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Optimal Synthesis of the Asymmetric Sinistral/Dextral Markov–Dubins Problem

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Abstract

We consider a variation of the classical Markov–Dubins problem dealing with curvature-constrained, shortest paths in the plane with prescribed initial and terminal positions and tangents, when the lower and upper bounds of the curvature of the path are not necessarily equal. The motivation for this problem stems from vehicle navigation applications, when a vehicle may be biased in taking turns at a particular direction due to hardware failures or environmental conditions. After formulating the shortest path problem as a minimum-time problem, a family of extremals, which is sufficient for optimality, is characterized, and subsequently the complete analytic solution of the optimal synthesis problem is presented. In addition, the synthesis problem, when the terminal tangent is free, is also considered, leading to the characterization of the set of points that can be reached in the plane by curves satisfying asymmetric curvature constraints.

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Authors and Affiliations

  1. School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, USA

    Efstathios Bakolas & Panagiotis Tsiotras

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  1. Efstathios Bakolas
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  2. Panagiotis Tsiotras
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Correspondence to Panagiotis Tsiotras.

Additional information

Communicated by H.J. Pesch.

This work has been supported in part by NASA (award No. NNX08AB94A). The first author also acknowledges support from the A. Onassis Public Benefit Foundation.

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Bakolas, E., Tsiotras, P. Optimal Synthesis of the Asymmetric Sinistral/Dextral Markov–Dubins Problem. J Optim Theory Appl 150, 233–250 (2011). https://doi.org/10.1007/s10957-011-9841-3

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