of significantly reducing collision speed in some important scenarios. It is also important to remember that not all accidents can be avoided or mitigated. CM systems can greatly improve the car’s safety, but not replace passive safety systems.

6.1

Summary

In this thesis we have studied tracking and decision making for automotive collision avoidance systems. Several approaches to measurement association, as well as several different tracking filters have been reviewed. For decision making, the metric “probability of collision” was proposed to determine when a collision mitigation system should perform an intervention. The main advantages of using this metric are that it becomes easy to deal with time varying measurement uncertainties, missed detections and time varying process noise. It is also easy to incorporate vehicle dynamics limitations and driver models by choosing a more detailed tracking model. The drawback of using this metric is that it is not as intuitive to chose 97

98

Conclusions

intervention thresholds in terms of probability compared to accelerations for example. Calculating the probability of collision is also computationally demanding. This is a severe limitation when it comes to automotive applications. For CM systems, much effort is spent on avoiding faulty interventions. Looking at intervention strategies for CM systems, one can divide systems into two categories. • Systems that perform interventions when the collision is still avoidable – For these systems, there will always be a risk that the system makes a faulty intervention. • Systems that only intervene when the collision is unavoidable – These system can be quite effective in reducing the accident severity, but can never completely prevent an accident. Most examples and results in this thesis were from a CMbB system that performs braking only when a collision is unavoidable. Simulations and field tests show that for some scenarios it was possible to achieve a collision speed reduction of up to 15 km/h (compared to the driver taking no action at all) for some scenarios. There are still many obvious improvements that can be made on this prototype system. This means that there might be a possibility for even larger speed reductions. The conclusion from these results is that a notable reduction of accident severity can be achieved for real life accidents, with a system that only performs braking when a collision is unavoidable. Assumptions that must hold in order to avoid making faulty interventions are that detected obstacles must be correctly classified as valid and invalid objects, and the measurements have to be unbiased. This was not the case in the prototype system.

6.2

Future Work

The main cause for faulty interventions in the prototype system was sensor deficiencies and failure to reject false positives. One of the main focuses of future work will therefore be to study how to make the CMbB system more robust to these kind of faults. One of the main areas here is to examine how measurements should be fused in order to minimize the risk for faulty intervention. The sensor fusion is of course dependent on what types of sensors are used. Therefore different sensor set-ups will be also be studied. To improve target classification, it is also important to study the classification capabilities of each sensor more thoroughly. Another important issue is to decrease the computational complexity of the algorithm. This can be achieved by calculating the probability of collision in a more effective way, or by choosing another metric that is not as computationally de-

6.2 Future Work

99

manding. Also future work should include a more careful study of CMbB systems that perform braking before the collision unavoidable state is reached.

100

Conclusions

Bibliography

[1] A review of automotive radar systems - devices and regulatory framework. Technical Report SP 4/01, Australian Communication Authority, http://www.atnf.CSIRO.AU/SKA/intmit/, april 2001. [2] Dipl.-Ing.(FH) U. Adler. Automotive Handbook. Number ISBN: 0-7680-0669-4. Robert Bosch GmbH, 5 edition, 2000. [3] V. Aidala and S. Hammel. Utilization of modified polar coordinates for bearing-only tracking. IEEE Tran. on Automatic Control, 1983. [4] B. D. O. Anderson and J. B. Moore. Optimal Filtering. Prentice-Hall, 1979. [5] E. Bakker, L. Lidner, and H. B. Pacejka. A new tire model with an application in vehicle dynamics studies. In SAE paper no 890087, 1989. [6] Y. Bar-Shalom and T. Fortmann. Tracking and Data Association, volume 179 of Mathematics in Science and Engineering. Academic Press, 1988. [7] N. Bergman. Recursive Bayesian Estimation Navigation and Tracking Applications. PhD thesis, Link¨ oping University, 1999. [8] M. Bertozzi, A. Broggi, and A. Fascioli. A stereo vision system for real-time automotive obstacle detection. In Proceedings ICIP - Third IEEE International Conference on Image Processing. 101

