Lazy Probabilistic Roadmaps Revisited

TL;DR

This paper revisits the Lazy PRM algorithm by integrating it with a Branch-and-Cut method to improve path quality and scalability in motion planning, validated on the BARN benchmark.

Contribution

It introduces a novel combination of Lazy PRM with a Branch-and-Cut algorithm for more efficient and feasible path planning.

Findings

Enhanced scalability demonstrated on BARN benchmark

Dynamic constraint cuts improve path feasibility

Spline-based plan validation avoids fixed discretization

Abstract

This paper describes a revision of the classic Lazy Probabilistic Roadmaps algorithm (Lazy PRM), that results from pairing PRM and a novel Branch-and-Cut (BC) algorithm. Cuts are dynamically generated constraints that are imposed on minimum cost paths over the geometric graphs selected by PRM. Cuts eliminate paths that cannot be mapped into smooth plans that satisfy suitably defined kinematic constraints. We generate candidate smooth plans by fitting splines to vertices in minimum-cost path. Plans are validated with a recently proposed algorithm that maps them into finite traces, without need to choose a fixed discretization step. Trace elements exactly describe when plans cross constraint boundaries modulo arithmetic precision. We evaluate several planners using our methods over the recently proposed BARN benchmark, and we report evidence of the scalability of our approach.