Error Correction Methods in Numerical Simulation for Unilateral Constraint Dynamics

Abstract

Abstract: Aiming at problem of calculation errors and constraint violation in numerical simulation for dynamics of unilateral constraint such as contact and collision, the error projection correction methods were put forward. On the basis of dynamical behavior of unilateral constraint described by linear programming model, mixed linear complementarity dynamics was built. Numerical simulation methods for the mixed linear complementarity dynamics were derived. In order to reduce calculation error and constraint violation caused by this error in the numerical simulation, an error correction method was built for correcting position and velocity error of numerical solution on the base of bilateral constraint model, then solving precision of unilateral constraint dynamics was improved. The correction method was verified by example and the results show that this correction method is able to improve effectively numerical simulation accuracy of unilateral constraint dynamics.

Key words: unilateral constraint, dynamical model, numerical simulation, correction method

CLC Number:

TP391.9

Gao Haitao, Han Yali, Xu Youxiong, Zhu Songqing, Wu Zailuo. Error Correction Methods in Numerical Simulation for Unilateral Constraint Dynamics[J]. Journal of System Simulation, 2015, 27(2): 240-245.

References

[1] 刘才山, 陈滨, 彭瀚,等. 多体系统多点碰撞接触问题的数值求解方法[J]. 动力学与控制学报, 2003, 1(1): 59-64.
[2] 王琪, 庄方方, 郭易圆, 等. 非光滑多体系统动力学数值算法的研究进展[J]. 力学进展, 2013, 43(1): 101-111.
[3] 姚文莉, 王育平, 边力, 等. 多刚体系统接触碰撞动力学研究进展[J]. 力学与实践, 2007, 29(6): 9-12.
[4] Baraff D.Issues in computing contact forces for non-penetrating rigid bodies[J]. Algorithmica (S0178-4617), 1993, 10(2): 292-352.
[5] Glocker C, Pfeiffer F.Complementarity problems in multibody systems with planar friction[J]. Archive of Applied Mechanics (S0939-1533), 1993, 63(7): 452-463.
[6] Pfeiffer F.Unilateral multibody dynamics[J]. Meccanica (S0025-6455), 1999, 34(6): 437-451.
[7] Pang J S, Trinkle J C.Complementarity formulation and existence of solutions of dynamic multi-rigid-body contact problem with coulomb friction[J]. Mathematical Programming (S0025-5610), 1996 (73): 199-266.
[8] Stewart D, Trinkle J C.An implicit time-stepping scheme for rigid body dynamics with coulomb friction[C]// Proceeding of the 2000 IEEE International Conference on Robotics & Automation, San Francisco, USA. USA: IEEE, 2000 (1): 162-169.
[9] Pfeiffer F, Forg M, Ulbrich H.Numerical aspects of non-smooth multibody dynamics[J]. Computer Methods in Applied Mechanics and Engineering (S0045-7825), 2006 (195): 6891-6908.
[10] Miller A T, Christensen H I.Implementation of multi-rigid-body dynamics with a robotic grasping simulator[C]// Proceeding of the 2003 IEEE International Conference on Robotics & Automation. Taipei, Taiwan, China. USA: IEEE, 2003: 14-19.
[11] 刘德贵, 朱珍民. 实时仿真算法的研究进展[J]. 系统仿真学报, 2001, 13(1): 60-63.
(Liu Degui, Zhu Zhenmin.Research Advance for Real-Time Simulation Algorithms[J]. Journal of System Simulation (S1004-731X), 2001, 13(1): 60-63.)
[12] 高海涛, 张志胜, 曹杰, 等. 基于稀疏矩阵技术的多体动力学仿真快速算法[J]. 系统仿真学报, 2009, 21(14): 4238-4247.
(Gao Haitao, Zhang Zhisheng, Cao Jie, et al. Fast Algorithm of Multibody Dynamic Simulation Based on Sparse Matrix Technique[J]. Journal of System Simulation (S1004-731X), 2009, 21(14): 4238-4247.)

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