Nonlinear adaptive control of a two link flexible robot arm

The problem of adaptively controlling the endpoint trajectory of a two-link flexible robot arm is addressed. Payload mass variations are considered. By means of a simple, finite-dimensional model of the robot, it is shown that the well-known self-tuning adaptive scheme can be successfully implemented in combination with a recently developed nonlinear controller. For the nonminimum-phase robot system, an indirect adaptive controller is presented. A least-squares identification scheme generates an estimate of the payload mass that tunes both the computation of a bounded solution for the reduced inverse system and the computation of the nominal torques. A stabilizing linear error-state feedback, with fixed gains and robustness with respect to payload mass variations, is added to the nominal torques to guarantee the total stability of the system. This is the main ingredient used in the proof of the adaptive controller properties by means of a Lyapunov-like approach. The controller performance is finally tested by numerically simulating the tracking of an endpoint angular velocity step