Time optimal paths for a mobile robot with one trailer

Optimal paths are in many ways interesting to motion planning. Not only they are obviously the most interesting ones with respect to the optimized criterion, but also they offer a way of studying the topological aspects associated to the controllability of the system. Many works have been carried out successfully on the optimal paths for unicyle and carlike system. This paper aims to extend those results when adding trailers. Characterizing the time optimal paths for a mobile robot with n-trailers is an ambitious task. As a first step, we give an explicit description of the abnormal and singular extremals for a mobile robot with one trailer. This is done with the help of the maximum principle.

[1]  Philippe Martin,et al.  Feedback linearization and driftless systems , 1994, Math. Control. Signals Syst..

[2]  Bernard Bonnard,et al.  On Singular Extremals in the Time Minimal Control Problem in $\mathbb{R}^3 $ , 1985 .

[3]  Jean-Paul Laumond,et al.  Controllability of a multibody mobile robot , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

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

[5]  Florent Lamiraux,et al.  Motion planning and control for Hilare pulling a trailer: experimental issues , 1997, Proceedings of International Conference on Robotics and Automation.

[6]  Jean-Paul Laumond,et al.  Topological property for collision-free nonholonomic motion planning: the case of sinusoidal inputs for chained form systems , 1998, IEEE Trans. Robotics Autom..

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

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

[9]  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 .

[10]  R. Murray,et al.  Trajectory generation for the N-trailer problem using Goursat normal form , 1995 .

[11]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[12]  Philippe Souères.  Commande optimale et robots mobiles non holonomes , 1993 .