A singular perturbation approach to modeling and control of manipulators constrained by a stiff environment

Mathematical models for robot manipulator dynamics which incorporate the effects of interaction forces between the manipulator end effector and a stiff environment are presented. With appropriate assumptions, the model is transformed into a standard singularly perturbed form expressed in terms of a small parameter which is inversely proportional to the stiffness and the damping of the environment. The model for the slow time scale dynamics, corresponding to the case where the environment is rigid, is shown to be equivalent to the differential-algebraic equations which have been developed previously for mechanical systems with holonomic constraints. the model for the fast time scale dynamics is also derived. A feedback structure based on control of the slow time scale dynamics is proposed and justified. A simple example is presented to illustrate the concepts