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

2025-08-27

AI Summary

To address the low efficiency of single-query optimal motion planning in high-dimensional spaces, this paper proposes an environment-feedback-driven adaptive sampling method. Our approach integrates three key innovations: (1) Coulomb’s-law-inspired virtual-force-guided sampling with nonlinear charge modulation for dynamic bias toward unexplored regions; (2) adaptive batch sampling coupled with elliptical *r*-nearest-neighbor search to enhance local connectivity quality; and (3) informed-set hypervolume control and elongated tree restructuring to strengthen convergence guidance. Embedded within the FDIT* framework, the method enables progressive path optimization. Experiments across 4–16D simulated environments demonstrate significant improvements over baselines—including RRT*-Connect and Informed RRT*—achieving 12%–37% lower path cost and 1.8×–3.5× faster convergence. Practical validity and robustness are further verified on a real-robot grasping task.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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

Problem

• Develops adaptive motion planning algorithm for high-dimensional spaces
• Integrates dynamic batch-sizing and obstacle-aware nearest neighbor selection
• Improves convergence rate and solution cost in path planning

Innovation

• Adaptive batch-sizing for dynamic path searching
• Elliptical nearest neighbors with Coulomb's law charges
• Non-linear prolate methods for force definition