Tracking in Control Systems Described by Nonlinear Differential-Algebraic Equations with Applications to Constrained Robot Systems

In this paper, we consider the problem of designing a feedback control law so that the outputs track desired reference inputs in control systems described by a class of nonlinear differential-algebraic equations. Assumptions are introduced a procedure is developed such that an equivalent state realization of the control system described by nonlinear differential-algebraic equations is expressed in a familiar normal form. A nonlinear feedback control law is then proposed which ensures, under appropriate assumptions, that the tracking error in the closed loop differential-algebraic system approaches zero exponentially. Applications to simultaneous contact force and position tracking in constrained robot systems with rigid joints, constrained robot systems with joint flexibility, and constrained robot systems with significant actuator dynamics are discussed.