102

Bibliography

[9] M. Betke, E. Haritaoglu, and L. S. Davis. Multiple vehicle detection and tracking in hard real time. Technical Report CS-TR-3667, 1996. [10] S. Blackman. Multiple-Target Tracking with Radar Applications. Number ISBN: 0-89006-179-3. Artech House, 1986. [11] J. Breen and R. Condon. Possibilities for future developments in primary safety requirements. In IMechE, volume 210, 1996. [12] A.L. Burgett, A. Carter, R.J. Miller, W.G. Najim, and D.L. Smith. A collision warning algorithm for rear-end collisions. In 16th International Techical Conference on Enhanced Safety of Vehicles Abstracts, 98-S2-P-3 1, 1998. [13] E. Dickmanns. Computer vision and highway automation. Vehicle System Dynamics, (31):325–343, 1999. [14] A. Doi, T. Butsuen, T. Niibe, T. Takagi, Y. Yamamoto, and H. Seni. Development of a rear-end collision avoidance system with automatic brake control. In JSAE Review, volume 15, pages 335–340. 1994. [15] C. Eberhard, D. Moffa, J. Philip, and W. R. Swihart. Collision warning. Automotive Engineering (Warrendale, Pennsylvania), 105(3):86–90, March 1997. [16] FARS. Fatality analysis reporting system, fars.nhtsa.dot.gov/.

2002.

http://www-

[17] Folksam. S¨ akerhetsrankning, 2002. http://www.folksam.se/forskning/index.htm. [18] Insurance Institute for Highway Safety, 2002. http://www.hwysafety.org/. [19] GES. General estimates system, 2002. nrd.nhtsa.dot.gov/departments/nrd-30/ncsa/GES.html.

http://www-

[20] T. D. Gillespie. Fundamentals of Vehicle Dynamics. SAE, 1992. [21] H. Glawing. Meassurement data selection and association in a collision mitigation system. Master Thesis LITH-ISY-EX-3213-2002, Dept of Elec. Eng. Link¨ oping University, S-581 83 Link¨ oping, Sweden, 2002. In English. [22] H.P. Groll and J. Detlefsen. History of automotive anticollision radars and final experimental results of a mm-wave car radar developed by the Technical University of Munich . IEEE Aerospace and Electronic Systems Magazine, 12 (8):15–19, 1997. [23] F. Gustafsson. Adaptive Filtering and Change Detection. Number ISBN: 0471-49287-6. Wiley, 2000. [24] F. Gustafsson, M. Drev¨ o, U. Forssell, M. L¨ ofgren, N. Persson, and H. Quicklund. Virtual sensors of tire pressure and road friction. In SAE paper no 2001-01-0796, 2001.

Bibliography

103

[25] D.L. Hall and J. Llinas, editors. Handbook of Multisensor data fusion. CRC Press, 2001. [26] U. Handmann, T. Kalinke, C. Tzomakas, M. Werner, and W. v. Seelen. Computer vision for driver assistance systems. In Proceedings of SPIE, volume 3364, 1998. [27] K. F. Honda, H. Higashida, R. Nakamura, M. Hitotsuya, and N. Sima. Fusion sensor for an assist system for low speed in traffic congestion by using millimeter-wave radar and image recognition sensor. In Inteligent Vehicle Initiative (IVI). Technology and Navigation Systems, 2001. [28] J. Jansson, J. Ekmark, and F. Gustafsson. Decision making for collison avoidance systems. In SAE paper no 2002-01-0403, 2002. [29] J. Jansson and F. Gustafsson. A probabilistic approach to collision risk estimation for passenger vehicles. In In procedings of the 15th IFAC World Congress, pages T–Th–M05:Model–based fault diagnosis of automotive systems/Area code 8b : Automotive Control, Barcelona, Spain, July 2002. [30] JNCAP. New car assessment program, 2002. http://www.osa.go.jp/. [31] H. C. Joksch. Velocity change and fatality risk in a crash – a rule of thumb 25/1. Accident Analysis and Prevention, 25, 1993. [32] T. Kailath, A. H. Sayed, and B. Hassibi. Linear Estimation. Prentice Hall, 2000. [33] H. Kawazoe, T. Murakami, O. Sadano, K. Suda, and H. Ono. Development of a lane-keeping assistance system. In Inteligent Vehicle Initiative (IVI). Technology and Navigation Systems, number SAE SP-1593, 2001. [34] R. Kiefer, D. LeBlanc, M. Palmer, J. Salinger, R. Deering, and M. Shulman. Development and validation of functional definitions and evaluation procedures for collision warning. Technical report, U.S. Department of Transportation, 1999. [35] L. K¨ upper and J. Schug. Active night vision systems. In SAE paper no 200201-0013, 2002. [36] D. J. LeBlanc, R. J. Kiefer, R. K. Deering, M. A. Schulman, M. D. Palmer, and J. Salinger. Forward collision warning: Preliminary requirements for crash alert timing. In Inteligent Vehicle Initiative (IVI). Technology and Navigation Systems, 2001. [37] R. W. Lorenz, J. Coleman, and S. Mehring. Lane Departure Warning for CVO in the USA. In International Truck and Bus Meeting and Exposition, number 982779. SAE, 1998.

