A rigorous dynamical-systems-based analysis of the self-stabilizing influence of muscles

In this paper, dynamical systems analysis and optimization tools are used to investigate the local dynamic stability of periodic task-related motions of simple models of the lower-body musculoskeletal apparatus and to seek parameter values guaranteeing their stability. In particular, the dynamics of a two-link model of a leg undergoing periodic excitation through one or several contractile muscle elements corresponding to a simple knee-bending motion is studied. Several muscle models incorporating various active and passive elements are included and the notion of self-stabilization of the rigid-body dynamics through the imposition of muscle-like actuation is investigated. It is found that self-stabilization depends both on muscle architecture and configuration as well as the properties of the reference motion. Additionally, antagonistic muscles (flexor-extensor muscle couples) are shown to enable stable motions over larger ranges in parameter space and that even the simplest neuronal feedback mechanism can stabilize the repetitive motions. The work provides a review of the necessary concepts of stability and a commentary on existing incorrect results that have appeared in the literature on muscle self-stabilization.