Time-Optimal Paths for High-Speed Maneuvering

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.

[1]  David B. Reister.  A new wheel control system for the omnidirectional HERMIES-III robot , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[2]  L. Dubins.  On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents , 1957 .

[3]  J. Sussmann,et al.  SHORTEST PATHS FOR THE REEDS-SHEPP CAR: A WORKED OUT EXAMPLE OF THE USE OF GEOMETRIC TECHNIQUES IN NONLINEAR OPTIMAL CONTROL. 1 , 1991 .

[4]  M. L. Chambers.  The Mathematical Theory of Optimal Processes , 1965 .

[5]  D. B. Reister.  A new wheel control system for the omnidirectional HERMIES-III robot , 1992, Robotica.

[6]  Parag A. Pathak,et al.  Massachusetts Institute of Technology , 1964, Nature.

[7]  Jean-Daniel Boissonnat,et al.  Shortest paths of Bounded Curvature in the Plane , 1991, Geometric Reasoning for Perception and Action.

[8]  E. Blum,et al.  The Mathematical Theory of Optimal Processes. , 1963 .

[9]  John F. Canny,et al.  Planning smooth paths for mobile robots , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[10]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[11]  F. G. Pin,et al.  Autonomous Trajectory Generation for Mobile Robots with Non-Holonomic and Steering Angle Constraints , 1990, Proceedings of the IEEE International Workshop on Intelligent Motion Control.

[12]  L. Shepp,et al.  OPTIMAL PATHS FOR A CAR THAT GOES BOTH FORWARDS AND BACKWARDS , 1990 .

[13]  François G. Pin,et al.  Navigation of a car-like mobile robot using a decomposition of the environment in convex cells , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[14]  Barry L. Burks,et al.  Hermies-III: A step toward autonomous mobility, manipulation and perception , 1990, Robotica.