Stability analysis for postural control in a two-joint limb system.

The stability behavior of a multi-joint limb with electrically activated muscles provides important clues for postural control of motor tasks. The stability property of the musculoskeletal system can be characterized with its eigenvalues evaluated at operating postures in the workspace. A planar arm model with shoulder and elbow joints and three pairs of antagonistic muscles was constructed in ADAMS. Stability behavior of shoulder and elbow joints was analyzed using the loci of eigenvalues in the s-plane. In the analysis of open-loop cocontraction of antagonist muscles with increasing activation from 5% to 100%, the eigenvalues of the shoulder and elbow joints were confined within the left half of the s-plane in a stripe of +/- j 0.5, and moved toward left onto the real axis. The shoulder eigenvalues were generally nearer to the imaginary axis than the elbow ones, indicating a more oscillatory behavior at the shoulder joint than that at the elbow joint. The effects of joint configuration evaluated within the workspace from 40 degrees to 110 degrees for the elbow and from 40 degrees to 120 degrees for the shoulder showed that the elbow eigenvalues were more prone to configuration changes, particularly elbow angles. We also developed a simulation paradigm for sampled data FES control systems that contain a mixture of continuous time components and sampling and hold effects. This simulation paradigm is useful for realistic simulation of local feedback controller performance.