Cut Locus and Optimal Synthesis in Sub-Riemannian Problem on the Lie Group SH(2)

@article{Butt2015CutLA,
  title={Cut Locus and Optimal Synthesis in Sub-Riemannian Problem on the Lie Group SH(2)},
  author={Y. Butt and Y. Sachkov and A. I. Bhatti},
  journal={Journal of Dynamical and Control Systems},
  year={2015},
  volume={23},
  pages={155-195}
}
Global optimality analysis in sub-Riemannian problem on the Lie group SH(2) is considered. We cutout open dense domains in the preimage and in the image of the exponential mapping based on the description of Maxwell strata. We then prove that the exponential mapping restricted to these domains is a diffeomorphism. Based on the proof of diffeomorphism, the cut time, i.e., time of loss of global optimality, is computed on SH(2). We also consider the global structure of the exponential mapping and… Expand
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