Geodesic
Extremals in the Markov – Dubins Problem with Control on a Triangle
Russian journal of nonlinear dynamics, Tome 20 (2024) no. 1, pp. 27-42

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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 
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     author = {A. A. Ardentov},
     title = {Extremals in the {Markov} {\textendash} {Dubins} {Problem} with {Control} on a {Triangle}},
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     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2024_20_1_a2/}
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A. A. Ardentov. Extremals in the Markov – Dubins Problem with Control on a Triangle. Russian journal of nonlinear dynamics, Tome 20 (2024) no. 1, pp. 27-42. http://geodesic.mathdoc.fr/item/ND_2024_20_1_a2/