BENCHMARKING GAUSS AND LAPLACE ARTIFICIAL POTENTIAL FIELD APPROACHES FOR REAL-TIME OBSTACLE AVOIDANCE IN VIRTUAL SCENARIOS

Background . Autonomous mobile robots require robust real-time obstacle avoidance algorithms to navigate dynamic environments safely. The Artificial Potential Field (APF) method remains widely adopted for local path planning due to its computational efficiency and conceptual simplicity. However, conventional implementations suffer from two well-documented limitations: local minima and computational inefficiencies. This study investigates two probabilistic APF variants – a Gaussian formulation (ODG-PF) and a Laplace-based approach to address these limitations Materials and Methods. A comparative framework was developed using ROS2/Gazebo with TurtleBot3 as target platform. The Gaussian APFM (ODG-PF) and Laplace APFM were mathematically modeled, with key differences in their repulsive force calculations: Gaussian uses squared terms, while Laplace employs absolute values. Both methods were tested in identical static environments with 25 repeated runs (28 steps each). Performance metrics included computational time and path length, analyzed via boxplots, kernel density estimation, and Mann-Whitney U tests (p<0.05). Results and Discussion. The Laplace APFM demonstrated superior efficiency, with 34% faster median execution time (68 µs vs. 104 µs) and tighter interquartile range (28 µs vs. 52 µs). Its unimodal time distribution contrasted with the Gaussian's bimodal pattern, attributed to simpler arithmetic operations. While both methods achieved collision-free navigation, Laplace generated statistically shorter paths (p=0.0001), though with marginally higher variability. The Gaussian method's squaring operations introduced computational overhead without navigational benefits. Conclusion. The Laplace-based APFM outperforms its Gaussian counterpart in computational speed and path optimization, making it ideal for resource-constrained systems. These findings suggest that simpler mathematical formulations can yield superior real-world performance in obstacle avoidance applications. Future work should validate these findings in dynamic environments and explore hybrid implementations with global planners. Keywords : cyber-physical system, information technologies, obstacle avoidance, mobile robotic platforms, IoT concepts, wheeled mobile platform