Extremals in the Markov – Dubins Problem with Control on a Triangle
Received 20 September 2023; accepted 30 November 2023; published 25 December 2023
2024, Vol. 20, no. 1, pp. 27-42
Author(s): Ardentov A. A.
We formulate a time-optimal problem for a differential drive robot with bounded positive
velocities of the driving wheels. This problem is equivalent to a generalization of the classical
Markov – Dubins problem with an extended domain of control. We classify all extremal controls
via the Pontryagin maximum principle. Some optimality conditions are obtained; therefore, the
optimal synthesis is reduced to the enumeration of a finite number of possible solutions.
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