End-effector Cartesian stiffness shaping - sequential least squares programming approach

Control of robot end-effector (EE) Cartesian stiffness matrix (or the whole mechanical impedance) is still a challenging open issue in physical humanrobot interaction (pHRI). This paper presents an optimization approach for shaping the robot EE Cartesian stiffness. This research targets collaborative robots with intrinsic compliance - serial elastic actuators (SEAs). Although robots with SEAs have constant joint stiffness, task redundancy (null-space) for a specific task could be used for robot reconfiguration and shaping the stiffness matrix while still keeping the EE position unchanged. The method proposed in this paper to investigate null-space reconfiguration's influence on Cartesian robot stiffness is based on the Sequential Least Squares Programming (SLSQP) algorithm, which presents an expansion of the quadratic programming algorithm for nonlinear functions with constraints. The method is tested in simulations for 4 DOF planar robot. Results are presented for control of the EE Cartesian stiffness initially along one axis, and then control of stiffness along both planar axis - shaping the main diagonal of the EE stiffness matrix.