Closed-loop positive real optimal control of variable stiffness actuators

Abstract

Series elastic actuators decouple stiff motors and gear trains from the load by an mechanic elastic element. This elastic element can be used as torque sensor, acts as an energy storage, decouples the actuator from exogenous high frequency excitation and contributes towards shock resistance and safety in human–robot interaction scenarios. A series elastic element, however, fundamentally limits the achievable actuator bandwidth. Variable stiffness actuators (VSA) were introduced to overcome bandwidth limitations in series elastic actuators and to provide the flexibility necessary for energy efficient operation. The variable elastic element, however, complicates the design of torque and impedance controllers, which have to be synthesised by employing contradicting design objectives, such as minimisation of the output impedance, robust stability and performance. To overcome these synthesis problems, we present a new controller design procedure that imposes a positive real constraint on the load output port function to guarantee a stable interaction with respect to a passive, yet otherwise unknown environment. Additional design requirements are subsequently cast into a generalised plant. A H∞ design procedure is employed to design a gain-scheduled torque controller, which adapts to the varying mechanical stiffness of the actuator. It is then extended with a new procedure for the parametrisation of a superimposed impedance control-loop. The space of parameters for the impedance controller is determined in such way that it guarantees a positive real actuator output port function. The control strategy is tested in an in silico environment and in experiments on a test-bench with the Mechanical-Rotary Impedance Actuator (MeRIA).