Path Homotopy Invariants and their Application to Optimal Trajectory Planning

Understand

We consider the problem of optimal path planning in different homotopy classes in a given environment.

• Though important in robotics applications, path-planning with reasoning about homotopy classes of trajectories has typically focused on subsets of the Euclidean plane in the robotics literature.
• The problem of finding optimal trajectories in different homotopy classes in more general configuration spaces (or even characterizing the homotopy classes of such trajectories) can be difficult.
• In this paper we propose automated solutions to this problem in several general classes of configuration spaces by constructing presentations of fundamental groups and giving algorithms for solving the \emph{word problem} in such groups.