Multi-Priority Cartesian Impedance Control

Manipulator compliance is well known to be important to robot manipulation and assembly. Recently, this has been highlighted by the development of new higly-compliant robot manipulators such as the Barrett arm or the DLR lightweight manipulator [1], [2]. It is also clear that dexterous manipulation involves touching the environment at different locations simultaneously (perhaps at different points on the robot hand or fingers). In these situations, it is particularly attractive to control the system using a multi-priority strategy where several contact points are commanded in parallel. Multi-priority Cartesian impedance control is the natural combination of these two ideas. The system realizes several impedances with different reference positions at different points on the robot with a specified order of priority. We find a controller that minimizes an arbitrary quadratic norm on the second-priority impedance error subject to constraints deriving from the first priority impedance task. We also show that the locally optimal controller does not require force feedback in its implementation for passive desired inertias. The results are illustrated in simulation.