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Motion feasibility of a wheeled vehicle with a steering angle limit

Published online by Cambridge University Press:  09 March 2009

Yongji Wang ,
J.A. Linnett  and
J.W. Roberts
Yongji Wang
Affiliation:
(Mechanical Engineering Department, Edinburgh University, Kings Buildings, Edinburgh EH93JL U.K.)
J.A. Linnett
Affiliation:
(Mechanical Engineering Department, Edinburgh University, Kings Buildings, Edinburgh EH93JL U.K.)
J.W. Roberts
Affiliation:
(Mechanical Engineering Department, Edinburgh University, Kings Buildings, Edinburgh EH93JL U.K.)
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Summary

In the problem of automatically controlling a wheeled vehicle so that a given reference point on the vehicle follows a prescribed path, several factors determine how the task can be accomplished; they are the shape of the path, the initial orientation angle, the steering angle limit and the position of the reference point on the vehicle. If the required steering angle exceeds the limit set by the steering mechanism or the required orientation angle is discontinuous at any point along the path, then the path cannot be followed. This paper investigates this motion feasibility problem, taking steering angle limit into consideration. First of all, we determine the dependence of the continuity of the orientation angle, steering angle and their derivatives on the continuity of the reference path and its derivatives, then discuss .the relationship between the steering angle limit and the feasible deviation angle intervals. Furthermore, we analyze in detail two typical motions, namely straight line motion and circular motion; some simulation results have been given based on a practical vehicle dimension.

Keywords

VehicleMotionSteering angleAutomatic control.
Type
Article
Information
Robotica , Volume 12 , Issue 3 , May 1994 , pp. 217 - 226
Copyright
Copyright © Cambridge University Press 1994

