Robust Formation Control based on Virtual Structure for Nonholonomic Mobile Robots

In this paper, formation control based on the virtual structure for the non-holonomic mobile robot system with two models of certain and uncertain kinematic equations is discussed. First, the formation equations of a certain model are calculated and then it is proved that it is possible to create a geometric shape and maintain that state by using the sliding model control theory for any two moving mobile robots. Then, after deriving the formation equations of the uncertain model, a sliding model controller is designed that is able to control the uncertain model provided that the uncertainty range of the kinematic equation is present. For each design, the stability of the system is guaranteed using the Lyapunov stability theorem. Finally, in order to compare the performance of the designed controllers, a pre-designed back-stepping controller is introduced and the results will be presented in the form of simulations. The simulation results show the effective performance of the designed controllers.