Near optimal control of mobile robot formations

In this paper, the infinite horizon optimal tracking control problem is solved online and forward-in-time for leader-follower based formation control of nonholonomic mobile robots. Using the backstepping design approach, the dynamical controller inputs for the robots are approximated from nonlinear optimal control techniques in order to track the control velocities designed to keep the formation. The proposed nonlinear optimal control technique, referred to as adaptive dynamic programming, uses neural networks (NN´s) to solve the optimal formation control problem in discrete-time in the presence of unknown internal dynamics and a known control coefficient matrix. All NN´s are tuned online using novel weight update laws, and the stability of the entire formation is demonstrated using Lyapunov methods. Simulation results are provided to demonstrate the effectiveness of the proposed approach.