A systems-theoretic analysis of low-level human motor control: application to a single-joint arm model

Continuous control using internal models appears to be quite straightforward explaining human motor control. However, it demands both, a high computational effort and a high model preciseness as the whole trajectory needs to be converted. Intermittent control shows great promise for avoiding these drawbacks of continuous control, at least to a certain extent. In this contribution, we study intermittency at the motoneuron level. We ask: how many different, but constant muscle stimulation sets are necessary to generate a stable movement for a specific motor task? Intermittent control, in our perspective, can be assumed only if the number of transitions is relatively small. As application case, a single-joint arm movement is considered. The muscle contraction dynamics is described by a Hill-type muscle model, for the muscle activation dynamics both Hatze's and Zajac's approach are considered. To actuate the lower arm, up to four muscle groups are implemented. A systems-theoretic approach is used to find the smallest number of transitions between constant stimulation sets. A method for a stability analysis of human motion is presented. A Lyapunov function candidate is specified. Thanks to sum-of-squares methods, the presented procedure is generally applicable and computationally feasible. The region-of-attraction of a transition point, and the number of transitions necessary to perform stable arm movements are estimated. The results support the intermittent control theory on this level of motor control, because only very few transitions are necessary.