Design and implementation of a vehicle dynamics control system by means of torque vectoring for a scaled vehicle S. Reuter, H. Diab, S. Kowalewski, E. Hauck, S. Jeschke
Abstract— This paper describes to which extent the operational envelope of scaled vehicles can be extended by integrating a vehicle dynamics control system using torque vectoring. A detailed description for the construction of a mechatronic basis for an autonomous model car in a 1:10th scale is given. The design of the vehicle only uses standardized components and allows the most possible flexibility of controlling the vehicles dynamics behavior by applying individual driving moments to the wheels.
I. INTRODUCTION
T
he development of autonomous vehicles has become a field of interest of both, academia and industry [1,2]. To enable bachelor and master students to face the challenges of developing autonomous vehicles, the CaroloCup was initiated [3]. The Carolo-Cup can be considered the “little brother” of the DARPA Grand Challenge. In this competition, German student teams develop autonomous cars in a 1:10th scale and compete against each other in various disciplines [3]. In the discipline “Rundkurs” (engl.: “circuit”), the autonomous vehicles have to travel the greatest possible distance within three minutes on an unknown route. For developing the control logic for the discipline it is expected that the vehicles can precisely follow the desired trajectory. However, especially during operation in high-speed and severe maneuvers, the vehicles have problems to follow the generated trajectory. In these situations, the dynamics of the vehicles have to be considered explicitly so that the vehicles can be operated safely. In full-scale vehicles, vehicle dynamics control systems are utilized for stabilization purposes. Through these systems, it is possible to extend the operational envelope of vehicles at high speeds and cornering [4]. To utilize the full potential of vehicle dynamics control systems, instead of directly connecting the vehicle steering angle to the demanded trajectory, the vehicles yaw rate has to be actively controlled [5]. The separation of the trajectory
tracking and the steering angle allows the use of additional actuators for lateral stabilization instead of the restriction to one actuator [6,7] and gains its maximum potential by regulating the torque of the individual wheels of the vehicle [8]. The concept of regulating the individual torque of the wheels is also known as torque vectoring. To extend the operational envelope in the context of the Carolo-Cup discipline “Rundkurs”, the authors developed a mechatronic basis for the implementation of a torque vectoring system on a model car consisting of sensors, actuators and a computing unit (Figure 1). Furthermore, a vehicle dynamics control system was designed, implemented, and tested. The remainder of this paper is structured as follows: Section II describes the design and implementation of the system. Section III describes the dynamics and the control system. Section IV deals with the evaluation of the system dynamics in two test cases. Section V gives a summary of this paper and gives an outlook on further research in this field.
Figure 1 - Scaled vehicle
II. RELATED WORK S. Reuter is with the Department of Information Management in Mechanical Engineering, RWTH Aachen, 52064 Aachen, Germany (email:
[email protected]). E. Hauck is with the Department of Information Management in Mechanical Engineering, RWTH Aachen, 52064 Aachen, Germany (email:
[email protected]). S. Jeschke is with the Department of Information Management in Mechanical Engineering, RWTH Aachen, 52064 Aachen, Germany (email:
[email protected]). H. Diab is with the Chair of Computer Science 11 – Embedded Software Laboratory, RWTH Aachen, 52064 Aachen, Germany (email:
[email protected]). S. Kowalewski is with the Chair of Computer Science 11 – Embedded Software Laboratory, RWTH Aachen, 52064 Aachen, Germany (email:
[email protected]).
While yet not being used by the participating teams of the Carolo-Cup, the application of vehicle dynamics control systems on scaled vehicles is discussed in recent literature [9,10]. Though, the scaled vehicles serve as a testbed for the cost-effective development of vehicle dynamics control systems [11,12]. The tests are mostly based on specially developed vehicles, which are used on test equipment, such as treadmills or conveyors known as Roadway-Simulators [9-15]. Probably the most active research in this area is conducted by the University of Urbana-Champaign [15] and Penn State University [14]. In [13], Brennan et al. reported of vehicle dynamics control system tests on the Illinois
Roadway Simulator (IRS). On the IRS the authors use an elaborate inhouse produced vehicle in an 1:10th scale with an electric single-wheel-drive. A more economical solution is pursued by Diomidis et al. [16] who equipped a 1:5th scale RC car with an electronic brake system for the implementation of an electronic stability control system. An approach to utilize a modified 1:10th scale RC car for investigating the influence of rollover propensity was proposed by Travis et al [10]. However, to the authors' knowledge, a low-cost solution for the implementation of a vehicle dynamics control system on an 1:10th scale RC car does not exist yet. III. CONCEPT AND IMPLEMENTATION A. The mechatronic basis The basis of the system is the DF-01 chassis by Tamiya. The DF-01 chassis is a proven 1:10th scale chassis, with a fourwheel electric drive and a particularly wide track of 204mm. The individual wheels are equipped with spring and damper elements and double wishbones. With a length of 427mm between the axles, the chassis provides enough room for the remaining components. B. Mechanical design Concerning the design and integration of the drivetrain, it is appropriate to leave the chassis unmodified as the reason full designed suspension- and steering-system and the springdamper-elements of the chassis can be further used. The propulsion of the chassis is an electric four-wheel drive using a standard servo motor. For the individual wheel drive, small brushless outrunner-motors were selected, which generate a high torque at low speeds and have a very good ratio of size and weight to power. As the track width of the chassis is too small for housing motors and transmission stages in an axial mounted drive, the motors are moved along the x-and z-axis in the direction of the vehicle center point (Figure 2).
