Feedback-Based Mobile Robot Navigation in 3-D Environments Using Artificial Potential Functions Technical Report

TL;DR

This paper develops polynomial navigation functions for 3-D robot motion planning in environments with spherical and cylindrical obstacles, ensuring safe navigation without local minima, validated through theoretical analysis and simulations.

Contribution

It introduces a novel class of polynomial navigation functions for 3-D environments that guarantee convergence to the target while avoiding local minima, even with intersecting obstacles.

Findings

Navigation functions have a unique minimum at the target

The functions avoid local minima in complex obstacle configurations

Numerical simulations confirm theoretical guarantees

Abstract

This technical report presents the construction and analysis of polynomial navigation functions for motion planning in 3-D workspaces populated by spherical and cylindrical obstacles. The workspace is modeled as a bounded spherical region, and obstacles are encoded using smooth polynomial implicit functions. We establish conditions under which the proposed navigation functions admit a unique non-degenerate minimum at the target while avoiding local minima, including in the presence of pairwise intersecting obstacles. Gradient and Hessian analyses are provided, and the theoretical results are validated through numerical simulations in obstacle rich 3-D environments.