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

2026-01-14

AI Summary

This work proposes a smooth polynomial implicit-function-based artificial potential field navigation function for mobile robot navigation in three-dimensional environments containing spherical and cylindrical obstacles. The method constructs a potential field within a bounded spherical workspace that possesses a unique, non-degenerate global minimum, thereby eliminating local minima even when obstacles intersect. Safe obstacle-avoidance motion is achieved through gradient-based feedback control, and the optimality and safety of the navigation function are rigorously established via Hessian analysis. Numerical simulations in complex 3D obstacle scenarios demonstrate the effectiveness and robustness of the proposed approach.

Technology Category

Intelligent Robots: Localization, Mapping, and NavigationNatural Language Processing: Safety and RobustnessHumans and AI: Human-Aware Planning and Behavior Prediction

Application Category

Responsible Web: Machine-in-the-loop, human agency and autonomySecurity and Privacy: Large-scale security measurementsSystems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• mobile robot navigation
• 3-D environments
• artificial potential functions
• local minima
• obstacle avoidance

Innovation

• polynomial navigation functions
• 3-D motion planning
• artificial potential fields
• obstacle avoidance
• implicit polynomial encoding