Optimal synthesis in the Reeds and Shepp problem with a free final direction

Andrey Dmitruk (avdmicemi.rssi.ru)
Ivan Samylovskiy (barbudo.samcs.msu.su)

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

Keywords: Reeds and Shepp car, time-optimal problem, Pontryagin Maximum Principle, reachability sets, optimal synthesis.

Category 1: Applications -- Science and Engineering

Category 2: Applications -- Science and Engineering (Mechanical Engineering )

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Entry Submitted: 09/09/2011
Entry Accepted: 09/09/2011
Entry Last Modified: 05/23/2012

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