Alexey Mashtakov, Extremal Controls for the Duits Car

Authors: Alexey Mashtakov
Title: Extremal Controls for the Duits Car

We study a time minimization problem for a model of a car that can move forward on a plane and turn in place. Trajectories of this system are used in image processing for the detection of salient lines. The problem is a modification of a well-known sub-Riemannian problem in the roto-translation group, where one of the controls is restricted to be non-negative. The problem is of interest in geometric control theory as a model example in which the set of admissible controls contains zero on the boundary. We apply a necessary optimality condition—Pontryagin maximum principle to obtain a Hamiltonian system for normal extremals. By analyzing the Hamiltonian system we show a technique to obtain a single explicit formula for extremal controls. We derive the extremal controls and express the extremal trajectories in quadratures.

Citation: Mashtakov A. (2021) Extremal Controls for the Duits Car. In: Nielsen F., Barbaresco F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science, vol 12829. Springer, Cham.
Conference: International Conference on Geometric Science of Information

Paris, France

Year: 2021
Pages: 73-81
File: Download