محدودیت و بهره برداری از درجات برکنار شده آزادی در پیاده روی

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.

Redundant degrees of freedom (DOFs) in our bodies are sources of adaptability and dexterity because the redundancy allows for a variety of solutions to accomplish a task. In this paper, we consider the following two problems to understand the underlying control mechanisms that manipulate redundancy during human walking: (1) how the redundancy is constrained and (2) how it is exploited. The first is a traditional problem that asks what kinds of criteria are adopted in the selection of a trajectory from an infinite number of possibilities that can accomplish a given task. This question also asks what the goal of learning is for living bodies, a question that is also important for understanding the learning mechanism of living bodies. The latter is a problem well described in a story told by Bernstein “a skilled blacksmith’s hammer hits a given target correctly, but his joint trajectories are not constant and show variability across a series of strikes”. From this observation, Bernstein concluded that the variance of each joint trajectory is not independent and that to accomplish a task, variance at critical points (in this case, the hammer position) is suppressed by joint coordination that exploits redundancies [1]. What, then, are the critical points used for stable walking, and how are redundant degrees of freedom in our leg joints exploited during walking? The following sections detail our results concerning these two problems. Section 2 discusses a result about the constraint on DOFs in the selection of leg swing trajectories during forward and backward walking, and Section 3 shows analytical results on joint coordination (i.e., joint synergy) during walking.

The results in this study on the constraint in the selection of the leg trajectory during walking correspond to the swing phase; however, the results and many previous studies discussing the relation between energy cost and locomotor parameters would support the hypothesis that the basic strategy to determine a locomotor pattern is to minimize the energy cost. The results of our analyses have also suggested that the control strategy for walking would not be to make the entire joint trajectory approach the optimal one but to adjust the foot position at some critical points that stabilize walking by exploiting redundant DOFs. For instance, the toe height when it passes through its lowest position from the ground is precisely tuned by joint synergy, which would contribute to the avoidance of stumbling. This finding is also consistent with the result obtained in Section 2, which suggests that elastic components contribute to the rising of the foot during leg swing. Just before the beginning of the double-support phase, the hip height is controlled by joint synergy and the variance of the posture of the swing leg decreased, which would suppress the variance of the impact at touch-down and effectively avoid falling down. The UCM analysis also showed that joint synergy is exploited to adjust the horizontal toe position at the kick-off phase as well. These findings tell us that joint synergy is utilized at some critical points to produce stable walking, providing a new perspective for understanding the control strategy of human walking. Our study also includes some limitations that should be considered in future studies. For instance, in the analysis of the constraint in the selection of the leg swing trajectory, we assumed the extensions of the tendon in the iliopsoas for forward walking and the Achilles tendon for backward walking. However, because few studies have measured the length of tendons during walking, we have no physiological data that support our assumptions. In the analysis of the exploitation of redundancies, we analyzed the leg trajectory in terms of two kinds of UCMs, the horizontal and vertical toe position relative to the hip joint. However, there would be many other possible UCMs to find control points for walking. For instance, the toe velocity could be a potential candidate for examination, because Wisse (2006) suggested that the velocity control of the foot just before touch-down improves the stability of walking [10]. It would also be interesting to consider how such forms of joint synergy are realized, in other words, whether these forms of synergies are controlled by the nervous system or intrinsically embodied in the physical structure of our bodies.