Open-loop stochastic optimal control of a passive noise-rejection variable stiffness actuator: Application to unstable tasks

In this paper we propose a methodology to control a novel class of actuators that we called passive noise rejection variable stiffness actuators (pnrVSA). Differently from nowadays classical VSA designs, this novel class of actuators mimics the human musculoskeletal ability to increase noise rejection without relying on feedback. To fully highlight the potentialities behind these actuators we consider movement planning under two constraints: (1) absence of feedback, i.e. purely open-loop planning¹; (2) uncertain dynamic model. Under these constraints, movement planning can be formalized as an open-loop stochastic optimal control. Due to the lack of classical methods forcing the open-loop nature of the computed solution, we used here a slight modification of available methodologies based on importance sampling of trajectories using forward diffusion processes. Simulations show that the proposed algorithm can be effectively used to plan open-loop movements with pnrVSA. In particular, two different scenarios are considered: the control of a single joint pnrVSA and the control of a two degrees of freedom planar arm equipped with antagonist pnrVSAs at each joint. In both cases, movement has to be planned in presence of uncertain dynamics for unstable tasks. It is shown that open-loop stochastic optimal control can modulate the intrinsic stiffness of the system to cope with both instability and noise.