大型空间可展桁架结构展开过程多体动力学优化控制

Based on dynamics of flexible multibody systems, comprehensive studies of optimal control for the deployment of large deployable space truss structures are developed, which include dynamic modelling, solving of dynamic equations, sensitivity analysis and nonlinear constrained optimization. With the former studies on the numerical solution methods for differential-algebraic equaitons, adjoint variable method for sensitivity analysis and argued Lagrange multiplier method for design optimization of multibody dynamics, the high-order structure preserving integrators with high efficiency and stability are studied firstly for the dynamic equations of the deployment of large space truss structure modelled by absolute nodal coordinate method. Then, based on the discrete variational principle, more efficient algrithms for optimal control of the deployment are presented, and more accurate algrithms for multiobjective optimal control are studied based on multiobjective optimization methods. Finally, with visual simulation technologies and reliability analysis, simulations of the deployment of large deployalbe space truss structures under control are studied to verify the efficiency of the optimal control methods. These studies are useful for the deployment control of large space truss stuctures such as masts and satellite deployable antenna, and important to the development of optimal control of flexible multibody dynamics.

基于柔性多体系统动力学，针对大型空间可展桁架结构展开过程，系统地进行多体动力学优化控制研究，其中包括动力学建模、动力学方程求解、灵敏度分析、非线性约束优化等过程。在前期多体系统动力学微分-代数方程数值求解、伴随变量法灵敏度分析、增广Lagrange乘子法动态优化设计研究的基础上，首先使用绝对节点坐标方法建立大型空间可展桁架结构展开过程多体动力学模型，基于展开过程多体动力学方程，研究高效、稳定的高阶保结构数值积分方法；然后基于离散变分原理研究高效的展开过程多体动力学优化控制方法，并结合多目标优化方法研究高精度的展开过程多体动力学多目标优化控制方法；最后利用可视化技术进行展开过程仿真实验，结合可靠性分析进行模拟和验证。本项目研究对大型空间伸展臂、大型星载可展天线等可展桁架结构的展开控制有重要的实际应用价值，对柔性多体系统动力学优化控制的发展也有重要的科学意义。

本项目针对大型空间可展桁架结构，基于柔性多体系统动力学，以剪叉式伸展臂和索杆铰接式伸展臂为例，对展开过程动力学优化控制问题进行了动力学建模、动力学方程求解、非线性约束优化控制、可视化仿真等方面的研究。建立了展开过程单目标、多目标多体动力学优化控制模型和时间离散变分模型；基于展开过程多体动力学方程，设计了高阶变分数值积分方法和李群数值积分方法，在长时间仿真情况下提高计算精度和算法稳定性，为高效、稳定的展开过程多体动力学优化控制提供基础；研究了基于灵敏度分析的多体动力学优化方法和多体动力学优化遗传算法，应用于空间可展桁架结构展开过程单目标和多目标优化控制，提出了空间可展结构展开过程优化控制的改进遗传算法；结合可视化仿真技术，设计并实现了多体系统动力学仿真软件，进行了空间可展桁架结构展开过程可视化仿真实验，分析了数值仿真的可靠性并验证了优化控制方法的有效性。该项目研究对柔性多体系统动力学优化控制的发展有重要的科学意义，对大型空间伸展臂等可展桁架结构的设计和展开控制也有重要的实际应用价值。