104

Bibliography

[38] N. Martinelli and S. A. Boulanger. Cadillac deville thermal imaging night vision system. In SAE paper no 2002-01-0323, 2002. [39] P. Maybeck, W. Worsely, and P. Flynn. Investigation of constant turn-rate dynamics for airborn vehicle tracking. In NAECON, pages 896–903, 1982. [40] Australian NCAP. http://www.nrma.com.au/.

New

car

assessment

program,

2002.

[41] Euro NCAP. New car assesment program, 2002. http://www.euroncap.com/. [42] U.S. NCAP. New car assessment http://www.nhtsa.dot.gov/cars/testing/ncap/.

program,

2002.

[43] L. Nielsen and U. Kiencke. Automotive Control System. Number ISBN: 3-54066922-1. Springer, 2000. [44] J. O’Day and J. Flora. Alternative measures of restraint system effectiveness: interaction with crash severity factors. In SAE technical paper 820798. SAE, 1982. [45] N. Persson, M. Drev¨ o, and F. Gustafsson. Indirect tire pressure monitoring using sensor fusion. In SAE paper no 2002-01-1250, 2002. [46] N. Persson, F. Gustafsson, U. Forssell, and S. Ahlqvist. Low tire pressure warning using sensor fusion. In In procedings of ATTCE 2002, number 01 ATT-272, 2001. [47] B. Philip and C. Niegel. Advanced collision warning systems. Industrial Automation and Control: Applications in the Automotive Industry, (234), 1998. [48] A. Samman, L. Rimai, J.R. McBridge, R.O. Carter, and W.H. Weber. Potential use of near and far infrared laser diodes in automotive lidar applications. Technical report, 2000. [49] P. Seiler, B. Song, and J. K. Hedrick. Development of a collision avoidance system. In SAE Congress 1998. [50] E. D. R. Shearman, E. G. Hoare, and A. Hutton. Trials of automotive radar and lidar in road spray. Technical report, IEE, 1998. [51] M. Skolnik. Introduction To Radar Systems. Number 0-07-066572-9. McGrawHill, 1983. [52] A. Takahashi and N. Asanuma. Improvement of visibility for vulnerable parties in traffic accidents. In SAE paper no 2002-06-0142, 2001. [53] M. Tamura, H. Inoue, T. Wtanabe, and N. Maruko. Research on a brake assist system with a preview function. In SAE paper no 2001-01-0357, 2001.

Bibliography

105

[54] S. Tanaka, T. Nakagawa, M. Akasu, Y. Fukushima, and W. Bracken. Devleopment of a compact scan laser radar. In SAE paper no 1999-01-1044, 1999. [55] B. Ulmer. VITA II - Active Collision Avoidance in Real Traffic. In Proceedings of the Intelligent Vehicles ’94 Symposium, 1994. [56] G. R. Widmann, M. K. Daniels, L. Hamilton, L. Humm, B. Riley, J. K. Schiffmann, D. E. Schnelker, and W. H. Wishon. Comparison of lidar-based and radar-based adaptive cruise control systems. In SAE paper no 2000-010345, 2000. [57] J.Y. Wong. Theory of Ground Vehicles. John Wiley and Sons, 1993. [58] P.L. Zandor, S.A. Krawchuk, and R.B. Voas. Final Report - Automotive Collision Avoidance Systems (ACAS) Program. Technical Report DOT HS 809 080, U.S. Department of Transportation, 2000. [59] B. Zhu. Potential effects on accidents from forward collision warning/avoidance system. Master Thesis LITH-ITN-EX-150-SE, ITN, Link¨oping University, S581 83 Link¨ oping, Sweden, 2001. In English.

106

Bibliography