In this chapter, the resistance ability of the walking patterns generated by the control system against perturbations was evaluated. First, the role of the phases modulations based on leg loading information was assessed by using a condition based on the leg controller phase to trigger the transition from stance to swing. This resulted in the incapacity for the controller to properly compensate the asymmetry of the body rolling motion caused by the perturbation. As a consequence, small intensities of lateral per-turbation led to the disappearance of the walk gait coordination.
In contrast, when the transition condition based on leg loading information is used, asymmetry in the rolling motion amplitude results in an adjustment of the respective duty ratios of the legs on the right and left sides due to the modulation of the stance phase duration. This generates a recovery force that compensates the asymmetry and restores the posture through phase modulations. When applying a lateral perturbation at various timings during the walking cycle, it appeared that the control system with independent leg controllers was quite resistant to perturbations increasing the rolling motion amplitude, hence accelerating the lateral transfer of leg loading. In that case,
the controller was able to reject the perturbation within a few steps, thanks to the phase modulations. On the other hand, when the applied perturbation resulted in the decrease of the rolling motion amplitude, the lateral transfer of leg loading was slowed down. When the perturbation was over a certain threshold, the load supported by the foreleg did not become smaller than the threshold regulating the stance-to-swing transition, so that the foreleg could not swing. This perturbed the leg coordination, often leading to the fall of the model.
Consequently, an ascending coordination mechanism that promotes the transition to the swing phase in the foreleg when the ipsilateral hind leg is swinging, while reducing the duration of the subsequent foreleg swing phase, was implemented. It improved considerably the resistance ability of the control system against perturbations decreasing the rolling motion amplitude while preserving the good performances obtained in the other cases.
The influence of the walking cyclic period and speed on the stability was investigated and, in both cases, the stability was found to decreases. As the cyclic period increases, the rolling motion amplitude becomes larger so that the model falls more easily on the side when laterally perturbed. As regards the increase of the speed, the longitudinal transfer of leg loading mechanism increasingly interferes with the lateral transfer mechanism in the control of the stance termination of the legs, hence limiting the extent of the duty ratios adjustments that can be achieved.
With the proposed control system, the model could stably walk on terrains of medium degree of irregularity (including steps and slopes), demonstrating the achievement of a certain level of postural control.
Conclusions
6.1 Conclusions
This thesis considered the use of phase modulations based on leg loading information in a CPG controller to generate stable quadrupedal dynamic walk. Phase modulations are adjustments of the CPG activity resulting from the modulation of the respective durations of the stance and swing phases of the stepping motion. In this thesis, the stress was put on the role of the regulation of the stance to swing transition by the leg loading sensory information. The contribution of this mechanism to rhythmic motion control and posture control during locomotion in the range from low- to medium-speed was investigated using dynamics simulations.
These issues were considered both in the case of two-dimensional stepping, with the mo-tion in the frontal plane prevented, and three-dimensional dynamic walking. Although the implementations of the control systems used in each situation are quite different, both of them are grounded on the same common principles. In agreement with the objectives of this thesis, the transitions between the swing and the stance phases of the leg controller are regulated using leg loading sensory information. This, together with other considerations about adaptability, motivated the choice of a sensor-dependent CPG model.
A biologically-inspired approach was used to generate two-dimensional stepping with musculoskeletal models faithful to the anatomy of the cat. A neural controller able to induce adaptive stepping at various walking speeds with that model was developed in agreement with the common principles. Two-dimensional alternate stepping at constant speed with the fore and the hind legs separately was realized using independent leg controllers. The contribution of the control of the stance-to-swing transition using leg loading information to the emergence and the stabilization of the alternate coordination was explained and verified. Finally, adaptive stepping at various walking speeds with the
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hind legs was realized and the adaptations of the stepping patterns that occurred in the simulations were compared with the ones happening in real animals. Similar tendencies were found and an interesting conclusion about the role of leg-loading-information-based regulation of the stance-to-swing transition in animals was drawn accordingly.
Limitations related to the complexity of the neural controller implementation became evident when trying to extend the control system architecture to generate walking pat-terns in three dimensions. Accordingly, a more traditional approach, combining trajec-tory generation and local PD control, was substituted to the muscular model and the synergies for the generation of the motor patterns, resulting in a great simplification of the leg controller structure. Using phase modulations based on leg loading informa-tion, left-right alternate stepping coordination naturally emerges as a consequence of the entrainment between the stepping of the legs, the body rolling motion and the phase modulations. The vertical coordinate of the AEP position, as well as the PD control gains of the knee and ankle joints, were found to influence the emergent gait. Appropri-ate setting of these two cAppropri-ategories of parameters resulted in the emergence of a walking gait that could be generated with independent leg controllers. Walking patterns could be realized in a broad range of cyclic periods and speeds by adjusting only a few number of the controller parameters.
Next, the stability of the walking patterns was investigated using lateral perturbations.
Phase modulations could stabilize the disturbed posture subsequent to the application of a perturbation at all the timings considered, except when the perturbation resulted in a reduction of the modulus of the next extremum of the body roll angle, hence slowing down the lateral transfer of leg loading that occurs during left-right alternate stepping. As a consequence, the foreleg on the loaded side could not swing anymore. An original ascending coordination mechanism was implemented, preventing this situation and contributing to the global stabilizing action of the phase modulations. After the addition of this mechanism, the control system achieved good performances for all the perturbation application timings. Moreover, the model could walk on terrains with a medium level of irregularity both with short (around 0.40 s) and long (around 0.63 s) cyclic periods.
In conclusion, the work presented in this thesis supports the evidence that phase modula-tions based on leg loading information, and in particular the regulation of the transition from stance to swing using this sensory information, plays a great role in rhythmic motion control and posture control during the locomotion. This mechanism contributes to the emergence and the stabilization of alternate stepping coordination in two-dimensional stepping and left-right alternate stepping in quadrupedal dynamic walk, so that loco-motion can be generated even with independent leg controllers in both cases. Regarding quadrupedal dynamic walk, phase modulations adjust the rhythmic motion of the legs to stabilize the rolling motion of the body against various disturbances. To cope with
perturbations slowing down the lateral transfer of leg loading, against which the per-formances realized by the phase modulations mechanism alone were relatively low, an additional coordination mechanism, promoting stance-to-swing transition in the fore-leg when the ipsilateral hind fore-leg is swinging, was implemented. With that additional mechanism, the control system was able to tackle terrain irregularities (such as steps and slopes) while stabilizing the posture, hence demonstrating basic integration of pos-ture and rhythmic motion controls. As using phase modulations based on leg loading information allows to make use of the embodiment for walking (such as the alternate stepping of the legs and rolling motion of the body), this could be realized with a simple and distributed control system.