MATHEMATICAL MODEL OF MODIFIED REAL-TIME OBSTACLE AVOIDANCE METHOD BASED ON LAPLACE ARTIFICIAL POTENTIAL FIELD

Abstract

In the domain of robotics, a critical area of focus is autonomous mobile robots. These are sophisticated machines engineered with the ability to traverse through space autonomously, and endowed with the capacity to execute specific decisions in a real-time context. This implies that these robots can function independently, devoid of human intervention, and can adapt to their environment by making decisions predicated on the real-time data they acquire.

A fundamental component of the software infrastructure in such machines pertains to the algorithms for path planning and obstacle avoidance. These algorithms are pivotal as they endow the machines with capabilities such as automatic parking, circumventing emergency situations on the road, and even achieving full autonomy.

This highlights the complexity and sophistication of autonomous mobile robots and underscores the importance of ongoing research in this field. The development and refinement of effective obstacle detection and avoidance algorithms continue to be a key focus in robotics research, with the aim of enhancing the safety and efficiency of autonomous mobile robots. The Artificial Potential Field (APF) method is a classic technique in the field of robotics, particularly for path planning and obstacle avoidance. In the APF method, a virtual potential field is created where the target location and any obstacles in the environment generate attractive and repulsive forces, respectively. The robot, or autonomous agent, is then guided by these forces. It experiences an attractive force towards the target and a repulsive force away from obstacles. The robot moves under the action of the resultant force [1].

The subject matter of the article is a mathematical model that modifies the method of artificial potential fields, incorporating the use of Laplace functions. The method that has been developed is capable of identifying obstacles and calculating the likelihood of the robot colliding with these obstacles. The study delves into the process of deriving a mathematical model that can compute both attractive and repulsive fields. It also discusses the selection of equation parameters and a methodology for determining a safe trajectory for the robot’s movement. Future work aims to put the derived model to the test, both in a ROS2/Webots simulation environment and on an actual hardware platform. This will provide a practical application and validation of the theoretical model.