Constraint and exploitation of redundant degrees of freedom during walking

Abstract

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.

Optimality of Upper-Arm Reaching Trajectories Based on the Expected Value of the Metabolic Energy Cost

“…These studies have not focused on the expected value of energy cost; however, the results indicate that the design of the movement trajectory is not independent of the energy cost. As noted in section 1, it has been reported that the characteristics of locomotor parameters, such as stride frequency and stride length, can also be explained well by the criterion of the minimum energy cost (Zarrugh & Radcliffe, 1978;Nishii, 2000Nishii, , 2006Nishii et al, 2012;Minetti & Alexander, 1997;Donelan et al, 2001). Although a simple 1-DOF linear musculo-skeletal model was used in our study due to the difficulty of computing the optimal trajectory, our results and the previous studies noted suggest that minimization of the energy cost would be a basic strategy in motor planning in living beings (Nishii & Taniai, 2009).…”

“…On the other hand, many studies have reported that the characteristics of legged locomotor patterns can be explained well by the minimum metabolic energy cost model (Zarrugh & Radcliffe, 1978;Nishii, 2000Nishii, , 2006Nishii, Hashizume, Kaichida, Suenaga, & Tanaka, 2012;Minetti & Alexander, 1997;Donelan, Kram, & Kuo, 2001). Saving energy costs would be an important strategy for sustaining life in organisms.…”

An analysis of leg joint synergy during backward walking

“…Recent our analysis has shown that the joint trajectories during walking show some fluctuations for each stride, however, such fluctuations are mutually compensated each other so as to suppress the fluctuation of the toe position at some specitic moments in a stride cycle, e.g., during double support phase and at the moment when stumbling often occurs in the middle of the swing phase [3]. Such cooperative joint movements are called joint synergy, and our analysis suggested that high joint synergy is often observed at critical points to realize stable walking.…”

“…On the other hand, our previous study have suggested that the leg swing trajectories of forward and backward walking are designed so as to minimize the energy cost under some constraints that stabilizes walking [3]. Many other previous studies also have shown the evidences that legged locomotor patterns are well optimized on energy cost [4]- [9].…”

Hierarchical control by a higher center and the rhythm generator contributes to realize adaptive locomotion

“…The second point is that it is unclear how the period and amplitude of the motor command from the rhythm generator are controlled independently in order to realize a target motion. Many studies on walking patterns have suggested that many locomotor parameters, such as the stance length and stride period, are optimized for each locomotion speed, depending on the energy cost (Zarrugh & Radcliffe, 1978; Minetti & Alexander, 1997; Nishii, 2000; Donelan, Kram, & Kuo, 2001; Nishii, 2006; Nishii, Hashizume, Kaichida, Suenaga, & Tanaka, 2011). These results imply that not only the period of the motor command, but also the amplitude, is precisely controlled.…”