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Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2023, Volume 15, Issue 2, Pages 89–104 (Mi mgta325)  
Reachable set of the Dubins car with an integral constraint on control

Valerii S. Patskoa, Georgii I. Trubnikovb, Andrey A. Fedotova

a N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of RAS
b Ural Federal University
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Abstract: A three-dimensional reachable set for a nonlinear controlled object “Dubins car” is investigated. The control is the angular velocity of rotation of the linear velocity vector. The control action is constrained by an integral quadratic constraint. Based on the Pontryagin maximum principle, a description of the motions generating the boundary of the reachable set is given. The motions leading to the boundary are globally optimal Euler elastics. Simulation results are presented.
Keywords: Dubins car, integral constraint on control, three-dimensional reachable set, Pontryagin maximum principle, Euler elastics, numerical constructions.
Received: 01.05.2023
Revised: 17.05.2023
Accepted: 05.06.2023
Document Type: Article
UDC: 517.977
BBC: 22.18
Language: Russian
Citation: Valerii S. Patsko, Georgii I. Trubnikov, Andrey A. Fedotov, “Reachable set of the Dubins car with an integral constraint on control”, Mat. Teor. Igr Pril., 15:2 (2023), 89–104
Citation in format AMSBIB
\Bibitem{PatTruFed23}
\by Valerii~S.~Patsko, Georgii~I.~Trubnikov, Andrey~A.~Fedotov
\paper Reachable set of the Dubins car with an integral constraint on control
\jour Mat. Teor. Igr Pril.
\yr 2023
\vol 15
\issue 2
\pages 89--104
\mathnet{http://mi.mathnet.ru/mgta325}
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