Control of Nonholonomic Mobile Robot Formations: Backstepping Kinematics into Dynamics

In this paper, we seek to expand framework developed to control a single nonholonomic mobile robot to include the control of formations of multiple nonholonomic mobile robots. A combined kinematic/torque control law is developed for leader-follower based formation control using backstepping in order to accommodate the dynamics of the robots and the formation in contrast with kinematic-based formation controllers. The asymptotic stability of the entire formation is guaranteed using Lyapunov theory, and numerical results are provided The kinematic controller is developed around control strategies for single mobile robots and the idea of virtual leaders. The virtual leader is replaced with a physical mobile robot leader and the assumption of constant reference velocities is removed An auxiliary velocity control is developed allowing the asymptotic stability of the followers to be proved without the use of Barbalat´s Lemma which simplifies proving the entire formation is asymptotically stable. A novel approach is taken in the development of the dynamical controller such that the torque control inputs for the follower robots include the dynamics of the follower robot as well as the dynamics of its leader, and the case when all robot dynamics are known is considered.