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.
    Keywords: differential drive robot, Markov – Dubins problem, extremal trajectories, Pontryagin maximum principle
    Citation: Ardentov A. A., Extremals in the Markov – Dubins Problem with Control on a Triangle, Rus. J. Nonlin. Dyn., 2024, Vol. 20, no. 1, pp.  27-42

    Download File
    PDF, 1.4 Mb

    Creative Commons License
    This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License