Flexible-link manipulator force control

The flexible-link-manipulator force control problem is considered. The force controller is separated into two parts based on the inner- /outer-loop strategy. The inner-loop controller is based on a composite strategy, where a slow feedback linearization scheme acts on the underlying rigid arm dynamics, recovered by the singular perturbation method. Subsequently, the input is convolved with a sequence of impulses in order to produce a near vibration-free output. The amplitude of the impulses is related to the modal damping, and the spacing between them on the modal frequencies. The outer-loop controller modifies its structure according to the environment impedance, and through a selection matrix assigns the force and the position control subspaces. The resulting input is colored around the modal frequencies through a notch filter, so that no energy is injected into the flexible states. A low-pass filter in cascade is used to avoid excitation of the high-frequency unmodeled dynamics.