Title:
Optimal Synthesis of the Zermelo–Markov–Dubins Problem in a Constant Drift Field
Optimal Synthesis of the Zermelo–Markov–Dubins Problem in a Constant Drift Field
Author(s)
Bakolas, Efstathios
Tsiotras, Panagiotis
Tsiotras, Panagiotis
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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 semi-analytic scheme for the characterization of a (nearly) 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.
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Date Issued
2012-01-16
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Pre-print