The role of intrinsic muscle properties for stable hopping--stability is achieved by the force-velocity relation

A reductionist approach was presented to investigate which level of detail of the physiological muscle is required for stable locomotion. Periodic movements of a simplified one-dimensional hopping model with a Hill-type muscle (one contractile element, neither serial nor parallel elastic elements) were analyzed. Force-length and force-velocity relations of the muscle were varied in three levels of approximation (constant, linear and Hill-shaped nonlinear) resulting in nine different hopping models of different complexity. Stability of these models was evaluated by return map analysis and the performance by the maximum hopping height. The simplest model (constant force-length and constant force-velocity relations) outperformed all others in the maximum hopping height but was unstable. Stable hopping was achieved with linear and Hill-shaped nonlinear characteristic of the force-velocity relation. The characteristics of the force-length relation marginally influenced hopping stability. The results of this approach indicate that the intrinsic properties of the contractile element are responsible for stabilization of periodic movements. This connotes that (a) complex movements like legged locomotion could benefit from stabilizing effects of muscle properties, and (b) technical systems could benefit from the emerging stability when implementing biological characteristics into artificial muscles.