Position tracking and force control of robotic manipulators with a descriptor system model. I. Linearization and solution for position and force control

This paper deals with the position and force control of a robot manipulator in which the end-effector is required to move along a specified trajectory with a specified contact force on a plane or general surface. Such a system is modeled as a nonlinear descriptor system consisting of a set of nonlinear differential equations and algebraic equations. A method of nonlinear state feedback and state space transformation is used to globally, exactly and totally linearize the nonlinear descriptor system into a linear descriptor system in the working space of the manipulator. Based on the resultant linear descriptor system, a necessary and sufficient condition for position and force control of robot manipulator is then obtained, and a synthesis method to design a controller is given. In the special case when the contact force is required to be zero, the controller becomes considerably simpler