Passivity constraints for the impedance control of series elastic actuators

Robots operating in close contact with humans require actuators capable of accurately and safely modulating the delivered torque. To this aim, rotary series elastic actuators are largely adopted. Torque control is often implemented using a cascade control scheme involving proportional-integral regulators (velocity controller nested in a torque controller) for its simplicity and its potential of ensuring coupled stability. A high-level impedance control loop is also commonly added to regulate the interaction with the external agents. In the present work, conservative passivity conditions are derived when a cascade-controlled series elastic actuator is used to haptically display different models of virtual impedance. In particular, the case of a null impedance, of a pure spring and of series and parallel spring-damper systems (corresponding to standard linear viscoelastic bodies) are analyzed in order to derive design guidelines useful for the selection of the control gains as well as for determining the ranges of renderable virtual impedance.