Robot’s Cartesian Stiffness Adjustment Through the Stiffness Ellipsoid Shaping

One of the key properties that define the behaviour of the compliant robot with its environment is end-effector (EE) Cartesian stiffness. Typically, EE stiffness is represented as a stiffness matrix whose design can be impossible due to the lack of degrees of freedom to adjust all the elements within the stiffness matrix. Therefore, a tradeoff between matrix elements must be made. This paper proposed an approach for offline shaping of the stiffness matrix using stiffness ellipsoids as an alternative, where stiffness is shaped by adjusting the ellipsoid orientation and axis magnitudes. Shaping of the ellipsoid requires fewer parameters that need to be adjusted relative to the stiffness matrix. A criteria function for shaping the ellipsoid stiffness has been proposed. Optimal values of joint positions and stiffness were computed using the algorithm based on SLSQP (Sequential Least SQuare Programming). Further analysis is conducted on parts of the trajectory that cannot satisfy EE ellipsoid shaping criteria. This is overcome by starching the critical parts of the trajectory by dividing it into smaller increments. Results show improvement in ellipsoid shaping and reduced orientation error. The algorithm is tested in a simulation environment on the KUKALWR model.