Elliptical K-Nearest Neighbors -- Path Optimization via Coulomb's Law and Invalid Vertices in C-space Obstacles

TL;DR

This paper introduces FDIT*, a novel sampling-based path planning algorithm that leverages Coulomb's law and invalid vertices to improve efficiency and cost in high-dimensional robotic navigation tasks.

Contribution

FDIT* extends informed sampling methods by integrating physical force principles and elliptical nearest neighbor search to enhance pathfinding in complex environments.

Findings

FDIT* outperforms existing planners in high-dimensional spaces.

It achieves faster convergence and lower path costs.

Demonstrated effectiveness on real-world mobile manipulation tasks.

Abstract

Path planning has long been an important and active research area in robotics. To address challenges in high-dimensional motion planning, this study introduces the Force Direction Informed Trees (FDIT*), a sampling-based planner designed to enhance speed and cost-effectiveness in pathfinding. FDIT* builds upon the state-of-the-art informed sampling planner, the Effort Informed Trees (EIT*), by capitalizing on often-overlooked information in invalid vertices. It incorporates principles of physical force, particularly Coulomb's law. This approach proposes the elliptical $k$-nearest neighbors search method, enabling fast convergence navigation and avoiding high solution cost or infeasible paths by exploring more problem-specific search-worthy areas. It demonstrates benefits in search efficiency and cost reduction, particularly in confined, high-dimensional environments. It can be viewed as an extension of nearest neighbors search techniques. Fusing invalid vertex data with physical dynamics facilitates force-direction-based search regions, resulting in an improved convergence rate to the optimum. FDIT* outperforms existing single-query, sampling-based planners on the tested problems in R^4 to R^16 and has been demonstrated on a real-world mobile manipulation task.