Design principles for muscle-like variable impedance actuators with noise rejection property via co-contraction

In this paper we suggest basic principles to design a novel type of passive variable impedance actuator aimed at replicating a specific property of human co-contraction, related to the ability to cope with uncertainties affecting any physical/biological system. In particular the dynamical model of the proposed actuator is such that the variance of the state vector in response to noisy disturbances can be reduced by tuning the passive stiffness of the system. By means of a linearization analysis we characterize the mathematical properties that a non-linear dynamical system should have in order to possess this noise rejection property. We provide a practical example of such a system based on non-linear springs whose critical feature is to attach some elastic elements to a fixed reference (e.g. “ground”). We then show that this antagonist actuator structure is actually analog to Hill´s model of the human muscle/tendon system, emphasizing its biological relevance. We finally illustrate how time-varying stiffness can be efficiently planned feedforwardly to reject disturbances that may affect task achievement. To this aim, we use the formalism of stochastic optimal control to derive open-loop controls anticipating the consequences of unpredictability and instability linked to the task. We conclude that the suggested actuators are well-suited to mimic the main features of human co-contraction and plan to implement this type of actuator on the robot platform iCub in a near future.