Optimal Synthesis in the Reeds and Shepp Problem with Onesided Variation of Velocity (original) (raw)

Abstract

We consider a time-optimal problem for the Reeds and Shepp model describing a moving point on a plane, with a onesided variation of the speed and a free final direction of the velocity. Using the Pontryagin Maximum Principle, we obtain all possible types of extremal and, analyzing them and discarding nonoptimal ones, construct the optimal synthesis.

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Acknowledgements

The authors thank the anonymous referee for valuable remarks.

This research was supported by the Russian Foundation for Basic Research under grant No. 11-01-00795.

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Authors and Affiliations

1. Central Economics and Mathematics Institute of the Russian Academy of Sciences, Nakhimovskii prospekt, 47, 117418, Moscow, Russia
   A. V. Dmitruk
2. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskiye Gory, MSU, 119899, Moscow, Russia
   I. A. Samylovskiy

Authors

1. A. V. Dmitruk
2. I. A. Samylovskiy

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Correspondence toA. V. Dmitruk.

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Communicated by Felix L. Chernousko.

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Dmitruk, A.V., Samylovskiy, I.A. Optimal Synthesis in the Reeds and Shepp Problem with Onesided Variation of Velocity.J Optim Theory Appl 158, 874–887 (2013). https://doi.org/10.1007/s10957-013-0286-8

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• Received: 30 April 2012
• Accepted: 13 February 2013
• Published: 02 March 2013
• Issue date: September 2013
• DOI: https://doi.org/10.1007/s10957-013-0286-8

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