Journal of Optimization Theory and Applications

, Volume 156, Issue 2, pp 469–492 | Cite as

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

Article

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 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.School of Aerospace EngineeringGeorgia Institute of TechnologyAtlantaUSA

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