Leader-Follower Formation Control in Cluttered Environments via APF-Based Reference Shaping and Variable-Structure Control

Leader-follower formation control is attractive for multi-robot systems due to scalability and limited communication, yet maintaining formation accuracy in cluttered environments is challenging under nonholonomic constraints, curvature variations, and obstacle-induced maneuvers. This paper presents a leader-follower formation-control framework for nonholonomic mobile robots that incorporates obstacle avoidance at the reference level. Here, an artificial potential field (APF) continuously reshapes leader-Attached formation virtual targets, enabling collision-Aware motion without interrupting the tracking structure. To improve tracking performance, a variable-structure proportional controller (VS-P) is proposed. It enhances the performance by switching between two predefined gain sets based on error dynamics. Simulations on lemniscate tracking in an obstacle-populated workspace show that VS-P reduces overall formation RMSE by 5.4% compared to a constant-gain P controller and yields modest improvements in leader-frame separation and bearing regulation while preserving comparable obstacle clearance.