Research on Constraint Violation Elimination based on Projection Method

Jia Liu; Yaru Xu; Kai Yang; Hongqiang Sun

doi:10.16578/j.issn.1004.2539.2022.02.004

您当前的位置：

首页 >

文章列表页 >

Research on Constraint Violation Elimination based on Projection Method

Theory·Reserach | 更新时间：2022-09-25

- Research on Constraint Violation Elimination based on Projection Method
- Journal of Mechanical Transmission Vol. 46, Issue 2, Pages: 23-27(2022)
- 作者机构：
  
  1.石家庄学院机电学院，河北石家庄 050035
  2.北京联合大学机器人学院，北京 100020
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2022.02.004
  CLC：
扫描看全文
刘佳,徐亚茹,杨凯等.基于投影法的约束违约抑制研究[J].机械传动,2022,46(02):23-27.

Liu Jia,Xu Yaru,Yang Kai,et al.Research on Constraint Violation Elimination based on Projection Method[J].Journal of Mechanical Transmission,2022,46(02):23-27.
刘佳,徐亚茹,杨凯等.基于投影法的约束违约抑制研究[J].机械传动,2022,46(02):23-27. DOI： 10.16578/j.issn.1004.2539.2022.02.004.

Liu Jia,Xu Yaru,Yang Kai,et al.Research on Constraint Violation Elimination based on Projection Method[J].Journal of Mechanical Transmission,2022,46(02):23-27. DOI： 10.16578/j.issn.1004.2539.2022.02.004.

摘要

针对解算动力学方程时存在的约束违约问题，给出了一种将投影法与Udwadia-Kalaba方程相结合的方法。该方法将系统零阶、1阶广义变量的数值解向由约束方程定义的约束流形投影，进而获得数值解的偏移量，再将其转化为系统的约束力，并将其融入Udwadia-Kalaba方程，以达到抑制约束违约的目的。与仅考虑1阶约束方程的改进Udwadia-Kalaba方程相比，基于运动受限的工业机械臂的动力学模型仿真结果表明，该修正方法能有效提高系统广义变量及零阶、1阶约束误差的计算精度。

Abstract

Aiming at problem of constraint violation in solving the dynamics equation， a method combining the projection method with Udwadia-Kalaba equation is proposed. In this method，the numerical solutions of the zero-order and first-order generalized variables of the system are projected to the constrained manifold defined by the constraint equation， the offsets of the numerical solution are obtained， then the offsets are transformed into the constraint force and integrated into Udwadia-Kalaba equation to achieve the purpose of restraining the constraint violation. Compared with the improved Udwadia-Kalaba equation which only considers the first order constraint equation， the simulation results of dynamics model of industrial manipulator subject to constraint show that the modified method can effectively improve the calculation accuracy of generalized variables and zero-order and first-order constraint errors.

关键词

投影法约束违约Udwadia-Kalaba方程动力学建模

Keywords

Projection methodConstraint violationUdwadia-Kalaba equationDynamics modeling

references

BAUMGARTE J.Stabilization of constraints and integrals of motion in dynamical systems［J］.Computer Methods in Applied Mechanics & Engineering，1972，1（1）：1-16.

CHO H ，UDWADIA F E.Explicit solution to the full nonlinear problem for satellite formation-keeping［J］.Acta Astronautica，2010，67（3）：369-387.

LIN S T，HONG M C.Stabilization method for the numerical integration of controlled multibody mechanical system：a hybeid integration approach［J］.JSME International Journal Series C，1998，120（1）：565-572.

LIN S T，HUANG N J.Numerical integration of multibody mechanical systems using Baumgarte's constraint stabilization method［J］.Journal of the Chinese Institute of Engineers，2011，25（2）：243-252.

PAULO F，MARGARIDA M，EURICO S，et al.A parametric study on the baumgarte stabilization method for forward dynamics of constrained multibody systems［J］.Journal of Computational and Nonlinear Dynamics，2009，6（1）：1-9.

RAHMATALLA S，LEE E T，EUN H C.Numerical integration scheme to reduce the errors in the satisfaction of constrained dynamic equation［J］.Journal of Mechanical Science and Technology，2013，27（4）：941-949.

刘佳，史源平，孙宏强，等.基于改进Udwadia-Kalaba方程的双机械臂动力学建模与仿真［J］.机械传动，2020，44（1）：94-98.

LIU Jia，SHI Yuanping，SUN Hongqiang，et al.Dynamics modeling and simulation of dual-arm robot based on the improved Udwadia-Kalaba equation［J］.Journal of Mechanical Transmission，2020，44（1）：94-98.

BLAJER W.Elimination of constraint violation and accuracy aspects in numerical simulation of multibody systems［J］.Multibody System Dynamics，2002，7（3）：265-284.

BLAJER W.Methods for constraint violation suppression in the numerical simulation of constrained multibody systems-a comparative study［J］.Computer Methods in Applied Mechanics and Engineering，2011，200（13）：1568-1576.

高海涛，韩亚丽，许有熊，等.单边约束动力学模型数值仿真中的误差修正方法［J］.系统仿真学报，2015，27（2）：240-245.

GAO Haitao，HAN Yali，XU Youxiong，et al.Error correction methods in numerical simulation for unilateral constraint dynamics［J］.Journal of System Simulation，2015，27（2）：240-245.

高海涛，张志胜，曹杰，等.冗余约束多刚体系统摩擦碰撞问题的数值求解方法［J］.振动与冲击，2010，29（1）：26-29.

GAO Haitao，ZHANG Zhisheng，CAO Jie，et al.Numerical resolution method for frictional collision problems of multi-rigid-body with redundant constraints［J］.Journal of Vibration and Shock，2010，29（1）：26-29.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Dynamics Modeling and Simulation of Industrial Manipulator Subject to Constraint

A Normative Modeling Method for Complex Gear Coupled Rotor-bearing System Dynamics

Establishment of Hysteresis Stiffness Model and Kinematic Precision Analysis of Manipulators

Simulation Analysis and Experimental Research on Vibration Characteristic of Roller Brush Gearbox of Intelligent Sweeper

Research on Nonlinear Dynamics Modeling and Simulation of Harmonic Gear Drive

Related Author

No data

Related Institution

School of Mechanical Engineering & Automation,Beihang University

School of Mechanical Engineering,Tianjin University of Commerce

Department of Mechanical and Electrical Engineering,Tianjin Electronic Information College

School of Mechanical Engineering,Hebei University of Technology

School of Mechanical and Power Engineering, Zhengzhou University

⁰