Computation of a stabilizing set of feedback matrices of a large-scale nonlinear musculoskeletal dynamic model

The purpose of this study is to present a general mathematical framework to compute a set of feedback matrices which stabilize an unstable nonlinear anthropomorphic musculoskeletal dynamic model. This method is activity specific and involves four fundamental stages. First, from muscle activation data (input) and motion degrees-of-freedom (output) a dynamic experimental model is obtained using system identification schemes. Second, a nonlinear musculoskeletal dynamic model which contains the same number of muscles and degrees-of-freedom and best represents the activity being considered is proposed. Third, the nonlinear musculoskeletal model (anthropomorphic model) is replaced by a family of linear systems, parameterized by the same set of input/output data (nominal points) used in the identification of the experimental model. Finally, a set of stabilizing output feedback matrices, parameterized again by the same set of nominal points, is computed such that when combined with the anthropomorphic model, the combined system resembles the structural form of the experimental model. The method is illustrated in regard to the human squat activity.