Force Sharing Problem During Gait Using Inverse Optimal Control

Abstract

Human gait patterns have been intensively studied, both from medical and engineering perspectives, to understand and compensate pathologies. However, the muscle-force sharing problem is still debated as acquiring individual muscle force measurements is challenging, requiring the use of invasive devices. Recent studies, using various objective functions, suggest muscle-force sharing may result from an optimization process. This study proposes using inverse optimal control to identify an objective function. Two popular methods of inverse optimal control, bilevel and inverse Karush-Kuhn-Tucker, were investigated. The identified objective functions were then used to predict muscle forces during gait, and their performances were compared to an exhaustive list of biological cost functions from the literature. The best prediction was achieved by the bilevel inverse optimal control method, with a root-mean-squared error of 176 N (162 N) and a correlation coefficient of 0.76 (0.68) for the stance (swing) phase of the gait cycle. These muscle force predictions were thereafter used to compute joint stiffness, exhibiting an average root-mean-square error of 42 Nm.rad <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{-1}$</tex-math></inline-formula> and a correlation coefficient of 0.90 when compared to the reference. The bilevel method's prevalence in terms of robustness over inverse Karush-Kuhn-Tucker was demonstrated on human data and explained on a toy example.