Quiet standing: The Single Inverted Pendulum model is not so bad after all

Abstract

In the study of balance and postural control the (Single) Inverted Pendulum model (SIP) has been taken for a long time as an acceptable paradigm, with the implicit assumption that only ankle rotations are relevant for describing and explaining sway movements. However, more recent kinematic analysis of quiet standing revealed that hip motion cannot be neglected at all and that ankle-hip oscillatory patterns are characterized by complex in-phase and anti-phase interactions, suggesting that the SIP model should be substituted by a DIP (Double Inverted Pendulum) model. It was also suggested that DIP control could be characterized as a kind of optimal bi-axial active controller whose goal is minimizing the acceleration of the global CoM (Center of Mass). We propose here an alternative where active feedback control is applied in an intermittent manner only to the ankle joint, whereas the hip joint is stabilized by a passive stiffness mechanism. The active control impulses are delivered to the ankle joint as a function of the delayed state vector (tilt rotation angle + tilt rotational speed) of a Virtual Inverted Pendulum (VIP), namely a pendulum that links the ankle to the CoM, embedded in the real DIP. Simulations of such DIP/VIP model, with the hybrid control mechanism, show that it can reproduce the in-phase/anti-phase interaction patterns of the two joints described by several experimental studies. Moreover, the simulations demonstrate that the DIP/VIP model can also reproduce the measured minimization of the CoM acceleration, as an indirect biomechanical consequence of the dynamic interaction between the active control of the ankle joint and the passive control of the hip joint. We suggest that although the SIP model is literally false, because it ignores the ankle-hip coordination, it is functionally correct and practically acceptable for experimental studies that focus on the postural oscillations of the CoM.

Force accuracy rather than high stiffness is associated with faster learning and reduced falls in human balance

“…7B, 8B). Experimental and modelling studies on quiet standing suggest that the goal of the central nervous system is not to keep the centre of mass at a constant position, but rather to minimize its acceleration 2,26 .…”

“…Postural balance requires the whole body centre of mass (CoM) to be maintained within the base of support during both self-initiated and externally triggered disturbances of stability. In human postural sway, the dynamic relationship between the combined sagittal ankle joint moment and sagittal position of the CoM is similar to the control of an unstable, inverted pendulum 1,2 . Since the passive stiffness of the ankle joint is lower than the growth-rate of the gravitational toppling torque, an active feedback control mechanism is needed for upright standing 3,4 .…”

Modeling the neuro-mechanics of human balance when recovering from a fall: a continuous-time approach

“…These delays are difficult to reconcile with the stable behavior observed and would require a high cognitive load to be managed appropriately. A recent simulation-based study [38] has proposed a control mechanism where the ankle is controlled via an intermittent control, while the hip is control using an intrinsic stiffness modality. It was hypothesized that the critical stiffness value to maintain the stability of the trunk hinged at the hip joint is much smaller than for the whole body hinged at the ankle.…”

Standing Balance Assessment by Measurement of Body Center of Gravity Using Smartphones

“…Attempts to improve the model accuracy and explanatory capabilities encompass the Double Inverted Pendulum, which involves the coordinated control of ankle and hip joints, and the association of a Virtual Inverted Pendulum to the double pendulum. The virtual inverted pendulum is an inverted pendulum that doesn't exist physically but can be thought as an ideal connection between the ankle joint and the center of mass of the body, also enabling the stabilization of the system with mechanisms similar to those studied for the single inverted pendulum [18].…”