Sampling-Based Nonlinear Stochastic Optimal Control for Neuromechanical Systems

Determining how the nervous system controls tendon-driven bodies remains an open question. Stochastic optimal control (SOC) has been proposed as a plausible analogy in the neuroscience community. SOC relies on solving the Hamilton-Jacobi-Bellman equation, which seeks to minimize a desired cost function for a given task with noisy controls. We evaluate and compare three SOC methodologies to produce tapping by a simulated planar 3-joint human index finger: iterative Linear Quadratic Gaussian (iLQG), Model-Predictive Path Integral Control (MPPI), and Deep Forward-Backward Stochastic Differential Equations (FBSDE). We show that averaged over 128 repeats these methodologies can place the fingertip at the desired final joint angles but–because of kinematic redundancy and the presence of noise–they each have joint trajectories and final postures with different means and variances. iLQG in particular, had the largest kinematic variance and departure from the final desired joint angles. We demonstrate that MPPI and FBSDE have superior performance for such nonlinear, tendon-driven systems with noisy controls.Clinical relevance— The mathematical framework provided by MPPI and FBSDE may be best suited for tendon-driven anthropomorphic robots, exoskeletons, and prostheses for amputees.