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Abstract

Recent theoretical results have completely solved the problem of determining the minimal length path for a vehicle moving from an initial configuration to a final configuration. Time- optimal paths for a constant-speed vehicle are a subset of the minimum length paths. The time-optimal paths consist of sequences of arcs of circles and straight lines. The Pontrya gin Maximum Principle introduces concepts (dual variables, bang-bang solutions, singular solutions, and transversality conditions) that provide important insight into the nature of the time-optimal paths. We have created a module that finds the time-optimal path from an initial canfrguration to a final configuration. We have demonstrated that the paths can be followed by a large (820-kg) mobile robot.

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References

Boissonnat, J.D. , Cerezo, A. , and Leblond, J. 1992. Shortest paths of bounded curvature in the plane. Proc. IEEE International Conference on Robotics and Automation , 2315-2320.

Cybermotion. 1991. Roanoke, VA.

Denning Mobile Robotics , Inc. 1991. Wilmington , MA.

Dubins, L.E. 1957. On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents . Am. J. Math. 79:497-516.

Jacobs. P. , and Canny, J. 1989. Planning smooth paths for mobile robots. Proc. IEEE International Conference on Robotics and Automation , pp. 2-7.

Nomadic Technologies, Inc. 1991. Palo Alto, CA.

Pin, F.G. , and Vasseur, H.A. 1990. Autonomous trajectory generation for mobile robots with non-holonomic and steering angle constraints. Proc. IEEE International Workshop on Intelligent Motion Control, pp. 295-299.

Pontryagin, L.S. , Boltyanskii, V.G. , Gamkrelidze, R.V. , and Mishchenko, E.F. 1962. The Mathematical Theory of Optimal Processes. New York: John Wiley.

Reeds, J.A. , and Shepp, L.A. 1990. Optimal paths for a car that goes both forwards and backwards . Pacific J. Math. 145:367-393.

10.

Reister, D.B. 1992. A new wheel control system for the omnidirectional HERMIES-III robot. Robotica 10:351-360.

11.

Soueres, P. , and Laumond, J.P. 1992. Synthese des plus courts chemins pour la voiture de Reeds et Shepp. LAAS/CNRS 92234, Laboratory d'Automatique et d'Analyse des Systems, Toulouse, France.

12.

Sussmann, H.J. , and Tang, G. 1991. Shortest paths for the Reeds-Shepp car: A worked out example of the use of geometric techniques in nonlinear optimal control . SYCON-91-10. Rutgers University, New Brunswick, NJ.

13.

Vasseur, H.A. , Pin, F.G. , and Taylor, J.R. 1991. Navigation of a car-like mobile robot using a decomposition of the environment in convex cells. Proc. IEEE International Conference on Robotics and Automation, 1496-1502.

14.

Weisbin, C.R. , Burks, B.L. , Einstein, J.R. , Feezell, R.R. , Manges, W.W. , and Thompson, D.H. 1990. HERMIES-III: A step toward autonomous mobility, manipulation, and perception. Robotica 8:7-12.

Time-Optimal Paths for High-Speed Maneuvering

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