Stability analysis of the λ-model during fast elbow movements

In control, stability insures the reproducibility of motions and the robustness to external and internal perturbations. In this short paper, the stability of the λ-model during fast elbow movements are analyzed, and the operation regions of the unmeasurably descending commands are calculated to guarantee the stabilizing ability of the motor control system. In this system, the elbow is modeled as a pair of antagonist muscles around the hinge joint in the horizontal plane. Both extensor and flexor muscles are described by a Hill-type muscle model. The muscle activation is produced by the physiological lambda version of the equilibrium point hypothesis (EPH). Conditions for global stability are calculated analytically by the Lyapunov theory and contraction theory. The results suggest that to guarantee the stability, the descending commands R, C and μ from central nervous system (CNS) must be tuned to the muscle properties, the muscle geometry and the geometric properties of the linkage system.