l6  + l7 Foot 0。04 m

l2 , l3 , l4 Spring Attach。 0。02 m

l7 , l8 , l9

S1 Spring const。 100a

S2 Spring const。 200a

S3 Spring const。 800a

S4 Spring const。 450a

M Total mass 0。95 kg

a   Spring constants are dimensionless。

without any sensory feedback: through the dynamic interactions between the ground, musculoskeletal structure, and the motor torque, the leg movement is self-organized into a stable periodic pattern。

In order to analyze more detailed behavior, the body movement, knee and ankle joint angles, and ground reaction force are analyzed as shown in Fig。 5。 In this figure, for the analysis of the periodic gait, the data of 10 steps are aligned with respect to the stance phase measured by the ground reaction force。 In general, the behavior of this simulated robot largely resembles that of human locomotion in terms of the salient features explained in the previous section; Vertical rise of the body starts after the leg touchdown and before the takeoff; Significant knee flexion at the beginning of stance phase; Extension of ankle joint toward the end of stance phase; Multiple peaks in the ground reaction force。 The limit of this model is, however, reflected on the quantitative measures; The vertical body excursion is approximately 5% of the leg length, and the amplitude of knee flexion (i。e。 the difference between the maximum and minimum knee angles) is restricted to approximately 25 degrees (they are 4% and 60 degrees in the human experiment, respectively)。

The underlying dynamics of this gait pattern can be represented by observing the forces generated in the biarticular springs (Fig。 5)。 The dynamics of knee movement is mainly determined by the

Fig。 4。   Stick figures of the walking behavior in simulation。 (a) The behavior of one leg during four leg steps, and (b) the behavior of two legs during a single step。

Fig。 5。 Joint trajectories and force profiles in walking simulation。 Vertical body movement, angular trajectories of knee and ankle joints, and vertical ground reaction forces (left figures from top to bottom) are plotted over 5 leg steps。 Right figures show the forces F 1, F 2, F 3, and F 4 generated in the four springs S1, S2, S3, and S4 respectively (right figures from top to bottom)。 The data are aligned with respect to the stance phase depicted by gray  areas。

S1 spring。 The antagonistic force equilibrium generated by the springs S1 and S2 regulates the knee movement, and the knee extension toward the end of stance phase is mainly influenced by the spring S1 as the hip joint rotates backwards。 The dynamics of ankle movement is determined by the spring S3, and the spring S4 generates small force for holding the ankle joint。论文网

3。2。Robot experiment

The simulation model is now implemented in a physical robot platform as shown in Fig。 6。 This robot consists of passive joints in knees and ankles, and two servomotors (Conrad HS-9454) are used in the hip joints as in the simulation model。 We used four tension springs and rubber materials at the two ground contact points in a foot in order to gain high ground friction and to avoid impact force at touchdown。 The same control parameters were used to conduct a set of experiments。