Control of dynamical systems governed by constrained coordinates

In this paper we develop feedback control laws for systems described by constrained generalized coordinates. The use of constrained coordinates leads to differential algebraic equations of motion. Previous research on controlling systems has concentrated primarily on using mathematical models in terms of independent coordinates. For several complex dynamical systems, it is more desirable to develop a mathematical model using a constrained coordinate formulation in terms of dependent coordinates. Examples include closed kinematic chains, vehicle dynamics and path tracking problems. Research in the last few decades has led to several advances in the treatment and in obtaining the solution of differential algebraic equations. We take advantage of these advances and introduce the constrained coordinate formulation to control. We design feedback control laws based on a pointwise-optimal formulation for systems described in terms of dependent generalized coordinates. We also use the constrained formulation in pathtracking control problems where one traditionally uses independent coordinates. Because the constrained formulation permits explicit minimization of the tracking error higher levels of accuracy are reached.