Digital Powertrain Development, Mercedes-Benz AG, 70327, Stuttgart, Germany.
Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Nobelstraße 15, Stuttgart, Germany.
J Math Biol. 2020 Mar;80(4):1139-1158. doi: 10.1007/s00285-019-01455-z. Epub 2019 Nov 26.
Continuous control using internal models appears to be quite straightforward explaining human motor control. However, it demands both, a high computational effort and a high model preciseness as the whole trajectory needs to be converted. Intermittent control shows great promise for avoiding these drawbacks of continuous control, at least to a certain extent. In this contribution, we study intermittency at the motoneuron level. We ask: how many different, but constant muscle stimulation sets are necessary to generate a stable movement for a specific motor task? Intermittent control, in our perspective, can be assumed only if the number of transitions is relatively small. As application case, a single-joint arm movement is considered. The muscle contraction dynamics is described by a Hill-type muscle model, for the muscle activation dynamics both Hatze's and Zajac's approach are considered. To actuate the lower arm, up to four muscle groups are implemented. A systems-theoretic approach is used to find the smallest number of transitions between constant stimulation sets. A method for a stability analysis of human motion is presented. A Lyapunov function candidate is specified. Thanks to sum-of-squares methods, the presented procedure is generally applicable and computationally feasible. The region-of-attraction of a transition point, and the number of transitions necessary to perform stable arm movements are estimated. The results support the intermittent control theory on this level of motor control, because only very few transitions are necessary.
使用内部模型进行连续控制似乎可以很好地解释人类运动控制。然而，它既需要大量的计算工作，又需要高精度的模型，因为需要转换整个轨迹。间歇性控制似乎在一定程度上避免了连续控制的这些缺点。在本研究中，我们在运动神经元水平上研究了间歇性控制。我们提出了这样一个问题：为了完成特定的运动任务，生成稳定的运动，需要多少个不同但恒定的肌肉刺激集？在我们看来，只有在过渡次数相对较少的情况下，才能进行间歇性控制。作为应用案例，我们考虑了单关节手臂运动。肌肉收缩动力学由 Hill 型肌肉模型描述，肌肉激活动力学则同时考虑了 Hatze 和 Zajac 的方法。为了驱动小臂，我们实现了多达四个肌肉群。采用系统理论方法来找到恒定刺激集之间的最小过渡次数。还提出了一种用于分析人体运动稳定性的方法。指定了一个李雅普诺夫函数候选。由于使用了和的平方方法，所提出的方法具有广泛的适用性和计算可行性。还估计了过渡点的吸引区域和执行稳定手臂运动所需的过渡次数。结果支持了在这个运动控制层面的间歇性控制理论，因为只需要很少的过渡。
