2015 15th International Conference on Control,Automation and Systems (ICCAS 2015) Oct. 13-16,2015 in BEXCO,Busan,Korea
Three-Dimensional Time-Space Grid Allocation Algorithm for Traffic Control of Autonomous Vehicles at an Intersection Jaeyong Kim!, Jin Gyu Lee!, Seungjoon Lee!, Hyuntae Kim!, Hyungbo Shim!, Yongsoon Eun2, and Kangwon Lee3* 1 ASRI,Department
of Electrical Engineering,Seoul National University,Seoul 151-741,Korea
(Tel : +82-2-880-1786; E-mail: {jykim,ljgman,seungjoon.lee,htkim}@cdsl.kr,
[email protected]) 2 Department of Information & Communication Engineering, Daegu Gyeongbuk Institute of Science & Technology,Dae'gu,Korea (
[email protected]) 3Department of Mechanical Engineering,Korea Polytechnic University, SiHeung City,KyungGi Do,15073,Korea (
[email protected])
*
Corresponding author
Abstract: Two-dimensional (2-D) time-space diagram have been widely used to analyze the flow of the traffic. However,
it has limitations to make a plan that guarantees the collision avoidance of vehicles at the intersections. In this paper, we introduce the three-dimensional (3-D) time-space diagram and demonstrate its effectiveness in describing the movements of vehicles at the intersections. We also propose an algorithm based on the grid allocation of 3-D time-space diagram to avoid collision between vehicles to achieve the autonomous intersection. Keywords:
three-dimensional time-space diagram,collision avoidance,allocation,intersection
1. INTRODUCTION
lated idea has been found in [5],where a time-space cube concept has been proposed to evaluate the effectiveness
A number of companies with advanced technolo
of an vehicle-pedestrian evacuation plan.
gies have already demonstrated autonomous vehicles of
The rest of the paper is organized as follows. First ve
NHTSA classification level 3 [1] or higher [2]. The 2007
hicle motions in the 3-D time-space would be described.
DARPA Urban Challenge [3] also required the participat
Second, an algorithm utilizing time space grid cell allo
ing autonomous vehicles to be able to safely pass through
cation would be proposed. Lastly a discussion would be
the intersections with ambient vehicles driven manually.
followed by a conclusion.
Then the autonomous vehicles stopped every time before entering the intersection and determine which one of the
2. VEHICLE MOTION IN 3-D TIME SPACE
vehicles waiting at the intersection had the highest prior ity. If the vehicles could drive autonomously and commu nicate with the infrastructure and other vehicles,it would be possible to coordinate the traffic such that vehicles may be able to drive without stopping before entering the intersections; hence possibly reducing power loss for stopping and re-accelerating, fossil fuel emissions, and travel time and improving intersection efficiency. Audi tried to achieve such functionality at the Ingolstadt [6]. Using V 2X communication, Audi car suggests to the driver an appropriate speed in order to reach the inter section without stopping by red light. To improve the efficiency of the traffic flow and solve
x
a number of transportation-related problems, 2-D time
(m)
Fig. 1 2-D time-space diagram example
space diagram is commonly used. However,it is not suit able to see the turning movements and flow directions of vehicles in the 2-D time-space diagram.
In the traffic engineering,a curve on a 2-D plot called
This paper aims to propose one algorithm expanding
time-space diagram such as Fig. 1 keeps track of one
a map on 2-D plane (representing the intersection) by
point fixed on the vehicle under test on whose axes are
adding the time axis; hence tracking locations of vehicles
time and travel distance, respectively. Here, slope repre
in three-dimensional time-space diagram. A somehow re-
sents speed of the vehicle; if slope is steeper,the vehicle is moving slower. If a part of the curve goes vertical, it
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science, leT
means that the vehicle is stopped for a period of time.
& Future Planning
Fig. 2 shows another example of simulated highway traf-
(MSIP) (No.2009-0083495).
978-89-93215-09-0/15/$31.00 @lCROS
505
fico It is notable that the steep slope propagates upstream
•
as time increases; this is called shockwave propagation.
tory tube represents speed of the vehicle. •
Density:48.7veh/lane/km, Lane:1
Similar to 2-D time-space diagram,slope of the trajec If a vehicle passes through an intersection,the vertical
length of the trajectory tube correlates with the passage of time. •
Traffic density, which is typically defined as the num
ber of vehicles per unit length of the roadway can be
0' Q) (/)
considered as the property of 3-D time-space occupancy
W E i=
within either a specific space area or time interval. •
In order to determine whether the collision will occur
or not,we can simply check if the trajectory tubes collide.
Fig. 2 2-D time-space diagram of a simulated highway traffic [4] Even though the 2-D time-space diagram is useful for 4
understanding the traffic flow, it is difficult to check the collision between vehicles and the turning movements in the intersection.
Therefore, this paper aims to expand
the discussions (collision avoidance, speed of the vehi cle, efficiency of an intersection, etc) to the 3-D time space. The traffic flow and movement derived from the
Fig.
3-D time-space diagram are more realistic and detailed
4 3-D time-space trajectories of vehicles at an in
tersection with collision
than the traditional approaches.
Time axis
r, Fig.
Fig.
3 3-D time-space trajectories of vehicles at an in
5 3-D time-space trajectories of vehicles at an in
tersection with collision avoidance maneuver
tersection 3-D time-space diagram can be described by adding
As mentioned above, the 3-D time-space diagram is
the time axis to the 2-D space. Fig. 3 describes one pos
very useful to interpret the collision between vehicles at
sible scenario at an intersection.
