Adaptive trajectory tracking and rejection of sinusoidal disturbances with unknown frequencies for uncertain mechanical systems

The problem of adaptively tracking a pre-planned trajectory and rejecting multi-sinusoidal input disturbances with unknown amplitudes, phases and frequencies is addressed and solved for fully-actuated uncertain mechanical systems. We consider the case of disturbances occurring in joint space (adding up with the control torques) as well as the case of cartesian disturbances acting from the external environment. Largely inspired by the work of Chen and Huang [1] on the attitude dynamics of the rigid body, the proposed controller consists of an adaptive internal model unit which estimates in a joint fashion the mismatches in the disturbance frequencies and in the physical parameters. This work is very relevant, e.g., for mechanical systems with flexible appendages where vibrations arising from the flexibility are suppressed by being modeled as exogenous unknown sinusoidal disturbances.