Logarithmic Potential Field: A New Leader– Follower Robotic Control Mechanism to Enhance the Execution Speed and Safety Attributes

The leader-follower formation approach is a commonly used strategy in multi-robot systems, usually implemented with a hierarchical control architecture combining path planning and formation control. The leader robot determines the desired trajectory while the follower robots track the motion of the leader robot using a control system. However, this hierarchical architecture does not ensure successful obstacle avoidance for follower robots. Several solutions proposed adding an obstacle avoidance layer, but this can increase the system complexity and reduce the computational speed, hindering real-time performance. Improving the opposing attributes, namely the execution speed, path length, safety, and smoothness, together is a challenging path-planning problem in robotics. This paper proposes a novel leader-follower control mechanism that combines formation control and obstacle avoidance in one step. The new path planning technique focuses on enhancing execution speed and safety while ensuring the generation of smooth paths with acceptable path lengths. The main contribution of the proposed technique lies in the development of a novel potential field modeling approach specifically designed for follower robots in a multi-robot system. The proposed potential field model consists of three terms, namely, the Gaussian term, the Euclidean term, and the Logarithmic term, which are all optimized later using Particle Swarm Optimization (PSO) to generate the path. The Gaussian term, acting as a repulsive force, represents the Gaussian distance to each obstacle in the environment. It exhibits a strong value in close proximity to obstacles, while it gradually decays exponentially as the distance from the obstacles increases. The second term, the Euclidean term, which is the Euclidean distance to the leader robot, is responsible to find the shortest path to the leader robot. Finally, to ensure follower robot safety, a logarithmic term is integrated into the potential field model, facilitating automatic switching between attractive and repulsive forces generated by the leader robot. The incorporation of a logarithmic term into the potential field model stands as a significant innovation in the proposed technique. This inclusion enables the leader robot to generate an initial attractive force towards the followers, which dynamically transitions into a repulsive force as the follower robots approach. This automatic switching behavior enhances processing efficiency while ensuring collision avoidance. A kinematic control strategy is applied to the system in order to test the proposed path planning technique. The experimental results have proven the effectiveness of the proposed system, which has shown superior performance over the well-known techniques A*, RRT*, PRM, and also Hybrid-A* in terms of execution speed and the path length