基于空间算子代数理论的多体系统逆动力学递推计算

Recursive computation of multi-body inverse dynamics using spatial operator algebra

空间算子代数理论是近几年发展起来的一种高效建模方法,应用空间算子代数方法可以对空间多体系统进行动力学建模、分析和仿真.首先通过引入6维矢量构建了单个刚体的空间矢量动力学方程,随后进一步建立了整个铰链体的逆动力学方程,并且通过将动力学方程投影到随动坐标系的方法进行了该逆动力学递推算法的软件实现.应用空间算子代数理论建立的逆动力学递推算法具有O（N）的计算量级.通过平面三连杆的典型算例的求解,与商业软件Recurdyn@的仿真结果进行对比,验证了算法及软件实现的正确性.仿真结果表明,通过空间算子代数理论建立的逆动力学递推算法简单、计算精度及效率均能够满足工程需求,可应用于多体系统动力学的运动控制和轨迹优化设计中.

In recent years, spatial operator algebra becomes an efficient modeling method used in multi- body systems. Spatial operator algebra method is applied to spatial multibody system dynamics modeling, analysis and simulation. The dynamic equation of single rigid body with 6 dimension vector was introduced first, then the inverse dynamic equations of the hinge body were modeled and implemented by projection method. Recursive inverse dynamic algorithm using spatial operator algebra has time complexity of O （N） level. Plane three links system was implemented by spatial operator algebra method which was proved correct by compared with the commercial software Recurdyn~. The result shows that the recursive inverse dynamic algorithm has efficient formulation conversions for multi-body dynamical modeling. Its calculation accuracy and efficiency can meet the requirements of engineering. This algorithm can be used for motion control and trajectory optimization design.