Intermittent control of unstable multivariate systems with uncertain system parameters

Stabilization of a Cart Inverted Pendulum: Improving the Intermittent Feedback Strategy to Match the Limits of Human Performance

Stabilization of the CIP (Cart Inverted Pendulum) is an analogy to stick balancing on a finger and is an example of unstable tasks that humans face in everyday life. The difficulty of the task grows exponentially with the decrease of the length of the stick and a stick length of 32 cm is considered as a human limit even for well-trained subjects. Moreover, there is a cybernetic limit related to the delay of the multimodal sensory feedback (about 230 ms) that supports a feedback stabilization strategy. We previously demonstrated that an intermittent-feedback control paradigm, originally developed for modeling the stabilization of upright standing, can be applied with success also to the CIP system, but with values of the critical parameters far from the limiting ones (stick length 50 cm and feedback delay 100 ms). The intermittent control paradigm is based on the alternation of on-phases, driven by a proportional/derivative delayed feedback controller, and off-phases, where the feedback is switched off and the motion evolves according to the intrinsic dynamics of the CIP. In its standard formulation, the switching mechanism consists of a simple threshold operator: the feedback control is switched off if the current (delayed) state vector is closer to the stable than to the unstable manifold of the off-phase and is switched on in the opposite case. Although this simple formulation is effective for explaining upright standing as well as CIP balancing, it fails in the most challenging configuration of the CIP. In this work we propose a modification of the standard intermittent control policy that focuses on the explicit selection of switching times and is based on the phase reset of the estimated state vector at each switching time and on the simulation of an approximated internal model of CIP dynamics. We demonstrate, by simulating the modified intermittent control policy, that it can match the limits of human performance, while operating near the edge of instability.

The effect of fear of falling on vestibular feedback control of balance

Vestibular sensation contributes to cervical‐head stabilization and fall prevention. To what extent fear of falling influences the associated vestibular feedback processes is currently undetermined. We used galanic vestibular stimulation (GVS) to induce vestibular reflexes while participants stood at ground level and on a narrow walkway at 3.85 m height to induce fear of falling. Fear was confirmed by questionnaires and elevated skin conductance. Full‐body kinematics was measured to differentiate the whole‐body centre of mass response (CoM) into component parts (cervical, axial trunk, appendicular short latency, and medium latency). We studied the effect of fear of falling on each component to discern their underlying mechanisms. Statistical parametric mapping analysis provided sensitive discrimination of early GVS and height effects. Kinematic analysis revealed responses at 1 mA stimulation previously believed marginal through EMG and force plate analysis. The GVS response comprised a rapid, anode‐directed cervical‐head acceleration, a short‐latency cathode‐directed acceleration (cathodal buckling) of lower extremities and pelvis, an anode‐directed upper thorax acceleration, and subsequently a medium‐latency anode‐directed acceleration of all body parts. At height, head and upper thorax early acceleration were unaltered, however, short‐latency lower extremity acceleration was increased. The effect of height on balance was a decreased duration and increased rate of change in the CoM acceleration pattern. These results demonstrate that fear modifies vestibular control of balance, whereas cervical‐head stabilization is governed by different mechanisms unaffected by fear of falling. The mechanical pattern of cathodal buckling and its modulation by fear of falling both support the hypothesis that short‐latency responses contribute to regulate balance.