Valerii Patsko, Georgii Trubnikov, Andrey Fedotov, Numerical study of a three-dimensional reachable set for a Dubins car under an integral control constraint, Vol. 2025 (2025), Article ID 24, pp. 1-33

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DOI: 10.23952/cot.2025.24

Received February 11, 2023; Accepted May 14, 2024; Published online February 25, 2025

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, which is subjected to an integral quadratic constraint. Based on the Pontryagin maximum principle, a description of the motions generating the boundary of the reachable set is given. If the angles are identified by modulo $2\pi$ , then the motions leading to the boundary of~the~corresponding reachable set represent globally optimal Euler elasticae. Simulation results are presented.

How to Cite this Article:
V. Patsko, G. Trubnikov, A. Fedotov, Numerical study of a three-dimensional reachable set for a Dubins car under an integral control constraint, Commun. Optim. Theory 2025 (2025) 24.