Combined open-loop and funnel control for underactuated multibody systems

We consider tracking control for multibody systems which are modeled using generalized coordinates. Utilizing the two-degree- of-freedom approach to controller design, we combine a feedforward with a feedback controller. The feedforward control input is computed using the method of servo-constraints, which relies on an inverse model of the system. The feedback control input is generated by a dynamic output feedback which consists of the combination of a funnel controller with a funnel pre-compensator. This feedback controller is model free and hence inherently robust. The control design is restricted to multibody systems with relative degree two or three which have input-to-state stable internal dynamics. In the main result, we prove that the proposed controller is able to guarantee prescribed performance of the tracking error even in the presence of uncertainties and disturbances. We illustrate the application of the control design by a mass on car system (single-input, single-output) and a planar robotic manipulator (two-input, two-output). In the case of relative degree two, these systems contain an unknown friction term.