Safe Navigation in Cluttered Environments Via Spline-Based Harmonic Potential Fields

TL;DR

This paper introduces a spline-based harmonic potential field method for safe, obstacle-avoiding navigation in cluttered environments, ensuring target tracking through a sequence of controlled, safe regions.

Contribution

It presents a novel approach combining harmonic potential surfaces with spline-based boundary conditions for reliable motion planning.

Findings

Ensures safe navigation through cluttered spaces.

Explicitly computes harmonic potential surfaces for control.

Funnels agent safely from start to target.

Abstract

We provide a complete motion-planning mechanism that ensures target tracking and obstacle avoidance in a cluttered environment. For a given polyhedral decomposition of the feasible space, we adopt a novel procedure that constrains the agent to move only through a prescribed sequence of cells via a suitable control policy. For each cell, we construct a harmonic potential surface induced by a Dirichlet boundary condition given as a cardinal B-spline curve. A detailed analysis of the curve behavior (periodicity, support) and of the associated control point selection allows us to explicitly compute these harmonic potential surfaces, from which we subsequently derive the corresponding control policy. We illustrate that the resulting construction funnels the agent safely along the chain of cells from the starting point to the target.