Adaptive controllers and robustness analysis for curve tracking with unknown control gains

We study adaptive control and parameter identification for robotic curve tracking under unknown control gains. We build adaptive controllers that identify the unknown control gains and stabilize equilibria corresponding to a fixed constant distance to the curve and zero bearing. Our strict Lyapunov function method allows us to prove robust performance under actuator errors in terms of integral input-to-state stability under a bound on the disturbance that maintains forward invariance of a class of invariant hexagons. This extends existing curve tracking results to allow controller uncertainty and parameter identification. We demonstrate our work in simulations.