Robust Leader-follower Formation Control of Mobile Robots Based on a Second Order Kinematics Model

In this paper, we study the problem of modeling and controlling leader-follower formation of mobile robots. First, a novel kinematics model for leader-follower robot formation is formulated based on the relative motion states between the robots and the local motion of the follower robot. Using this model, the relative centripetal and Coriolis accelerations between robots are computed directly by measuring the relative and local motion sensors, and utilized to linearize the nonlinear system equations. A formation controller, consisting of a feedback linearization part and a sliding mode compensator, is designed to stabilize the overall system including the internal dynamics. The control gains are determined by solving a robustness inequality and assumed to satisfy a cooperative protocol that guarantees the stability of the zero dynamics of the formation system. The proposed controller generates the commanded acceleration for the follower robot and makes the formation control system robust to the effect of unmeasured acceleration of the leader robot. Furthermore, a robust adaptive controller is developed to deal with parametric uncertainty in the system. Simulation and experimental results have demonstrated the effectiveness of the proposed control method.