An Active-Subspace-Based Algorithm for Reducing Redundancy in a Hybrid Neuroprosthesis

Hybrid neuroprosthesis (HN) systems combine the use of a powered exoskeleton with functional electrical stimulation of muscles to restore mobility in persons with paraplegia. At the same time, HN systems suffer from increased complexity due to redundant actuators that require coordination to function effectively. Muscle synergy-inspired control that coordinates these actuators can reduce system complexity. The calculation of these synergies requires the solution of a constrained optimization problem. As a way to reduce complexity during dynamic optimizations, we have developed a novel technique based on active subspaces to reduce the dimensionality of the redundant control system. Given an initial system state, a set of random control trajectories were generated, and the gradient of the cost function was obtained through the derivation of an adjoint function. The active subspaces were then obtained by performing eigenvalue decomposition on the outer product of the gradient of the cost function, and choosing the appropriate eigenvectors based on the magnitude of their corresponding eigenvalues. By leveraging the algorithm's parallel nature as well as simplifications that can be utilized in adjoint calculation, we show that by using this algorithm, synergies can be calculated more quickly than performing dynamic optimization. Once the active subspace is found, it is used in a gradient-projection optimization scheme to control the redundant actuators.