A new approach to position and contact force regulation in constrained robot systems

A feedback control problem for regulation of contact force and position in constrained robot systems is considered. The nonlinear differential-algebraic equations which describe the dynamics of a constrained robot system are linearized about a constrained equilibrium. A method of obtaining an equivalent state realization for the resulting linear differential-algebraic equations is developed. This method is numerically efficient since it is based on a singular value decomposition. A linear quadratic optimal control problem associated with the linearized differential-algebraic equations is solved. The resulting linear feedback control law guarantees good regulation of both contact force and position of the constrained robot. Since the method is based on the linearization of the nonlinear differential-algebraic equations, it is valid only in a neighborhood about the point of linearization. Two robot examples are considered in order to illustrate the proposed method