Exponential stabilization of kinematic nonholonomic systems using adaptive backstepping

Abstract

We consider stabilization problem for n-dimensional kinematic nonholonomic systems with m-inputs. The control objective in exponential stabilization is to force the system states x ϵ Rn from an arbitrary initial state x0 to origin with a finite convergence rate γ. We employ adaptive back stepping to stabilize the nonholonomic system. Adaptive back stepping seeks to stabilize n system states in n + r dimensional manifold with r being the number of adaptation parameters. Using this approach, desired performance and robustness properties of the feedback control system can be guaranteed. The effectiveness of the proposed algorithm is established by applying it on a unicycle type system moving on hyperbolic plane. Simulation results confirm the mathematical developments.