Inverse optimal control for differentially flat systems with application to locomotion modeling

Abstract

Inverse optimal control is the problem of computing a cost function with respect to which observed trajectories of a given dynamic system are optimal. In this paper, we present a new formulation of this problem for the case where the dynamic system is differentially flat. We show that a solution is easy to obtain in this case, in fact reducing to finite-dimensional linear least-squares minimization. We also show how to make this solution robust to model perturbation, sampled data, and measurement noise, as well as provide a recursive implementation for online learning. Finally, we apply our new formulation of inverse optimal control to model human locomotion during stair ascent. Given sparse observations of human walkers, our model predicts joint angle trajectories for novel stair heights that compare well to motion capture data (R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = 0.97, RMSE = 1.95 degrees). These exemplar trajectories are the basis for an automated method of tuning controller parameters for lower-limb prosthetic devices that extends to locomotion modes other than level ground walking.