A Geometric Approach to Task-Specific Cartesian Stiffness Shaping

Controlling the exact Cartesian stiffness values of a robot end-effector (EE) is troublesome because of difficulties associated with estimating the stiffness and controllability of a full Cartesian stiffness matrix. However, most practical applications require only quantitative (high/low) stiffness values in the EE motion direction (or perpendicular direction). Full control of the stiffness matrix requiring too many control inputs which is hardly possible in practical applications. To ensure the efficiency of execution for a range of redundant robots, we present an algorithm for shaping a robot’s Cartesian stiffness ellipsoid, a more intuitive and visual stiffness representation, using a nonlinear sequential least square programming optimization. The algorithm is designed to optimize the joint stiffness values and the trajectory of the robot’s joints, using null-space exploration, for a given task. Using eigenvalue decomposition of the stiffness matrix, the algorithm minimizes the orientation difference between the major axis of the current and the desired stiffness ellipsoid and specify a scaling factor between the major and the minor axis. The presented approach allows the user to better understand and control of a robot, regardless of the user’s knowledge of the achievable stiffness range and the interdependencies of the Cartesian stiffness matrix elements.