Figure 2 - Mechanical design of the front/rear drivetrain
The axle compensation which is necessary by moving the engine positions will be created by a belt-drive. The transmission is realized by a single gear with a spur gear meshing the drive pinion of the engine. Thus, a fixed transmission ratio of 1:5 can be achieved by standard model components within a small space. For the bearing of the driving shafts, the use of a shafts-pair consisting of a solid and a hollow shaft is especially suitable. Thereby, a co-axial bearing of the full shaft inside the hollow shaft is realized. Since only small relative velocities of the two shafts are expected, negative effects such as fretting or deformations due to high temperatures can be prevented. To enable a low backlash toothing and to avoid slippage of the belt-drive, suspension parts were designed for the drivetrain and made in a 3D printing process. The ABS-plastic which is used in this process showed to be appropriate for the application case according to a finite element analysis. The structure of the resulting drive-train can be seen in Figure 3.
Figure 3 - Design of the test vehicle
C. Electronic design and computing unit Important characteristics for the driving conditions are the individual wheel-speeds, the vehicle speed values in vehicle x- and y-direction and the yaw velocity around the vehicles vertical axis. To determine the individual speed of the wheels, the gyroscope sensors of the type AS5045 [17] were used. Small boards for the sensors were manufactured, which were fixed to the axis of each spur gear so that the corresponding wheel velocity can be measured. The sensors measure the orientation of an opposing axial mounted every 0.25ms with a resolution of 0.0879°. Thus, the individual wheel speeds are available every 0.5ms. To determine the vehicles acceleration and the yaw rate, an integrated sensor module SMI540 from Bosch is used [18]. The module is designed for use as an ESP-Sensor and offers several filters and a fine resolution of 0.024 °/s or 0.002g. The SMI540 as well as the AS5045 are addressed via the serial peripheral interface (SPI). Therefore, the sensors can be connected to a single SPI bus which reduces wiring effort. To generate the three-phase current for the brushless motors Roxxy Brushless Control 918 (BL-controllers) are used as
controllers. These controllers use a pulse width modulated signal (PWM) with a minimum period of 7ms. As computing unit an AVR-CAN module by Olimex is used [19]. The AVR-CAN module is equipped with an AT90CAN128 microcontroller from Atmel and has with SPI, I²C, UART, 8 PWM channels and a CAN controller interface. The AT90CANM128 microcontroller provides hard real-time capabilities and offers enough computing capacity for the application. For online logging of data on an external PC, a BTM222 Bluetooth module by Rayson is used [20]. The module is addressed via UART1 which is suitable for data transmission over short distances and can easily be integrated through a serial port on the PC side. The Bluetooth module BTM222 requires a power supply and a signal level of 3.3 volts. The UART of the microcontroller operates with a signal level of 5 volts. Thus, the signal level of the UARTs and the voltage level are regulated to 3.3 Volts by a transistor circuit. A CAN2 interface is intended as the connection to the higher control logic for the later development to an autonomous vehicle. For the test of the vehicle dynamics control of the mechatronic basis, the command values are determined using the standard model RC receiver. The RC receiver outputs PWM signals for steering and speed which are read via external interrupt pins (INT) of the microcontroller. The battery of the vehicle provides a voltage up to 12V. To reduce the weight, the computing unit and the motors are operated by this source. The AVR-CAN and the BL-controllers are directly connected to the battery. The AVR-CAN regulates the input voltage to a 5V-level and supplies the other components with power. The BL-controller and the steering servo are each controlled by a PWM channel of the microcontroller. To avoid a reverse-polarity connection between the AVRCAN board and the different components, two adapter boards were developed. IV. SOFTWARE DESIGN To ensure the interchangeability of modules and support the changeability of the software, the architectural pattern of the "Data Indirection ABAS" was used to design the software [21]. In the resulting software structure (Figure 4), the data is the center of the architecture. The various read and write processes communicate through data container and are thus decoupled. Individual processes read the raw sensor values, calculate auxiliary values and determine the driving condition. In autonomous mode, the microcontroller will receive the desired values through the CAN interface from the higher-level logic. This interface is in the test case replaced by the interface to the RC receiver. The controlprocess derives the necessary control-values for the actuators according to the difference between the actual and demanded values. The software has consistently been written in C without floating-point arithmetic and complex software libraries to achieve high-performance of the code. Thus, a constant cycle time of 6ms is ensured.
