Motion planning for a rigid body using random networks on the medial axis of the free space

Abstract

Several motion planning methods using networks of randomly generated nodes in the free space have been shown to perform well in a number of cases, however their performance degrades when paths are required to pass through narrow passages in the,jree space. In [l S] we proposed MAPRM, a method of sampling the configumtion space in which randomly genemted configurations, free or not, are retracted onto the medial axis of the free space without having to first compute the medial axis; this was shown to increase sampling in narrow passages. In this paper we give details of the MAPRM algorithm for the case of a free-flying rigid body moving in three dimensions, and show that the retmction may be carried out without explicitly computing the Cobstacles or the medial axis. We give theoretical arguments to show that this improves sampling in narrow corridors, and present preliminary experimental results comparing the performance to uniform random sampling from the free space.

Retraction-based RRT planner for articulated models

“…The retraction-based approaches have been widely used to improve the performance of sample-based planners in narrow passages [1], [21], [23], [28], [31]. The main idea is to retract a randomly generated configuration that lies in CObstacle space towards a more desirable region, e.g.…”

“…For example, computing the closest boundary point for an incolliding configuration boils down to penetration depth computation, which has high complexity [30]. Other algorithms use heuristics to compute samples near the boundary of CObstacle space or near approximate medial axis [1], [23], [28]. These methods are mainly limited to closed models and are prone to robustness problems.…”

“…Most of the prior work on handling narrow passages has been mainly limited to rigid models, e.g. [1], [8], [28], [31]. In practice, articulated models result in some additional challenges with respect to sample-based motion planning.…”

Simultaneous shape decomposition and skeletonization

“…These methods approximate the free configuration space (C-space) of a movable object by sampling and connecting random configurations to form a graph (or a tree). However, they also have several technical issues limiting their success on some important types of problems, such as the difficulty of finding paths that are required to pass through narrow passages [46]. Using sampling biased toward the joints of the extracted skeleton, we can alleviate this so called "narrow passage" problem.…”

A general framework for sampling on the medial axis of the free space

“…However, the medial axis is difficult and expensive to compute explicitly, particularly in higher dimensions. The Medial Axis PRM (MAPRM) [16,17] combines these two approaches by generating random networks whose nodes lie on the medial axis of C f ree which yields improved performance on problems requiring traversal of narrow passages.…”