Dynamic Active Subspaces for Model Predictive Allocation in Over-Actuated Systems

Abstract

In this letter, we analyze dynamic optimization problem for robotic systems utilizing dynamic active subspaces ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Dy\mathcal {AS}$ </tex-math></inline-formula> ) to obtain a lower-dimensional control input space by performing a global sensitivity analysis. In doing so, we set up a Model Predictive Control Allocation (MPCA) problem wherein the actuators are dynamically allocated to track a desired stabilizing torque while satisfying state and control constraints. To improve computational efficiency of the MPCA, we develop Koopman operator-based linear prediction dynamics of an over-actuated nonlinear robotic system. We demonstrate the derived results on a hybrid neuroprosthesis model for a trajectory tracking task wherein we show a muscle fatigue-based joint torque allocation among motor and functional electrical stimulation (FES) actuators.