基于Cosserat弹性杆理论的柔性线缆物理建模方法

Physical Characteristic Oriented Modeling for Flexible Cable Harness Based on Cosserat Elastic Rod Theory

针对虚拟环境中线缆敷设过程仿真的线缆建模问题,提出一种基于Cosserat弹性杆理论的柔性线缆物理建模方法。该方法在线缆离散模型的基础上根据Cosserat弹性杆理论导出线缆的总体势能,并通过优化算法得到线缆总体势能最小时的线缆形态,即线缆的平衡状态。模型考虑到线缆的柔性和连续性,能够模拟线缆的弯曲和扭转变形;通过对线缆进行离散表达,实现了对线缆总体势能的数值求解;引入罚函数将求解线缆总体势能最小值问题转化为非线性无约束优化问题;非线性无约束优化问题的求解采用信赖域方法,提高了求解的稳定性。设计并开发了虚拟环境中的线缆敷设过程仿真原型系统,并进行实例验证,证明该方法的可行性。

To simulate laying process of cable harness, a physical characteristic oriented modeling for flexible cable harness is proposed based on Cosserat elastic rod theory. The cable＇s total energy is obtained by applying Cosserat elastic rod theory on discrete cable model. The cable＇s configuration with the lowest energy can be obtained by using optimization algorithm, which is the equilibrium state. The model takes into consideration the flexibility and continuity of the cable, which could simulate bending and twisting. From the discrete expression of the cable, the cable＇s energy can be calculated by numerical method. And penalty method is used to convert the constraint problem to an unconstrained problem. The trust region algorithm is implemented to get the configuration of the cable with minimum potential energy. This method is applied in the simulation of cable laying process in a virtual environment and a prototype system is developed, and the model is validated by this system.