一种变步长方法改进的刚体动力学仿真  

Variable Time Step Method to Optimize Rigid Body Dynamics Simulation

作　　者：李姗姗[1] 周明全[1] 谭小慧[1] 王学松[1] 

机构地区：[1]北京师范大学信息科学与技术学院,北京100875

出　　处：《系统仿真学报》2013年第10期2321-2326,共6页Journal of System Simulation

基　　金：国家自然科学基金(61170203);国家科技支撑计划(2012BAH33F04)

摘　　要：基于约束的模拟方法在刚体动力学仿真问题中有着广泛的应用,该方法求解精度高、模拟真实,但是也存在计算量大、响应时间长的缺点。为了解决虚拟现实中刚体动力学模拟计算量大与实时性的矛盾,结合休眠策略,提出了一种变步长优化方法,即在仿真开始时采用大步长以加快解算速度,当休眠物体数目达到特定阈值时采用小步长以提高仿真精度。该方法综合小步长积分的稳定性精确性以及大步长积分的求解快速的优点,既保证了仿真求解的正确性和精确性又提高了模拟速度,有效解决了准确性和实时性之间的矛盾。在自主研发的基于大规模三维模型数据库的快速三维场景重建平台VR Studio中,使用上述方法来模拟复杂场景中刚体的动力学行为。实验结果表明,该方法不仅能有效加速系统达到稳定状态,提升每帧更新的解算速度,且对刚体的动力学行为模拟真实,满足实时交互的要求。With the advantage of high accuracy and real behaviors, the constraint-based approach plays an important role in rigid body dynamics simulation, but it also has the disadvantage of expensive computation and long response time. To alleviate the contradiction between expensive computation and real-time requirement of rigid body dynamics in virtual reality, an optimization approach of variable time step was proposed. Supported by sleepy policy, this method took large time step at first to accelerate the simulation and took small time step to improve accuracy when the number of sleeping body reached a given threshold. Combined the stability and accuracy of small time step integration and the rapidity of large time step integration, this approach accelerated the simulation process. In the Rapid 3D Virtual Scene Reconstruct platform named VR studio based on large scale 3D models library, this method was used to construct 3D virtual scenes and simulate complex rigid bodies＇ dynamics. Experiment results show that the proposed method can effectively reduce the simulation time of each frame and accelerate the system to reach a steady state. At the same time, the simulation is real and can meet real-time interaction.

关 键 词：变步长 线性互补问题（LCP） 刚体动力学 物理模拟 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]