Our long-term goal is to use a musculoskeletal modeling approach for developing controller algorithms to restore standing balance to individuals with lower extremity paralysis using functional electrical stimulation. This paper describes a technique that facilitates this approach by avoiding the numerical problems associated with modeling the closed kinematic chain formed by the two lower extremities and the ground while standing. Specifically, we propose an optimization technique to estimate the magnitude and origin of the ground reaction force (GRF) vector on one of the feet, resulting in an equivalent open-chain formulation. Using this technique, we performed a series of inverse dynamic computations to determine the GRF and center of pressure (COP) values for five standing postures: neutral, neutral with forward lean, neutral with backward lean, wide, and tandem. The optimization procedure elicited force results that satisfy equilibrium and result in COP locations that are consistent and physically reasonable.
The authors are with the Dept. of Biomedical Engineering and Orthopaedics at Case Western Reserve University, Cleveland, and also with the Motion Study Laboratory, Cleveland VA Medical Center, Cleveland, OH 44106.