Choosing Stiffness and Damping for Optimal Impedance Planning

The attention given to impedance control in recent years does not match a similar focus on the choice of impedance values that the controller should execute. Current methods are hardly general and often compute fixed controller gains relying on the use of expensive sensors. In this article, we address the problem of online impedance planning for Cartesian impedance controllers that do not assign the closed-loop inertia. We propose an optimization-based algorithm that, given the Cartesian inertia, computes the stiffness and damping gains without relying on force/torque measurements and so that the effects of perturbations are less than a maximum acceptable value. By doing so, we increase robot resilience to unexpected external disturbances while guaranteeing performance and robustness. The algorithm provides an analytical solution in the case of impedance-controlled robots with diagonally dominant inertia matrix. Instead, established numerical methods are employed to deal with the more common case of nondiagonally dominant inertia. Our work attempts to create a general impedance planning framework, which needs no additional hardware and is easily applicable to any robotic system. Through experiments on real robots, including a quadruped and a robotic arm, our method is shown to be employable in real time and to lead to satisfactory behaviors.