A relation spectrum inheriting Taylor series: muscle synergy and coupling for hand

Abstract

There are two famous function decomposition methods in math: the Taylor series and the Fourier series. The Fourier series developed into the Fourier spectrum, which was applied to signal decomposition and analysis. However, because the Taylor series function cannot be solved without a definite functional expression, it has rarely been used in engineering. We developed a Taylor series using our proposed dendrite net (DD), constructed a relation spectrum, and applied it to decomposition and analysis of models and systems. Specifically, knowledge of the intuitive link between muscle activity and finger movement is vital for the design of commercial prosthetic hands that do not need user pre-training. However, this link has yet to be understood due to the complexity of the human hand. In this study, the relation spectrum was applied to analyze the muscle—finger system. One single muscle actuates multiple fingers, or multiple muscles actuate one single finger simultaneously. Thus, the research was focused on muscle synergy and muscle coupling for the hand. The main contributions are twofold: (1) The findings concerning the hand contribute to the design of prosthetic hands; (2) The relation spectrum makes the online model human-readable, which unifies online performance and offline results. Code is available at https://github.com/liugang1234567/Gang-neuron.

摘要

数学中有两种著名的函数分解方法:泰勒级数和傅里叶级数。傅里叶级数发展成为傅里叶频谱,用于信号分解和分析;而泰勒级数的求解需要已知具体函数表达式,所以其在工程领域很少被应用。本文使用树突网络发展了泰勒级数,构造了关系谱,并将其应用于模型或系统分解和分析。了解肌肉激活与手指运动之间的直观联系对于开发无需用户预训练的商业假肢至关重要。然而,由于人手的复杂性,该直观联系尚未被理解。本文使用关系谱分析了肌肉—手指系统。在手指运动中,一块肌肉同时驱动多个手指,多块肌肉同时驱动一个手指。因此,本研究聚焦于手部的肌肉协同与耦合。本文有两个主要贡献:(1)有关手部的发现有助于假肢手的设计;(2)关系谱使在线模型可读,从而统一了在线性能和离线结果。开源代码见https://github.com/liugang1234567/Gang-neuron。