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

Author

Listed:
  • Efstathios Bakolas

    (Georgia Institute of Technology)

  • Panagiotis Tsiotras

    (Georgia Institute of Technology)

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.

Suggested Citation

  • Efstathios Bakolas & Panagiotis Tsiotras, 2011. "Optimal Synthesis of the Asymmetric Sinistral/Dextral Markov–Dubins Problem," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 233-250, August.
    • Handle: RePEc:spr:joptap:v:150:y:2011:i:2:d:10.1007_s10957-011-9841-3
    DOI: 10.1007/s10957-011-9841-3
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