考虑非线性力矩传递迟滞的柔性关节机械臂迭代式动力学建模

Considering the great demands of flexible joint manipulator for high precision operations in aerospace, equipment manufacturing and other fields, how to improve its trajectory accuracy and dynamic response characteristics is still a research hotspot. .The model based high performance controller is an important way to improve the positioning accuracy, rapidity and stability of the manipulator. However, a variety of strong nonlinearities introduced by flexible joint lead to the traditional dynamic analysis methods which are not suitable for dynamics description of flexible joint manipulator with high degree of freedom. Considering the advantages of the axis-invariant theory to characterize manipulator system structures and operations, this project is going to propose a dynamic analysis method for flexible joint manipulators, which is concise, accurate and fast, and can clearly reflect the topology and chain-order relations of kinematic chains. Based on experimental analysis and theoretical deduction, we will reveal the mechanism and influencing factors of complex and strong nonlinearities such as static and dynamic friction its nonlocal hysteresis, and torsional rigidity introduced by harmonic drive joints, and the torque transfer hysteresis characterization of flexible joint with varying frequency and amplitude excitations will also be discussed. By analyzing the association form of joint flexibility and axis-invariant, we plan to establish a precise dynamic model of flexible joint, and parameterized and stylized explicit dynamic equations of multi-axis flexible joint manipulator based on axis-invariant, all which will provide theoretical basis on improving the positioning accuracy, real-time property and accuracy of modeling and calculation, and system development efficiency of manipulator.

面向航空航天、装备制造等高精密作业对柔性关节机械臂的重大需求，如何提高机械臂位置跟踪精度与动态响应特性是当前机器人领域研究的热点。基于模型的高性能控制器是提高机械臂定位精度、快速性和稳定性的重要手段，而柔性关节引入的强非线性导致传统动力学分析方法不适用于高自由度柔性关节机械臂动力学特性描述。鉴于轴不变量表征机械臂系统结构与运算的优势，本项目拟提出一种简洁、计算精度高速度快，能够清晰反映运动链拓扑及链序关系的柔性关节机械臂动力学分析方法。理论与实验相结合，揭示谐波传动关节的迟滞、静动态摩擦及其非局部滞回、扭转刚度等强非线性的产生机理与影响因素，给出变频变幅激励下关节力矩传递迟滞特性与表征方法，建立关节柔性与轴不变量的关联形式，基于轴不变量开展柔性关节精细动力学、多柔性关节机械臂参数化、程式化的显式动力学建模研究，为提高机械臂定位精度、建模与解算的实时性与精确性、以及开发效率提供理论支撑。

由于柔性关节引入的强非线性导致传统动力学分析方法不适用于高自由度柔性关节机械臂动力学特性描述。本研究首先建立了变频变幅激励下的非线性动态迟滞模型，通过将减速器内部阻尼引入到PI动态迟滞模型中，给出用来描述柔性关节非线性刚度的有效方法；其次，提出了一种采用弹性梁式的旋转式新型串联弹性关节，并结合关节的力矩输出特性和线性输出特性，对关节的SEA进行了力学分析与优化设计，实验结果表明该结构具有较好的线性输出特性，为柔性关节的优化设计与建模提供了理论指导；再次，提出了基于臂角优化方法的正逆运动学建模方法，通过引入“偏离中心度”与“二范数”指标，以及粒子群(PSO)优化算法对臂角进行优化，能够实现臂角不突变，关节偏离中心的幅度最小，保证关节活动裕量足够大，实现避关节限位，为轨迹规划和避障提供足够运动空间，同时保证关节运动连续，进而实现逆运动学优化；最后，建立关节柔性与空间矢量的关联形式，基于轴不变量开展了显式运动学、动力学建模的研究，鉴于空间矢量表征机械臂系统结构与运算的优势，提出了一种简洁、计算精度高速度快的柔性关节机械臂动力学分析方法，该研究为提高机械臂定位精度、建模与解算的实时性与精确性、以及开发效率提供了理论支撑。