Constraint and exploitation of redundant degrees of freedom during walking
What kind of leg trajectories are selected during human walking? To address this question, we have analyzed leg trajectories from two points of view: constraint and exploitation of redundant degrees of freedom. First, we computed the optimal leg swing trajectories for forward and backward walking that minimize energy cost for the condition of having some stretch of elastic components at the beginning of the leg swing and found that the optimal trajectories explain the characteristics of measured trajectories. Second, we analyzed how and when leg joints cooperate to adjust the toe position relative to the hip position during walking and found that joint coordination (i.e., joint synergy) is exploited at some control points during human walking, e.g., the toe height when it passes through its lowest position from the ground and the leg posture at the beginning of the double-support phase. These results suggest that the basic constraint in selecting a leg trajectory would be the minimization of energy cost; however, the joint trajectory is not strictly controlled over the entire trajectory and redundant degrees of freedom are exploited to adjust the foot position at some critical points that stabilizing walking.
backward walking joint synergy energetic optimality biped walking uncontrolled manifold analysis