Closed loop properties of constrained robots using position, velocity and force feedback

A mathematical model for constrained robot dynamics, incorporating the effects of contact forces required to maintain satisfaction of the constraints, is used to develop explicit conditions for stabilization and tracking using feedback control of displacements, velocities and the contact forces. Properties of the resulting closed loop system are presented. Specifically, effects of external force disturbances, effects of dynamics in the contact force feedback loops and effects of uncertainty in the constraint functions on the closed loop are studied. These closed loop properties clearly demonstrate the advantages to be gained by feedback of the contact force. In this work, the simplifying assumption is made that the constraint functions are linear; and only local closed loop properties are studied.