An exponentially stable adaptive control for force and position tracking of robot manipulators

The problem of controlling a robot manipulator while the end effector is in contact with an environment of finite but unknown stiffness is considered. An exponentially stable control law is derived starting from a passivity-based position control algorithm. The original position trajectory is scaled along the interaction direction so as to achieve force tracking as well as position tracking along the unconstrained directions. A passivity-based adaptive algorithm is designed to avoid the explicit computation of the scaling factor, which depends on the unknown stiffness of the environment, leading to time-varying PID control actions on the force error