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
DOI:10.20537/nd231207