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 引用本文: 张西南, 游浦, 刘铸永. 基于符号距离场的多体系统碰撞动力学研究. 力学学报, 待出版.
Zhang Xinan, You Pu, Liu Zhuyong. Study of multibody system contact dynamics based on signed distance field. Chinese Journal of Theoretical and Applied Mechanics, in press.
 Citation: Zhang Xinan, You Pu, Liu Zhuyong. Study of multibody system contact dynamics based on signed distance field. Chinese Journal of Theoretical and Applied Mechanics, in press.

## STUDY OF MULTIBODY SYSTEM CONTACT DYNAMICS BASED ON SIGNED DISTANCE FIELD

• 摘要: 多体系统动力学中的接触碰撞问题是典型的边界非线性问题, 对其动力学仿真面临着巨大的数值困难. 由于求解过程中需要一直进行复杂的接触碰撞检测, 严重地影响了数值计算效率. 为了实现对多体系统动力学中接触碰撞问题的快速求解, 文章提出一种改进的基于符号距离场的多体系统动力学接触碰撞检测算法. 通过对预先生成的符号距离场进行三线性插值, 求解出空间中任意一点距离物体表面的最短距离和法向量. 将接触碰撞检测分为全局检测和局部检测两个过程, 首先在全局检测时利用OBB包围盒技术对物体之间是否存在潜在接触可能性进行快速判断; 然后在局部检测时基于符号距离场信息并结合八叉树结构对接触碰撞检测算法进行优化. 分别采用Hertz接触力模型和基于速度的库伦摩擦力模型, 建立了多刚体系统非连续动力学方程. 最后, 通过对典型的算例和空间站交会对接的工程案例进行仿真, 验证了所提方法在解决复杂多体系统碰撞动力学问题时的正确性和高效性. 该方法可以进一步拓展到复杂构型刚体与柔性体的接触碰撞动力学研究.

Abstract: The contact/impact problem of the multibody system dynamics is a typical boundary nonlinear problem, which faces a huge numerical difficulty in dynamic simulation. The efficiency of numerical calculation is seriously affected for the necessity of constant and complex contact detection in the solving process. In order to solve the contact/impact problem of the multibody system dynamics quickly, an improved algorithm for the contact/impact problem of multibody system dynamics is proposed based on the signed distance field in this paper. The shortest distance and normal vector of any point from the object surface are solved by performing trilinear interpolation on the pre-generated signed distance field. The contact detection is divided into two essential processes: global detection and local detection. At first, the bounding box called OBB is used to quickly judge whether there is a potential contact between objects in global detection. Then, a contact detection algorithm is further optimized based on the information of signed distance field and octree structure in local detection. In addition, the Hertz contact force model and Coulomb friction force model based on velocity are used to establish the discontinuous dynamics equations of the multibody system. Finally, the correctness and high efficiency of the proposed method in solving the complex impact dynamics problem of multibody system are verified by the successful simulation of typical calculation examples and an engineering case of spacecraft rendezvous and docking. The proposed method can be further extended to study the contact/impact dynamics between rigid bodies with complex configurations and flexible bodies.

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