TRACKING IN NONLINEAR DIFFERENTIAL-ALGEBRAIC CONTROL-SYSTEMS WITH APPLICATIONS TO CONSTRAINED ROBOT SYSTEMS

We consider the design of a feedback control law for control systems d escribed by a class of nonlinear differential-algebraic equations so t hat certain desired outputs track given reference inputs. The nonlinea r differential-algebraic control system being considered is not in sta te variable form. Assumptions are introduced and a procedure is develo ped such that an equivalent state realization of the control system de scribed by nonlinear differential-algebraic equations is expressed in a familiar normal form. A nonlinear feedback control law is then propo sed which ensures, under appropriate assumptions, that the tracking er ror in the closed loop differential-algebraic system approaches zero e xponentially. Applications to simultaneous contact force and position tracking in constrained robot systems with rigid joints, constrained r obot systems with joint flexibility, and constrained robot systems wit h significant actuator dynamics are discussed.