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Optimal Synthesis of the Zermelo–Markov–Dubins Problem in a Constant Drift Field

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  • Efstathios Bakolas

    (Georgia Institute of Technology)

  • Panagiotis Tsiotras

    (Georgia Institute of Technology)

Abstract

We consider the optimal synthesis of the Zermelo–Markov–Dubins problem, that is, the problem of steering a vehicle with the kinematics of the Isaacs–Dubins car in minimum time in the presence of a drift field. By using standard optimal control tools, we characterize the family of control sequences that are sufficient for complete controllability and necessary for optimality for the special case of a constant field. Furthermore, we present a semianalytic scheme for the characterization of an optimal synthesis of the minimum-time problem. Finally, we establish a direct correspondence between the optimal syntheses of the Markov–Dubins and the Zermelo–Markov–Dubins problems by means of a discontinuous mapping.

Suggested Citation

  • Efstathios Bakolas & Panagiotis Tsiotras, 2013. "Optimal Synthesis of the Zermelo–Markov–Dubins Problem in a Constant Drift Field," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 469-492, February.
    • Handle: RePEc:spr:joptap:v:156:y:2013:i:2:d:10.1007_s10957-012-0128-0
    DOI: 10.1007/s10957-012-0128-0
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    References listed on IDEAS

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    1. V. Y. Glizer, 1997. "Optimal Planar Interception with Fixed End Conditions: Approximate Solutions," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 1-25, April.
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