Robust Passivity and Passivity Relaxation for Impedance Control of Flexible-Joint Robots with Inner-Loop Torque Control

Passivity is a canonical condition for the safety of interactive systems, but practical limitations restrict its utility as a design tool. A system with a passive model can be unstable in high-stiffness environments, passivity is difficult to show with inner-loop controllers, and as it is a binary condition it provides limited design comparison insight; as a result, it is rarely used for inner-loop design. As passivity safety claims are limited by model accuracy, conditions for the passivity of a system with bounded-magnitude model uncertainty (robust passivity) are developed in this paper. Additionally, a condition for coupled environment–robot stability is developed using mixed passivity and small-gain condition, allowing rigorous relaxation of passivity at high frequencies for typical impedance-controlled systems. These approaches are used in the analysis of an impedance-controlled series-elastic actuated system with inner-loop torque control and also compared with traditional design tools (bandwidth ratio, sensitivity function, etc.). The approach is then validated experimentally, identifying model uncertainty bounds under various load conditions, and then using the measured uncertainty for controller synthesis. Robust passivity is then compared with nominal passivity in a validation experiment under manual excitation and impact.