Computational evaluation of Laplace artificial potential field methods for real-time obstacle avoidance in Gazebo

The goal of this article is to present evaluation results for a proposed modification of the Artificial Potential Field Method (APFM). The mathematical model employs Laplace functions to compute repulsive fields to simplify calculations. Additionally, the study introduces a comprehensive evaluation framework using Gazebo and ROS2, designed to test various obstacle avoidance algorithms in simulated environments. Experiments have been conducted in a virtual room containing static obstacles of diverse shapes. The results demonstrate that the Laplace APFM effectively computes safe directional angles, enabling the robot to navigate smoothly and efficiently toward its target. The algorithm's performance have been validated through detailed analyses of LiDAR data, force calculations, and trajectory visualizations.