An intermittent control model of flexible human gait using a stable manifold of saddle-type unstable limit cycle dynamics

Abstract

Stability of human gait is the ability to maintain upright posture during walking against external perturbations. It is a complex process determined by a number of cross-related factors, including gait trajectory, joint impedance and neural control strategies. Here, we consider a control strategy that can achieve stable steady-state periodic gait while maintaining joint flexibility with the lowest possible joint impedance. To this end, we carried out a simulation study of a heel-toe footed biped model with hip, knee and ankle joints and a heavy head-arms-trunk element, working in the sagittal plane. For simplicity, the model assumes a periodic desired joint angle trajectory and joint torques generated by a set of feed-forward and proportional-derivative feedback controllers, whereby the joint impedance is parametrized by the feedback gains. We could show that a desired steady-state gait accompanied by the desired joint angle trajectory can be established as a stable limit cycle (LC) for the feedback controller with an appropriate set of large feedback gains. Moreover, as the feedback gains are decreased for lowering the joint stiffness, stability of the LC is lost only in a few dimensions, while leaving the remaining large number of dimensions quite stable: this means that the LC becomes saddle-type, with a low-dimensional unstable manifold and a high-dimensional stable manifold. Remarkably, the unstable manifold remains of low dimensionality even when the feedback gains are decreased far below the instability point. We then developed an intermittent neural feedback controller that is activated only for short periods of time at an optimal phase of each gait stride. We characterized the robustness of this design by showing that it can better stabilize the unstable LC with small feedback gains, leading to a flexible gait, and in particular we demonstrated that such an intermittent controller performs better if it drives the state point to the stable manifold, rather than directly to the LC. The proposed intermittent control strategy might have a high affinity for the inverted pendulum analogy of biped gait, providing a dynamic view of how the step-to-step transition from one pendular stance to the next can be achieved stably in a robust manner by a well-timed neural intervention that exploits the stable modes embedded in the unstable dynamics.

Beta activity in the premotor cortex is increased during stabilized as compared to normal walking

“…This would be in line with the findings of Ihlen et al ( 2012 ) who reported that gait is unstable during weight transfer. Moreover, in a recent study, Kim and Collins ( 2015 ) showed that a “once-per-step” control of an ankle-foot prosthesis during push-off, reduced the effort associated with medio-lateral stability control during walking, and similar findings have been reported in model studies (Kim and Collins, 2013 ; Fu et al, 2014 ). All in all, these findings suggest an important role for a well-controlled push-off to maintain a stable gait pattern, and our findings suggest that there may be cortical involvement in such control.…”

Phase-dependent changes in local dynamic stability during walking in elderly with and without knee osteoarthritis

“…Interestingly, a recent paper (Kim and Collin, in press) showed that by manipulating push off, stability could be either increased or decresed, thereby suggesting and important role for push-off in maintaining a stable gait. In addition, a recent modeling study (Fu et al, 2014) showed that an otherwise unstable limit cycle model could be stabilized by including intermittent control in the form of a push-off burst. Altogether, these findings highlight the importance of transition from the stance phase to the swing phase in gait stability.…”

Preparatory Body State before Reacting to an Opponent: Short-Term Joint Torque Fluctuation in Real-Time Competitive Sports

“…Therefore, maintaining less joint energy before the step initiation may be important to prevent a delay in initiation and can be considered as the preparatory body state for the step initiation in a competitive sport. For further understanding of the dynamics of the competitive interaction and preparatory body state, a forward simulation study modeling the visco-elasticity component of limb joints [ 45 ] implementing anticipatory decision making [ 24 ] is required. The present kinetic analysis of adaptive movements in a conflicting environment may contribute to coaching skilled movement, rehabilitation of impairment in motor function, and implementation of movements in multi-joint robotics in a conflicting situation.…”