预紧式并联六维加速度传感器的解耦算法研究

Research on the decoupling algorithm of pre-stressed parallel six-axis accelerometer

针对六维加速度传感器的解耦难度与构型复杂度存在矛盾的现状,给出了12支链预紧式并联六维加速度传感器的设计方案,并在四维位形空间内构建了解耦算法。通过重组输入量并联列求解正向动力学方程和力协调方程,剖析了输出量的构成成份。通过引入前置、后置矩阵以及"辅助角速度"的概念,将动力学方程转换成两组形式简单的一阶线性常微分方程,并运用梯形方法推导出关键特征量的显式递推公式。解耦算法与ADAMS仿真的相对误差为0.62%,且前者的计算效率更高;试验结果显示,实物样机在1 min内的测量误差为8.42%,验证了设计方案的可行性。通过在离散节点处进行Taylor展开,推导出局部截断误差的解析式,为解耦精度的提高提供了依据。进一步地,将解耦算法推广至更一般化的情形,通过引入两个关于向量独立元素的定理,证明出预紧式并联六维加速度传感器的最少支链数为7,对应拓扑构型的最少自由度为6。

Aiming at the present situation of the contradiction existing between the decoupling difficulty and configuration complexity of six-axis accelerometer, a new design scheme of pre-stressed parallel six-axis accelerometer with 12 branch chains is presented, and the decoupling algorithm in four dimensional configuration-space is constructed. By recomposing the input parallel items and solving forward dynamics equations and force coordination equations, the ingredients of the outputs are dissected. Through introducing pre-matrix, post- matrix and aided angular velocity, the complex dynamic equations are transformed into two simple linear ordinary differential equations, and the explicit recursive formulas of key characteristic quantities are derived using trapezoidal method. ADAMS simulation is conducted to verify the decoupling algorithm, and the relative composite error between the decoupling algorithm and ADAMS simulation is only 0.62% , and the decoupling algorithm has higher calculation efficiency. Laboratory test results show that within one minute the composite error of the real physical prototype is 8.42% , which verifies the feasibility and correctness of the proposed design scheme. Through Taylor expansion around discrete nodes, the analytic formulas of local truncation error are derived, which provides a basis for improving the decoupling accuracy. Furthermore, the decoupling algorithm is generalized to be suitable for general configuration. Through introducing two theorems concerning vector independent elements, it is proved that the least number of branch chains for the pre-stressed parallel six-axis accelerometer is 7, and the least degrees of freedom for corresponding topological configuration is 6.