APT*: Asymptotically Optimal Motion Planning via Adaptively Prolated Elliptical R-Nearest Neighbors

TL;DR

APT* is a new sampling-based motion planner that adaptively adjusts its sampling process using elliptical nearest neighbors and virtual forces, leading to faster convergence and lower-cost paths in high-dimensional spaces.

Contribution

It introduces APT*, a novel adaptive motion planning algorithm that dynamically modulates sampling and neighbor selection based on environmental feedback and virtual forces.

Findings

Outperforms existing planners in dimensions 4 to 16

Achieves faster convergence with lower solution costs

Validated on real-world robot manipulation tasks

Abstract

Optimal path planning aims to determine a sequence of states from a start to a goal while accounting for planning objectives. Popular methods often integrate fixed batch sizes and neglect information on obstacles, which is not problem-specific. This study introduces Adaptively Prolated Trees (APT*), a novel sampling-based motion planner that extends based on Force Direction Informed Trees (FDIT*), integrating adaptive batch-sizing and elliptical $r$-nearest neighbor modules to dynamically modulate the path searching process based on environmental feedback. APT* adjusts batch sizes based on the hypervolume of the informed sets and considers vertices as electric charges that obey Coulomb's law to define virtual forces via neighbor samples, thereby refining the prolate nearest neighbor selection. These modules employ non-linear prolate methods to adaptively adjust the electric charges of vertices for force definition, thereby improving the convergence rate with lower solution costs. Comparative analyses show that APT* outperforms existing single-query sampling-based planners in dimensions from $\mathbb{R}^4$ to $\mathbb{R}^{16}$, and it was further validated through a real-world robot manipulation task. A video showcasing our experimental results is available at: https://youtu.be/gCcUr8LiEw4