Экстремальные управления для машины Дайтса

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.

Proceedings: https://link.springer.com/chapter/10.1007/978-3-030-80209-7_9

Автор: Alexey Mashtakov
Дата: 22 июля, 2021

5th conference on Geometric Science of Information
Paris, France


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