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References

1. Nelson, W.L., “Continuous steering-function control of robot carts” IEEE Trans. on Industrial Electronics 36, 330–337 (1989).CrossRefGoogle Scholar
2. Lozano-Perez, T., “Spatial Planning: A configuration space approach” IEEE Trans. on Computers, C-32(2), 108–120 (1983).CrossRefGoogle Scholar
3. Billing, J.R. and Mercer, W.R.J., “Swept paths of large trucks in right turns of small radius” Transportation Research Record 1052, Symposium on Geometric Design for Large Trucks (1986) pp. 116–119.Google Scholar
4. Kanayama, Y. and Yuta, S., “Vehicle path specification by a sequence of straight lines” IEEE J. Robotics and Automation 4, 560–570 (1988).Google Scholar
5. Lozano-Perez, T. and Wesley, M., “An algorithm for planning collision-free paths among polyhedral obstacles” Commun. Assoc. Comput. Math. 22, 560–570 (1979).Google Scholar
6. Brooks, R.A. and Lozano-Perez, T., “A subdivision algorithm in configuration space for findpath with rotation” IEEE Trans. on Systems, Man and Cybernetics, SMC15(2),224–233 (1985).CrossRefGoogle Scholar
7. Latombe, J.C., Robot Motion Planning (Kluwer Academic Publishers, Boston, Mass., 1990).Google Scholar
8. Laumond, J.P., “Obstacle growing in a non-polygonal world” Information Processing Letters 25, 41–50 (1987).CrossRefGoogle Scholar
9. Liu, Y.H. and Arimoto, S., “Path Planning Using a Tangent Graph for Mobile Robots Among Polygonal and Curved Obstacles” Int. J. Robotics Research 11, 376–382 (1992).CrossRefGoogle Scholar
10. Cox, I.J., “Blanche - An experiment in guidance and navigation of an autonomous robot vehicle” IEEE Trans. on Robotics and Automation 7, 193–204 (1991).CrossRefGoogle Scholar
11. Wang, Y. and Linnett, J.A., “On the maneuvering problems of wheeled vehicles” Proc. of the First Conference of the Chinese Society of Electrical and Electronic Engineering in the UK (1993) pp. 34–60.Google Scholar
12. Alexander, J.C., “On the motion of a trailer-truck” SIAM Rev. 27, 578–579 (1985).Google Scholar
13. Alexander, J.C. and Maddocks, J.H., “On the maneuvering of vehicles” SIAM J. Appl. Math. 48, 38–51 (1988).CrossRefGoogle Scholar
14. Alexander, J.C. and Maddocks, J.H., “On the kinematics of wheeled mobile robots” Int. J. Robotics Research 8, 15–27 (1989).CrossRefGoogle Scholar
15. Baylis, J., “The mathematics of a driving hazard” Math. Gaz. 57, 23–26 (1973).CrossRefGoogle Scholar
16. Bender, E.A., “A driving hazard revisited” SIAM Rev. 21, 136–138 (1979).CrossRefGoogle Scholar
17. Fossum, T.V. and Lewis, G.N., “A mathematical model for trailer-truck jackknifing” SIAM Rev. 23, 95–99 (1981).CrossRefGoogle Scholar
18. Freedman, H.I. and Riemenschneider, S.D., “Determining the path of the rear wheels of a bus” SIAM Rey. 25, 561–568 (1983).CrossRefGoogle Scholar
19. Heald, K.L., “Use of the HWI offtracking formula” Transportation Research Record 1052, Symposium on Geometric Design for Large Trucks (1986) pp. 45–53.Google Scholar
20. Hillier, V. and Pittuck, F.W., Fundamentals of Motor Vehicle Technology (Hutchinson Education, London, 1966).Google Scholar
21. Sayers, M.W., “Vehicle offtracking models” Transportation Research Record 1052, Symposium on Geometric Design for Large Trucks (1986) pp. 53–62.Google Scholar
22. Smith, B.L., “Existing design standards” Transportation Research Record 1052, Symposium on Geometric Design for Large Trucks (1986) pp. 23–29.Google Scholar
23. Wong, J.Y., Theory of Ground Vehicles (John Wiley & Sons, New York, 1978).Google Scholar
24. Badcock, J.M., Dun, J.A., Ajay, K., Kleeman, L. and Jarvis, R.A., “An autonomous robot navigation system - integrated environmental mapping, path planning, localization and motion” Robotica 11, 97–103 (1993).CrossRefGoogle Scholar
25. Banaquand, J. and Latombe, J.C., “Controllability of mobile robots with kinematic constraints” Technical Report No. STAN-CS-90–1317 (Department of Computer Science, Stanford University, USA, 1990).Google Scholar
26. Graettinger, T.J. and Krogh, B.H., “Evaluation and time-scaling of trajectories for wheeled mobile robots” Trans. of ASME J. Dynamics, Systems, Measurement and Control 111, 222–231 (1989).CrossRefGoogle Scholar
27. Hemami, A., Mehrabi, M.G. and R.Cheng, M.H., “Synthesis of an optimal control law for path tracking in mobile robots” Automatica 28, 383–387 (1992).CrossRefGoogle Scholar
28. Kanayama, Y. and Bruce, I.H., “Smooth local path planning for autonomous vehicles” Proc. of IEEEE Int. Conf. on Robotics and Automation (1989) pp. 1256–1270.Google Scholar
29. Kanayania, Y., Kimura, Y., Miyazaki, F. and Noguchi, T., “A stable tracking control method for an autonomous mobile robot” Proc. of IEEE Int. Conference on Robotics and Automation (1990) pp. 384–389.CrossRefGoogle Scholar
30. Kyriakopoulos, K.J. and Saridis, G.N., “An integrated collision prediction and avoidance scheme for mobile robots in non-stationary environments” Automatica 29, 309–322 (1993).CrossRefGoogle Scholar
31. Laumond, J.P., “Feasible trajectories for mobile robots with kinematic and environment constraints” Preprints of the International Conference on Intelligent Autonomous Systems (1986) pp. 346–354.Google Scholar
32. Muir, P.F. and Neuman, C.P., “Kinematic modelling of wheeled mobile robots” J. Robotic Systems 4, 281–340 (1987).CrossRefGoogle Scholar
33. Nelson, W.L., “Continuous-curvature paths for autonomous vehicles” Proc. of IEEE Int. Conf. on Robotics and Automation (1989) pp. 1260–1264.Google Scholar
34. Steer, B., “Trajectory planning for a mobile robot” Int. J. Robotics Research 8, 3–14 (1989).CrossRefGoogle Scholar
35. Yap, C.K., “How to move a chair through a door” IEEE J. Robotics and Automation RA-3(3), 172–181 (1987).Google Scholar
36. Brooks, R.A., “Solving the find-path problem by good representation of free space” IEEE Trans. on Systems, Man and Cybernetics, SMC-13(3), 190–197 (1983).CrossRefGoogle Scholar
37. Designing for Deliveries (Freight Transport Association, St. John's Road, Tunbridge Wells TN49U2, U.K., 1983).Google Scholar