Reaction null-space filter: extracting reactionless synergies for optimal postural balance from motion capture data

This paper introduces the notion of a reactionless synergy: a postural variation for a specific motion pattern/strategy, whereby the movements of the segments do not alter the force/moment balance at the feet. Given an optimal initial posture in terms of stability, a reactionless synergy can ensure optimality throughout the entire movement. Reactionless synergies are derived via a dynamical model wherein the feet are regarded to be unfixed. Though in contrast with the conventional fixed-feet models, this approach has the advantage of exhibiting the reactions at the feet explicitly. The dynamical model also facilitates a joint-space decomposition scheme yielding two motion components: the reactionless synergy and an orthogonal complement responsible for the dynamical coupling between the feet and the support. Since the reactionless synergy provides the basis (a feedforward control component) for optimal balance control, it may play an important role when evaluating balance abnormalities or when assessing optimality in balance control. We show how to apply the proposed method for analysis of motion capture data obtained from three voluntary movement patterns in the sagittal plane: squat, sway, and forward bend.