Multi-experiment identification from short repeated transients:the human response to pushes in a Tai Chi posture
The effect of Tai Chi postures on the mechanical response of the body to external pushes is usually assessed with clinical balance scores, which say little about the underlying dynamics. We identify, for five subjects and eight postural conditions, linear models from the mechanical work transferred by a pendulum hitting the forearm to the change of the antero-posterior ground reaction force. Each trial contains 10 to 16 impacts, and each impact yields a transient of 0.55\,s only. Building on earlier analyses of these data, we improve the processing chain in three ways. The input is related to the energy lost by the pendulum and its repeatability is quantified. The output is defined component-wise, which makes it independent of the zeroing of the force plate. Finally, the impacts are stacked in a multi-experiment least-squares problem and validated on unseen impacts. Tenth-order ARX models then reach a median leave-one-impact-out fit of 65\%, against 72\% for the repeatability of the response itself, and never require stability enforcement, unlike estimation on averaged impacts. Closing the eyes lengthens the identified delay by about 70\,ms in all subjects, and the Tai Chi posture increases the antero-posterior force transmitted per joule in four of five subjects. Surface EMG envelopes show a tonic co-activation of the lower-leg muscles in this posture, a smaller reactive triceps burst and a fast habituation of the tibialis response. Together, they point to a stiffer, anticipatory postural strategy.