Abstract: The problem of how to design a controller for multirobot to form a formation under a slipping condition is discussed. The slipping phenomenon would lead the robot to deviate from its normal trajectory, and lead the performance of a controller designed under an idea condition to become worse, or even lead the robot to run out of control. Robot can adaptive a more common environment under a control algorithm proposed with the considering of the affection of slipping, and this algorithm can enhance the robot’s practical applications. The leader-follower based strategy is selected to coordinate the robots’ movement. The leader robot’s trajectory should be designed according to the task beforehand, and the follower robots are steered to follow the leader robot for some distance and bearing angle. Some dynamic equations of a single robot under a slipping condition are deduced according to the robot’s character, and according which a two-robot formation equation is derived based on the distance-angle model. A formation controller is proposed based on the second order sliding mode control algorithm, which forces the two robots to form a desired formation. Matlab simulations are presented to valid the algorithm proposed. Theory deduction and simulation results illustrate that the formation model proposed can describe the dynamics of the robots under a slipping condition accurately, and the second order sliding mode formation algorithm has good performance in anti-disturbance and applications.

Key words: Leader-follower, Robots formation, Second order sliding mode control, Slipping