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

Efstathios Bakolas () and Panagiotis Tsiotras ()
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Efstathios Bakolas: Georgia Institute of Technology
Panagiotis Tsiotras: Georgia Institute of Technology

Journal of Optimization Theory and Applications, 2013, vol. 156, issue 2, No 15, 469-492

Abstract: 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.

Keywords: Markov–Dubins problem; Optimal synthesis; Zermelo’s navigation problem; Non-holonomic systems (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-012-0128-0

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