The traffic flow and
an intersection. In Fig. 4, let us assume that a vehicle A
the movements of vehicles in the intersection can be eas
is approaching to an intersection I on a straight path PA
ily described from the proposed 3-D time-space diagram.
at a constant speed. If another vehicles BO, B1, and B2
The 3-D trajectories help pinpoint the place on the in
are approaching to the same intersection on a path PBO,
tersection at a certain time. Moreover, it can visualize
PB1,and PB2,respectively,perpendicular to the path PA,
an intersection conflict and congestion locations, which
each vehicle's trajectory on the time-space would show
are not usually identified by the 2-D time-space diagram.
whether the vehicles may collide or not. In this case, ve
The traditional assessment indexes in the 3-D time-space
hicles BO and B2 could avoid collision with A but B1 is
diagram can be considered as follows.
expected to collide if it does not change its speed.
•
The trajectory of vehicle in the 3-D time-space diagram
Fig. 5 depicts how maneuvers to avoid collision would
can be seen as a trajectory tube. The tube size depends on
influence time-space plots.
the size of the vehicle or the safety margin such as a static
avoid collision with vehicle A and then accelerate. Ve
buffer and headway distance.
hicle B2 also decelerates to avoid collision with B1. As
506
Vehicle B1 decelerated to
a result,trajectories of Bland B2 vehicles show changes
±3m along respective desired paths. At this point, there
in slope.
are still plenty of time-space grid cells within the inter section available such that more vehicles could be accom
3. TIME·SPACE GRID CELL ALLOCATION
modated.
4. DISCUSSIONS
If a vehicle does not stay at a specific location per manently, the area of the road occupied by the vehicle
Regarding the presented concepts and proposed al
can be seen as a resource shared by the vehicles. In this
gorithm, the following discussions would be potentially
perspective, the intersection is also a resource shared by
beneficial.
vehicles from multiple arms. One of the ways to manage
•
the shared resource is to keep a log of the usage; hence
The presented ideas emphasized the planning part; for
example, a suitable control algorithm would have to be
this paper proposes an algorithm dividing the time-space
able to maintain vehicle time-space trajectory within the
into a set of grid cells and allocating to the vehicles that
allocated grid cells. However, if the vehicle moves too
desires to pass the road.
slow or too fast, it might be necessary to allocate addi tional grid cells adjacent to the already allocated ones. • 20
reduce probability of collision.
15 10
If uncertainty is larger for example in measurements,
communications and controls, allocating more cells may •
Efficiency of an intersection could be measured in the
number of cells allocated within a given period of time
::r
and cells associated with the intersection.
Number of
time-space cells allocated but posteriorly revealed not oc cupied may potentially indicate confidence in the system.
10 -10
-5 x(m)
10
-10
-s
o
•
y(m)
Stationary objects would appear on the time-space grid
as a group of cells allocated in prism along the time axis. •
The presented ideas need more tests including but not
limited to expanding to more complicated traffic situa
Fig. 6 Time-space of an intersection divided as grid cells
tion; network of multiple intersections, more number of
to be allocated
lanes; merging traffic; highways; pedestrian cases,etc. •
Fig. 6 shows one possible way to divide time-space of
The shape of the grid cell does not have to be rectan
an intersection. The algorithm works as follows.
gular. For example, depending on the situation, a wedge
•
A driver decides destination.
or parallelogram shaped grid cell could be considered.
•
A desired path and associate speed profile is planned
•
•
a collision in the intersection could be clearly visualized
The desired path is overlapped on the time-space grid
on a 3-D time-space. For a 3-D road network such as an
cells. • •
Adding time axis to the space could help considering
more general cases of collision avoidance. For example,
using current location as the starting point.
Grid cells on the desired time-space path is allocated.
overpass, time-space should be expanded to accommo
The vehicle drives through the allocated cells.
date additional dimensionality. •
If the driver/user changes the destination during the
drive, the proposed algorithm may need to be verified and/or improved.
20
•
15 10
More survey on existing work especially on traffic sig
nal optimization,railroad scheduling and mobile robotics is still necessary.
E
It would be interesting to see if the
idea of time-space could be applied even before the widespread penetration of autonomous vehicles. •
10 -10
-5 x(m)
Fig.
7
10
-10
-s
o
Requirements for the proposed allocation algorithm
needs to be assessed more thoroughly; including but not limited to measurements, communications,controls, and
y(m)
computational costs.
Intersection time-space allocation example for
5. CONCLUSION AND FUTURE WORK
two vehicles This paper presented tracking of multiple vehicles on Fig. 7 shows an example of such time-space grid cell
a 3-D time-space and proposed an algorithm dividing the
allocation. Both vehicles allocated a group of cells within
time space into grid cells and allocating such that multi-
507
pIe vehicles could share an intersection possibly without collisions yet without stopping. The presented concept of the time-space description would be able to clearly visualize whether two objects would collide at any moment. The proposed algorithm has potential to make multi vehicle navigation easier to implement and test. Regarding the possible future work, verification of the concept through simulations and further refinement would be desirable.
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National Highway Traffic Safety Administration, U.S. Department of Transportation Release Policy on Automated Vehicle Development,May 30,2013.
[2]
R. Rosen, "Googles Self-Driving Cars: Miles
Logged, Not
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M. Montemerlo et.al., "Junior: The Stanford Entry in the Urban Challenge," Journal of Field Robotics, vol. 25,no. 9,pp. 569-597,2008.
[4]
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[5]
Z. Fang et aI., "A space-time efficiency model
for optimizing intra-intersection vehiclepedestrian evacuation movements," Transportation Research Part C: Emerging Technologies, vol. 31, pp. 112130,2013. [6]
Audi, Travolution Project, http: //www.travolutioningolstadt.de.
See
also
the
article
http://nationalspeedinc.com/audi-travolution never-stop-for-red-lights-again.
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