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Reachable Set of the Dubins Car with an Integral Constraint on Control

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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. An integral quadratic constraint is imposed on the control. 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 optimal Euler elasticae. Simulation results are presented.

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia

    V. S. Patsko & A. A. Fedotov

  2. Yeltsin Ural Federal University, Yekaterinburg, Russia

    G. I. Trubnikov

Authors
  1. V. S. Patsko
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  2. G. I. Trubnikov
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  3. A. A. Fedotov
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Correspondence to V. S. Patsko.

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Patsko, V.S., Trubnikov, G.I. & Fedotov, A.A. Reachable Set of the Dubins Car with an Integral Constraint on Control. Dokl. Math. 108 (Suppl 1), S34–S41 (2023). https://doi.org/10.1134/S106456242360080X

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  • DOI: https://doi.org/10.1134/S106456242360080X

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