Online Approximate Optimal Path-Following for a Mobile Robot

Online approximation of an infinite horizon optimal path-following strategy for a unicycle-type mobile robot is considered. An approximate solution to the optimal control problem is obtained by using an adaptive dynamic programming technique that uses adaptive update laws to estimate the unknown value function. The developed controller overcomes challenges with the approximation of the infinite horizon value function by using an auxiliary function that describes the motion of a virtual target on the desired path. The developed controller guarantees uniformly ultimately bounded (UUB) convergence of the vehicle to a desired path while maintaining a desired speed profile and UUB convergence of the approximate policy to the optimal policy without requiring persistence of excitation.