Cartesian Stiffness Optimization for Robots with Variable Stiffness Joints: Analysis and Control

Abstract

Robot arms with passively compliant joints become more and more important, as they allow highly dynamic motion and are more robust toward unforeseen contact with their environment. Variable stiffness joints additionally allow the robot to adapt its joint stiffnesses to the task requirements. Since many robotic tasks can be specified in Cartesian coordinates, the Cartesian stiffness behaviour of the tool center point (TCP) needs to be specified. In order to approximate a desired Cartesian stiffness using only the decoupled passive joint compliances the joint stiffnesses, as well as the robot’s null space pose need to be optimized. This thesis presents an online Cartesian stiffness controller, that adjusts both the null space pose and the individual joint stiffnesses. Stability conditions are derived and the effectiveness of the controller is validated in several experiments on the DLR Hand Arm System. Furthermore, the thesis investigates the importance of considering the kinematic null space for achieving a desired Cartesian stiffness behaviour. It is demonstrated that exploiting the null space greatly expands the achievable stiffness range of the robot. The effects of joint stiffness optimization are shown to be strongly dependent on the null space pose. Therefore, joint stiffness optimization is most beneficial when used in combination with null space optimization.