ランダム幾何グラフによるサンプリングベース運動計画の新視点
New perspective on sampling-based motion planning via random geometric graphs
サンプリングベース計画器のロードマップが障害物なしでランダム幾何グラフと一致するというKaraman-Frazzoliの予想を証明し、障害物空間への解析を容易にする局所化-テッセレーション枠組みを提案した。
著者: Kiril Solovey, Oren Salzman, Dan Halperin
分類: cs.RO, cs.CG, math.PR
原文アブストラクト
Roadmaps constructed by many sampling-based motion planners coincide, in the absence of obstacles, with standard models of random geometric graphs (RGGs). Those models have been studied for several decades and by now a rich body of literature exists analyzing various properties and types of RGGs. In their seminal work on optimal motion planning Karaman and Frazzoli (2011) conjectured that a sampling-based planner has a certain property if the underlying RGG has this property as well. In this paper we settle this conjecture and leverage it for the development of a general framework for the analysis of sampling-based planners. Our framework, which we call localization-tessellation, allows for easy transfer of arguments on RGGs from the free unit-hypercube to spaces punctured by obstacles, which are geometrically and topologically much more complex. We demonstrate its power by providing alternative and (arguably) simple proofs for probabilistic completeness and asymptotic (near-)optimality of probabilistic roadmaps (PRMs). Furthermore, we introduce several variants of PRMs, analyze them using our framework, and discuss the implications of the analysis.
