Phase-Relaxed-Passive Full State Feedback Gain Limits for Series Elastic Actuators

Full state feedback (FSF) controllers for series elastic actuators bridge the gap between impedance and admittance controllers. For humanoid robots-which must stably accomplish both stiff and soft behaviors-FSF controllers are ideal candidate joint controllers. However, previous work on FSF gain tuning has used a nonlinear passivity analysis which does not account for time delay and can result in unstable behavior. In this article, we introduce a phase-based frequency domain approach to limiting these gains. This strategy can guarantee phase-relaxed passivity according to a relaxation parameter-an a priori bound on the regenerative efficiency of springs appearing in the environment. A simple demonstration illustrates how relaxed phase passivity behaves differently than strict passivity in how it handles the load inertia, allowing stiffness beyond the passive limit.