New stability results for direct adaptive impedance control

Stable and robust execution of contact tasks is of paramount importance for robot manipulators in many applications. This paper presents two adaptive schemes for controlling the end-effector impedance of robot manipulators to enable reliable execution of contact tasks. The first scheme, position-based adaptive impedance control consists of two subsystems: a simple "filter" that modifies the end-effector position trajectory based on the sensed contact force and the desired dynamic relationship between the position and force, and an adaptive controller that produces the joint torques required to track this modified trajectory. The second control strategy is developed using a model reference adaptive impedance control approach by formulating the desired relationship between the end-effector position and contact force as a "reference model", and then devising a control scheme to ensure that the end-effector dynamics emulates this reference model. The proposed controllers are very general and computationally efficient since they do not require knowledge of the manipulator dynamic model or parameter values of the manipulator or the environment, and are implemented without calculation of the robot inverse dynamics or inverse kinematic transformation. It is shown that the control strategies are globally stable in the presence of bounded disturbances, and that in the absence of disturbances the ultimate bound on the size of the controller errors can he made arbitrarily small.