Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China.
J Neuroeng Rehabil. 2021 Mar 22;18(1):54. doi: 10.1186/s12984-021-00843-1.
Upright standing requires control of an inherently unstable multi-joint human body within a small base of support, despite biological motor and / or sensory noise which challenge balance. Without applying perturbations, system identification methods have been regarded as inadequate, because the relevant internal biological noise processes are not accessible to direct measurement. As a result, unperturbed balance studies have been limited to investigation of behavioral patterns rather than possible underlying control strategies.
In this paper, we present a mathemathically rigorous system identification method that is applicable to study the dynamics and control of unperturbed balance. The method is derived from autocorrelation matrices with non-zero time lags and identifies the system matrix of a discrete-time dynamic system in the presence of unknown noise processes, without requiring any information about the strength of the noise.
Unlike reasonable 'least-squares' approaches, the performance of the new method is consistent across a range of different combinations of internal and measurement noise strengths, even when measurement noise is substantial. We present a numerical example of a model that simulates human upright balancing and show that its dynamics can be identified accurately. With a biomechanically reasonable choice of state and input variables, a state feedback controller can also be identified.
This study provides a new method to correctly identify the dynamics of human standing without the need for known external perturbations. The method was numerically validated using simulation that included realistic features of human balance. This method avoids potential issues of adaptation or possible reflex responses evoked by external perturbations, and does not require expensive in-lab, high-precision measurement equipment. It may eventually enable diagnosis and treatment of individuals with impaired balance, and the development of safe and effective assistive and / or rehabilitative technologies.
直立站立需要在小支撑基础上控制固有不稳定的多关节人体，尽管存在挑战平衡的生物运动和/或感觉噪声。在不施加扰动的情况下，系统识别方法被认为是不充分的，因为相关的内部生物噪声过程无法进行直接测量。因此，未受扰的平衡研究仅限于行为模式的研究，而不是可能的潜在控制策略的研究。
在本文中，我们提出了一种严格的数学系统识别方法，适用于研究未受扰平衡的动力学和控制。该方法源自具有非零时滞的自相关矩阵，并在存在未知噪声过程的情况下识别离散时间动态系统的系统矩阵，而无需有关噪声强度的任何信息。
与合理的“最小二乘”方法不同，新方法的性能在不同的内部和测量噪声强度组合范围内是一致的，即使测量噪声很大。我们提出了一个模拟人体直立平衡的模型的数值示例，并表明可以准确识别其动力学。通过对状态和输入变量进行合理的生物力学选择，还可以识别状态反馈控制器。
这项研究提供了一种无需外部已知扰动即可正确识别人体站立动力学的新方法。该方法通过包括人体平衡的现实特征的模拟进行了数值验证。该方法避免了外部扰动引起的适应或可能的反射反应的潜在问题，并且不需要昂贵的实验室、高精度测量设备。它最终可能能够诊断和治疗平衡受损的个体，并开发安全有效的辅助和/或康复技术。
