A self-paced treadmill automatically adjusts speed in real-time to match the user’s walking speed, presumably leading to a more nature gait than fixed-speed treadmill. Previous studies based on nonlinear time serials analysis have proved that self-paced treadmill walking trends to be more unstable than fixed-speed treadmill walking for both upper body accelerations and lower extremity angles due to the treadmill accelerations. This instability would increase the risk of fall and influence the control of neuromuscular system. However, the conceptual model of dynamic stability for self-paced treadmill walking was in a state of lack, leading to the design of ideal self-paced control algorithms more difficulty.

Inverted pendulum model has already shown its advantages to explain many walking principles in spite of its simplicity. In dynamic situations ‘extrapolated center of mass’ (XcoM) was proposed as the condition of stability which also took the horizontal velocity of center of mass (CoM) relative the center of pressure (CoP) into account. In simulations, stable walking could be achieved by placing the CoP at a fixed offset from the XcoM in both anteroposterior and mediolateral directions, which called ‘constant offset control’. For self-paced treadmill walking, the CoP position was fluctuated during walking according the treadmill speed which meant the simulation must be transformed into the treadmill coordinate. However, due to the accelerations of treadmill, the treadmill coordinate was a non-inertial frame. Treadmill accelerations must be carefully considered before the stability condition was concluded. Meanwhile, as we all known, the gait phase when the accelerations were applied would have impacts on the walking stability. Studies have shown that earlier disturbance could be corrected by the foot placement according the ‘constant offset control’ and would not significantly affect the coming steps, while the later disturbance before foot placement could not be corrected merely by foot placement which would have more influence on the coming steps. It was meaningful to figure out the effect of the gait phase when disturbances were applied for self-paced treadmill control.

This paper proposed a non-inertial frame inverted pendulum model to analysis the condition of stability during continuous self-paced treadmill walking and evaluated the influence of the gait phase when the treadmill accelerations were applied. Simulations were done for 50 continuous self-paced treadmill walking at the walking speed of 0.5m/s, 1.0m/s, 1.5m/s, and the accelerations were applied at different gait phase such as toe-off, foot-flat and heel-strike. The stability conditions were concluded for different walking situations. The simulations results showed that the magnitude and gait phase of the accelerations would have significantly influence on the continuous self-paced treadmill walking and were meaningful for the development of better self-paced control algorithms.


The Condition of Dynamic Stability for Self-Paced Treadmill Walking Based on Inverted Pendulum Model

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Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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