Simulation-Based Evaluation of Hyperbolic Secant Potential Field for Real-Time Obstacle Avoidance

Obstacle avoidance is a fundamental capability for autonomous mobile robots, ensuring safe navigation in dynamic and unstructured environments. This paper presents a novel approach to real-time obstacle avoidance based on an Artificial Potential Field Method (APFM) utilizing a hyperbolic secant function. A mathematical formulation of the proposed model is developed and analyzed. To validate the approach, a simulation framework was implemented using ROS 2, the Gazebo simulator, and the TurtleBot3 Burger platform. Extensive simulations were conducted, generating LiDAR sample plots alongside corresponding repulsive, attractive, and total potential field distributions, demonstrating the correctness and effectiveness of the proposed method. Additionally, RViz visualization confirmed the smoothness of the robot’s path and continuous heading adjustments over 28 navigation steps. To assess computational efficiency, execution timesfor evaluating Gaussian and hyperbolic secant functions were measured using C++ implementations with varying compiler optimization flags. The results indicate that the computational cost of the hyperbolic secant function is approximately 2–3 % lower than that of the Gaussian, a negligible difference in practice. The findings support the suitability of the hyperbolic secant-based APFM for real-time obstacle avoidance in robotic applications. The hyperbolic secant function offers a sharper decay near the origin compared to the Gaussian distribution, resulting in stronger immediate repulsive forces when the robot is close to an obstacle and rapidly diminishing influence at greater distances. This property provides improved responsiveness and local obstacle avoidance without introducing excessive long-range effects that could unnecessarily distort the global path. Additionally, the hyperbolic secant’s symmetric, heavy-tailed nature maintains smoothness in the potential field, ensuring stable and predictable robot motion while enabling faster, more efficient trajectory adjustments in dynamic environments.