1 2
Universal Asynchronous Receiver Transmitter Controller Area Network
Figure 4 - Software design Fvls Fvrs
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Figure 5 - Composition of wheel forces
V. VEHICLE DYNAMICS CONTROL SYSTEM A. Background of Vehicle Dynamics During cornering, longitudinal as well as lateral forces act on the contact area between wheel and ground. If the resulting force exceeds the maximum transferable force from the wheel to the ground, the wheel loses its contact to the surface and thus its lane tracking ability. This effect has implications on the yaw moment of the vehicle , which results from the sum of the individual wheel torques (Figure 5). It leads to an over- or understeering behavior. An understeering vehicle drifts out of the curve with increasing velocity. An oversteering behavior is represented by a turning into the curve. In these cases, the vehicle deviates from its demanded path. The demanded path of an autonomous vehicle is determined by its trajectory. A trajectory is a path of consecutive location points, for which there is a temporal requirement - for example in terms of speed or acceleration values for each point [22]. By the trajectory, the desired yaw rate of the vehicle can be computed (1): ̇ ̇ (1) ( ) ̇ where the definitions of all parameters are listed in Table 1.
TABLE I PARAMETERS OF THE VEHICLE MODEL Symbol ̇ ̇ ̇ v EG ( )
Figure 6 - Torque Vectoring strategy
B. Vehicle Dynamics Control System The objective of the vehicle controller is to guide the vehicle along the desired path while ensuring stability. For this purpose, the vehicle can use the steering system as well as the individual wheel drive. To avoid a complex multivariable control, it is advisable to utilize the model of a human as a controller [23] and to feed forward the steering angle as an anticipating control. Thus the steering angle is responsible for guidance like an anticipatory open-loop control [23]. In this case, the dynamic relationship between the steering angle and the demanded yaw-velocity can be modeled by the single-track model [24] (2): ̇
s
Quantity
Unit
yaw velocity lateral Velocity longitudinal Velocity velocity of the vehicle understeer gradient Steering angle Yaw moment after control diff. between demanded and actual yaw velocity control-factors longitudinal forces on the tires lateral forces on the tires track of the vehicle moment of inertia around z-axis moment around z-axis demanded speed of the vehicle actual speed of the vehicle
°/s m/s m/s m/s
( )
∫ ( )
( )
N N m Nm Nm m/s m/s
Table 1
(5) Applying Newton’s law around the center of gravity of the vehicle with the forces of (4) and (5) results in: ( )
(2)
The compensation of the deviations from the demanded path and the stabilization of the vehicle are ensured by the closedloop torque-vectoring control system. By subtracting the actual from the desired yaw rate the deviation e(t) is formed. By using a simple PID controller, the required torque moment is determined, which is applied through the individual wheel drive:
rad Nm °/s
(6)
(
( ) According to the principle of angular momentum follows: ̈
(7)
Finally, by equating the torque on the vehicle's center of gravity ((6), (7)) leads to the following formulation: ̈
(3)
An efficient approach to distribute the required torque moment to the individual wheels was presented by Park and Ahn [25]. The mathematical model of this approach is based on the dynamics of a two-lane model [24] with neglecting rolling and pitching motions. At the different wheels, lateral and longitudinal (propulsion forces) occur. The forces act on their particular lever-arm around the center of gravity and form a resulting moment. Applying Newton’s law with respect to the longitudinal axis of the vehicle results in: (4) Applying Newton’s law with respect to the lateral axis of the vehicle results in:
( (
[ ( )]
[ (
)
(
)]
(
)
(
)
)
(8)
)
This illustrates the relationship between the yaw accelaration and the wheel-forces. According to (8), a yaw moment can be applied on the vehicle by adjusting a wheel-individual propulsion force. However, not all wheels are equally effective in influencing the yaw rate. The effectiveness of each wheel also varies with the individual driving condition. To reduce the impact on the vehicle's longitudinal dynamics,
Figure 7 – Test scenario and comparison of the test vehicle controlled with and without the torqe vectoring system (TV)
it is recommended to affect only the most effective wheel (interception wheel) to adjust the yaw rate [25]. (Figure 6) These are the front outside wheel and the rear inner wheel. In case of an understeering condition, the yaw rate is adapted by adjusting the propulsion force on the rear inner wheel. In the case of an oversteering driving condition, the yaw rate is adapted by adjusting the propulsion force on the front outside. In Figure 7, for all driving situations, the corresponding interception wheels can be seen. The force of the wheel which is applied on the ground is not directly measurable. According to Choi and Hong [26], a linear relationship between the wheel slip - the relative movement of the wheel to the ground - and the applied force for small sizes of the slip can be assumed. To simplify the conversion of the yaw rate error in a resulting torque, the determination of the corresponding force and the slip, a graphical solution can be used. Therefore, the delay of a wheel corresponds to a reduction of the velocity vector, which can be moved along its line of action on the level of the center of gravity in the longitudinal direction of the vehicle. Thus, the resulting angular velocity corresponds to a delta of the velocity according to the following equation: ̇
