Topological Complexity of Motion Planning

@article{Farber2003TopologicalCO,
  title={Topological Complexity of Motion Planning},
  author={Michael Farber},
  journal={Discrete & Computational Geometry},
  year={2003},
  volume={29},
  pages={211-221}
}
In this paper we study a notion of topological complexity TC(X) for the motion planning problem. TC(X) is a number which measures discontinuity of the process of motion planning in the configuration space X. More precisely, TC(X) is the minimal number k such that there are k different “motion planning rules”, each defined on an open subset of X×X, so that each rule is continuous in the source and target configurations. We use methods of algebraic topology (the Lusternik Schnirelman theory) to… CONTINUE READING
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