Vehicle Kinematics and Its Application to Highway Design
Publication: Journal of Transportation Engineering
Volume 121, Issue 1
Abstract
This paper presents a mathematical model for computing the path of any one point on a wheeled vehicle, which may be a bus, an articulated truck, or a wheeled robot, and the steering angle necessary for a reference point to travel a specified curve. This problem arises in applications that require determination of the swept space of a vehicle and in the automatic control of a mobile robot while the reference point on the vehicle moves along a specified path. The mathematical model is applicable to any dimension of a rigid vehicle or vehicle combination. It can be shown that the widely used Western Highway Institute (WHI) formula for highway design is a special case of the mathematical model presented in this paper. Based on this model, some inherent characteristics of wheeled vehicles, such as curvature, radius of instantaneous rotation of a point on the vehicle, and their relationship; and the independence of vehicle's orientation angle, steering angle, curvature, and radius of instantaneous rotation to its velocity, are also analyzed. The analytic solutions of two typical motions, circular and straight-line motions, have been developed, and the comparison of the simulation results with the existing standards has been conducted.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Alexander, J. C.(1985). “On the motion of a trailer-truck.”SIAM Rev., 27(4), 578–579.
2.
Alexander, J. C., and Maddocks, J. H.(1988). “On the maneuvering of vehicles.”SIAM J. Appl. Math., 48(1), 38–51.
3.
Alexander, J. C., and Maddocks, J. H.(1989). “On the kinematics of wheeled mobile robots.”Int. J. Robotics Res., 8(5), 15–27.
4.
Baylis, J.(1973). “The mathematics of a driving hazard.”Math. Gaz., 57(399), 23–26.
5.
Bender, E. A.(1979). “A driving hazard revisited.”SIAM Rev., 21(1), 136–138.
6.
Billing, J. R., and Mercer, W. R. J. (1986). “Swept paths of large trucks in right turns of small radius.”Transp. Res. Record 1052: Symp. on Geometric Des. for Large Trucks, Transportation Research Board, Washington, D.C., 116–119.
7.
Fossum, T. V., and Lewis, G. N.(1981). “A mathematical model for trailer-truck jackknifing.”SIAM Rev., 23(1), 95–99.
8.
Freedman, H. I., and Riemenschneider, S. D.(1983). “Determining the path of the rear wheels of a bus.”SIAM Rev., 25(4), 561–568.
9.
Graettinger, T. J., and Krogh, B. H.(1989). “Evaluation and time-scaling of trajectories for wheeled mobile robots.”J. Dynamic Systems, Measurement, and Control, 111(2), 222–231.
10.
Heald, K. L. (1986). “Use of the HWI offtracking formula.”Transp. Res. Rec. 1052: Symp. on Geometric Des. for Large Trucks, Transportation Research Board, Washington, D.C., 45–53.
11.
Hemami, A., Mehrabi, M. G., and Cheng, R. M. H.(1992). “Synthesis of an optimal control law for path tracking in mobile robots.”Automatica, 28(2), 383–387.
12.
Hillier, V., and Pittuck, F. W. (1966). Fundamentals of motor vehicle technology. Hutchinson Educational Ltd., London, England.
13.
Kanayama, Y., Kimura, Y., Miyazaki, F., and Noguchi, T. (1990). “A stable tracking control method for an autonomous mobile robot.”Proc., IEEE Conf. on Robotics and Automation, The Institute of Electrical and Electronics Engineers, Inc., New York, N.Y., 384–389.
14.
Lozano-perez, T., and Wesley, M.(1979). “An algorithm for planning collision-free paths among polyhedral obstacles.”Communications of the Assoc. for Computing Machinery, 22(10), 560–570.
15.
Muir, P. F., and Neuman, C. P. (1987). “Kinematic modelling of wheeled mobile robots.”J. Robotic Systems, 4(2), 281–340.
16.
A policy on design of urban highways and arterial streets. (1973). American Association of State Highway and Transportation Officials, Washington, D.C.
17.
Sayers, M. W. (1986). “Vehicle offtracking models.”Transp. Res. Record 1052: Symp. on Geometric Des. for Large Trucks, Transportation Research Board, Washington, D.C. 53–62.
18.
Smith, B. L. (1986). “Existing design standards.”Transportation Research Record 1052: Symp. on Geometric Des. for Large Trucks, Transportation Research Board, Washington, D.C., 23–29.
19.
Steer, B.(1989). “Trajectory planning for a mobile robot.”Int. J. Robotics Res., 8(5), 3–14.
20.
Synge, J. L.(1973). “A steering problem.”Quarterly of Appl. Math., 31(3), 295–302.
21.
Wong, J. Y. (1978). Theory of ground vehicles. John Wiley & Sons, Inc., New York, N.Y.
Information & Authors
Information
Published In
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Jan 1, 1995
Published in print: Jan 1995
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.