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