Data from: Control at stability's edge minimizes energetic costs: expert stick balancing

Stick balancing on the fingertip is a complex voluntary motor task that
requires the stabilization of an unstable system. For seated expert stick
balancers, the time delay is 0.23 s, the shortest stick that can be
balanced for 240 s is 0.32 m and there is a Embedded Image° dead zone for
the estimation of the vertical displacement angle in the saggital plane.
These observations motivate a switching-type, pendulum–cart model for
balance control which uses an internal model to compensate for the time
delay by predicting the sensory consequences of the stick's
movements. Numerical simulations using the semi-discretization method
suggest that the feedback gains are tuned near the edge of stability. For
these choices of the feedback gains, the cost function which takes into
account the position of the fingertip and the corrective forces is
minimized. Thus, expert stick balancers optimize control with a
combination of quick manoeuvrability and minimum energy expenditures.

指尖顶杆平衡是一项复杂的自主运动任务，需对不稳定系统进行稳定控制。对于坐姿的顶杆平衡专家而言，其反应延迟为0.23秒；可持续平衡240秒的最短杆长为0.32米；且在矢状面（sagittal plane）内的垂直位移角估计中存在一个Embedded Image°死区（dead zone）。这些观测结果启发了一种用于平衡控制的切换式摆-车模型（switching-type pendulum-cart model）——该模型通过预测顶杆运动的感官结果，利用内部模型（internal model）补偿时间延迟。采用半离散化方法（semi-discretization method）的数值模拟表明，反馈增益被调整至稳定边缘附近。在这些反馈增益的选择下，考虑指尖位置与修正力的代价函数（cost function）被最小化。因此，顶杆平衡专家通过快速机动性与最小能量消耗的结合实现控制优化。