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Fig。 1。 Behavior of human walking。 Vertical movement of the body, angular trajectories of hip, knee and ankle joints, and vertical ground reaction forces (from top to bottom figures) are shown over time-series 3 leg steps (a) and the data aligned with respect to the ground reaction force (b)。 Gray areas in figure (b) indicate the stance phase of the left leg。

a human subject。 In this experiment, we use an instrumented treadmill with a set of high-speed infrared cameras for motion capture (6 Qualisys motion capture units; sampling frequency of 240 Hz) and force plates (Kistler 9281B11; sampling frequency of 1000 Hz), with which we analyze the kinematics of human behavior as well as the ground reaction force。

A human subject was asked to walk on a treadmill at a constant speed of 1。0 m/s for  20  s,  and  the  kinematics  and the ground reaction force  were  analyzed。  Fig。  1  shows  a set of basic characteristics of human walking, which are generally agreed in biomechanics。 Firstly, walking dynamics can be clearly distinguished by observing the vertical GRF: the vertical GRF exhibits two peaks in a stance phase [12]。 Secondly, the vertical body excursion during walking increases toward the middle of the stance phase, and the lowest peaks occur slightly after the touchdown and before takeoff of a leg [6,13]。 And thirdly, the knee and ankle joints of the stance leg show flexion [1,14]。

It is important to note that the compass gait model cannot reproduce some of these aspects of human walking dynamics (Fig。 2)。 Firstly, there is a significant difference in the vertical movement of the body。 While the compass gait model shows the elliptic trajectory of the body movement around the foot–ground contact during a stance phase, in the human body excursion, vertical position of the body decreases at the beginning of the stance phase, then it increases and decreases; Toward the end of the stance phase, it starts increasing again。 An advantage of this movement of the body could be that it has less displacement of vertical oscillation of the body。

Secondly, the behavior of the knee joint during stance phase is also different from that of the compass gait model: At the beginning of stance phase, the knee angle first decreases  before a large peak。 A possible advantage of the first decrease is that the knee joint could absorb the impact force at touch down。 Thirdly, the ankle joint shows significant dynamics although the compass gait model has no ankle joint; There is a small peak at the beginning, and it increases toward the end of stance phase。 Finally, the ground reaction force shows an M-shape, whereas the compass gait model generally shows a single peak。

In the rest of this study, we investigate a model which exhibits some of these features in human locomotion。 By understanding the underlying mechanisms, we will be able to not only obtain additional insights into the nature of human locomotion, but also design and build better legged  robots。

2。2。Spring–mass model for walking

The spring–mass model was originally proposed for character- izing running behavior of animals [7–9]。 The model consists of a body represented as a point mass and a leg approximated by a lin- ear spring。 This extremely simple theoretical model has explained a number of eminent features of running behavior in animals in- cluding humans。 Recently, this model was extended for walking behavior, which explained a few aspects of human bipedal loco- motion including the complex dynamics introduced in the previ- ous subsection [6]。

Although the spring–mass model for walking shows a signif- icant plausibility as a walking model of human, this   theoretical