Asymptotically Optimal Sampling-Based Motion Planning Methods

TL;DR

This paper surveys asymptotically optimal sampling-based motion planning methods, highlighting their assumptions, convergence guarantees, and recent research developments in optimizing paths in robotics.

Contribution

It provides a comprehensive overview of the assumptions and theoretical guarantees of asymptotically optimal motion planning algorithms, summarizing recent advances.

Findings

Sampling-based methods probabilistically converge to optimal solutions

Assumptions behind popular asymptotically optimal techniques are summarized

Ongoing research enhances understanding of path-quality guarantees

Abstract

Motion planning is a fundamental problem in autonomous robotics that requires finding a path to a specified goal that avoids obstacles and takes into account a robot's limitations and constraints. It is often desirable for this path to also optimize a cost function, such as path length. Formal path-quality guarantees for continuously valued search spaces are an active area of research interest. Recent results have proven that some sampling-based planning methods probabilistically converge toward the optimal solution as computational effort approaches infinity. This survey summarizes the assumptions behind these popular asymptotically optimal techniques and provides an introduction to the significant ongoing research on this topic.