̇
For the individual interception wheel follows:
(9)
̇
(10)
VI. EVALUATION To test the performance of the vehicle, the vehicle behavior during a steady-state circular test and during a double lane change was examined. The steady-state circular test according to ISO 4138 [27] is the traditional method used to make statements about the vehicle stationary behavior and the understeering characteristics of the vehicle. The test procedure of the double lane change according to ISO 38881 is used to simulate a traffic-related situation [28]. At higher speeds, an avoidance maneuver is simulated by a fast change to the left lane with fast driving back to the right lane. (Figure 7) The quality of the vehicle is mainly assessed by the required steering movement and by the occurring lateral acceleration. During a quasi-steady-state circular test without the use of the vehicle dynamics control system an understeering gradient of 0.001 was determined. Thus, the vehicle has a slightly understeering behavior. The steady-state circular test was driven in a right curve with a maximum possible steering angle of 26 degrees and with 60% drive load. The experiment was conducted with and without the control system. Even without measuring the exact curvature one can visually determine that the use of the control system enables the vehicle to drive tighter turns with a constant steering angle. By using the control system, the yaw rate could be
increased by 60% from an initial 97°/s to 157°/s. The yaw rate error was reduced from 162°/s to 65°/s. In order to get reproducible results and to ensure an identical experiment conductance, the double lane-change maneuver was adapted to the vehicle. Instead of driving through pylons, the test vehicle was given a specified trajectory. The trajectory is defined by an array of command values for the steering servo and the driving motors. Figure 7 shows the resulting speed and steering angle during the test. The vehicle accelerates to about 3 m/s and steers right and left with a steering angle of 20°. The resulting yaw rate of the test with and without the use of the vehicle dynamics control system is shown in Figure 7. Comparing the actual yaw rates of the controlled and uncontrolled case, it becomes evident, that the controlled vehicle reaches higher yawing velocities at constant steering angle. Thus, the vehicle can follow the desired yaw rate in a better way. During straight driving, both yaw rates correspond to the desired yaw of zero. During cornering, the yaw rate of the controlled test vehicle increases faster and reaches a higher maximum yaw velocity. Both actual yaw rates respond quickly to a change in steering angle. However, the yaw acceleration of the controlled test vehicle is higher, so that both curves have nearly identical intersection points. The results show that the control system has a positive influence on the vehicle dynamics of the test vehicle. By the Torque Vectoring of the vehicle dynamics control system a supporting yaw moment is applied on the test vehicle. Thus, the test vehicle yaws faster with constant steering angle and velocity. Therefore, the controlled test vehicle requires a smaller steering angle for driving the same route. VII. CONCLUSION This work shows that the operational envelope of scaled vehicles can be extended by integrating a vehicle dynamics control system using torque vectoring. The implementation of a torque vectoring system by means of a single-wheel drive opens new degrees of freedom in controlling scaled vehicles throughout its area of application. Thus, this work contributes to increase the stability and enhances the safety of the test vehicle during high-speeds and severe maneuvers. By controlling the yaw rate as a basic principle of the vehicle dynamics control system, the steering angle is decoupled from the vehicle trajectory. Thus, the degrees of freedom in controlling scaled vehicles can be optimally utilized, as for any driving situation, the optimum combination of longitudinal and lateral forces on the wheel can be adjusted. The tests show that through the use of the control system higher yaw rates at constant steering angles are accessible. This stabilizes the dynamic behavior of the vehicle and extends its operational envelope. The developed test vehicle serves as a mechatronic basis for the development of an autonomous vehicle. Due to the vehicle dynamics control system, the vehicle is able to gain higher cornering-speeds and follow the demanded trajectories more accurate. In a next step, further sensors and a higher logic will be attached to test the vehicle dynamics in an autonomous state.
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