経路ホモトピー不変量と最適軌道計画への応用
Path Homotopy Invariants and their Application to Optimal Trajectory Planning
一般の配置空間におけるホモトピー類ごとの最適経路計画を、基本群の表示と語問題の解法アルゴリズムで自動化する手法を提案した論文。
著者: Subhrajit Bhattacharya, Robert Ghrist
分類: cs.RO, math.GR
原文アブストラクト
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. We present explicit results that apply to knot and link complements in 3-space, discuss how to extend to cylindrically-deleted coordination spaces of arbitrary dimension, and also present results in the coordination space of robots navigating on an Euclidean plane.
