Motor control model based on muscle synergy hypothesis.
A. Motor commands composed of linear combination of four basic signals. B. Coordinated muscles for each basic signals in quadrupedal walking. C. Coordinated muscles in bipedal walking. Note that the forelimb and hindlimb figures illustrate states at their respective phases and are not necessarily simultaneous.
Movement regulation based on forward speed, hip height, and trunk posture (trunk posture is regulated only during bipedal walking).
The control target and the muscles used for the control are shown in the same color.
Gait transition by using two additional pulses to trigger limb muscles.
Simulation results of quadrupedal and bipedal walking.
A. Stick diagram (see Supplementary Movies S1 and S2). Comparison of (B) elevation angle and (C) muscle activity with measured monkey data. These data show the right side during quadrupedal walking (blue) or bipedal walking (red). 0 and 100% of gait cycle indicate hindlimb liftoff. Vertical dotted, dashed, and solid lines indicate hindlimb touchdown and forelimb touchdown and liftoff, respectively. Gray regions indicate stance phase of each limb.
Simulation results of transition from quadrupedal to bipedal walking.
A. Stick diagram (see Supplementary Movie S3). B. Comparison of (B) elevation angle and (C) muscle activity with measured monkey data. These data show the ipsilateral side of the trigger limb (red) or trailing limb (blue). 0, 100, · · ·, 500% of gait cycle indicate hindlimb liftoff. Vertical dotted, dashed, and solid lines indicate hindlimb touchdown and forelimb touchdown and liftoff, respectively. Gray regions indicate stance phase of each limb. Elevation angles of the thigh and shank of the trigger limb are increased to take a large step before the transition, and then the trunk is raised by increasing the activity of the GM and BF muscles. These changes are indicated by red arrows.
Investigation of contribution of triger limb to gait transition using parameters and .
A. CoM-foot horizontal distance at touchdown of the trigger limb normalized by the stride length during quadrupedal walking before the transition. B. First criterion: CoM height averaged over one gait cycle after adding two pulses. Black lines are boundaries with a height greater than the success threshold (0.4 m). C. Second criterion: Time taken from touchdown to liftoff of the trigger limb when it took a large step. White lines are boundaries with a duration greater than the success threshold (0.6 s). From A, B, and C, the two criteria depending on the CoM-foot distance of the trigger limb are shown in D and E. White circles indicate the optimal result. Yellow and green circles indicate the examples used for comparison in Fig. 8. Successful gait transition is almost limited to a specific range (orange) of the CoM-foot distance of the trigger limb. The CoM-foot distance of the trigger limb is compared with the measured monkey data (arrow head).
Role of forward step length of trigger limb in gait transition based on inverted pendulum model.
A. Inverted pendulum model. B. Saddle dynamics. C. Application of simulation result of successful gait transition to inverted pendulum model, compared with application of measured monkey data. Dotted lines indicate the trajectories of rigorous inverted pendulum model. ‘Single stance’ and ‘double stance’ refer to the single and double stance phases of the hindlimbs, respectively. For both simulated and measured results of quadrupedal walking, the CoM position during the single stance phase starts just above the touchdown point of the trigger limb (θ ≃ 0) and moves forward. In contrast, during bipedal walking and gait transition, it starts behind the touchdown position (θ < 0) and advances forward through an inverted pendulum motion. D. Application of simulation result of failed gait transition due to small forward step length (see Supplementary Movie S4). E. Application of simulation result of failed gait transition due to too large forward step length (see Supplementary Movie S5).
Verification of role of large forward step length of trigger limb in gait transition.
A. Trajectories by applying simulation results for single stance phase of the hindlimbs during gait transtiion to inverted pendulum model with the CoM-foot horizontal distance at touchdown of the trigger limb. B. Error between the trajectories of simulation results and those of rigorous inverted pendulum model for the CoM-foot distance of the trigger limb. C. Onset angle θ. D. Duration when the trajectory is below the stable manifold. White circles indicate the optimal result (Fig. 8C). Yellow and green circles indicate the results of Figs. 8D and E, respectively.
