基于影响系数法的机器人动力学方程约束关系建立

doi:10.1007/s12204-023-2661-4

J Shanghai Jiaotong Univ Sci ›› 2024, Vol. 29 ›› Issue (3): 450-456.doi: 10.1007/s12204-023-2661-4

基于影响系数法的机器人动力学方程约束关系建立

徐亚茹1,2，李克鸿1,2，商新娜2，金晓明1,2，刘荣3，张建成1,2

（1. 北京联合大学北京市智能机械创新设计服务工程技术研究中心，北京 100027；2. 北京联合大学机器人学院，北京 100020；3. 北京航空航天大学机器人研究所，北京 100191）

接受日期:2023-02-27 出版日期:2024-05-28 发布日期:2024-05-28

Establishment of Constraint Relation of Robot Dynamics Equation Based on Kinematic Influence Coefficients Method

XU Yaru^1,2 (徐亚茹), LI Kehong^1,2(李克鸿), SHANG Xinna²（商新娜）, JIN Xiaoming^1,2(金晓明), LIU Rong³(刘荣), ZHANG Jiancheng^1,2（张建成）

(1. Beijing Engineering Research Center of Smart Mechanical Innovation Design Service, Beijing Union University, Beijing 100027, China; 2. College of Robotics, Beijing Union University, Beijing 100020, China; 3. Robotics Institute, Beihang University, Beijing 100191, China)

Accepted:2023-02-27 Online:2024-05-28 Published:2024-05-28

摘要/Abstract

摘要： 工作要求和环境的多样性使得工业机器人的自由度数和结构复杂性不断增加，难以建立其精确的动力学模型，对实现稳定、快速、准确的轨迹跟踪控制造成很大的阻碍。因此，在利用运动学影响系数法求解Jacobian矩阵和Hessian矩阵的基础上，推导了多自由度工业机器人解析动力学方程中约束关系的一般表达式，建立了基于Udwadia-Kalaba理论的含一般约束关系表达式的解析动力学方程，从而解决了多自由度工业机器人在完成复杂任务约束时增加约束关系建立时间的问题。以SCARA机器人为研究对象，仿真结果表明：该方法为复杂约束条件下的工业机器人系统建模提供了一种新的思路。

关键词: 工业机器人，约束关系，影响系数法，Jacobian矩阵，Hessian矩阵

Abstract: Due to the diversity of work requirements and environment, the number of degrees of freedom (DOFs) and the complexity of structure of industrial robots are constantly increasing. It is difficult to establish the accurate dynamical model of industrial robots, which greatly hinders the realization of a stable, fast and accurate trajectory tracking control. Therefore, the general expression of the constraint relation in the explicit dynamic equation of the multi-DOF industrial robot is derived on the basis of solving the Jacobian matrix and Hessian matrix by using the kinematic influence coefficients method. Moreover, an explicit dynamic equation with general constraint relation expression is established based on the Udwadia-Kalaba theory. The problem of increasing the time of establishing constraint relationship when the multi-DOF industrial robots complete complex task constraints is solved. With the SCARA robot as the research object, the simulation results show that the proposed method can provide a new idea for industrial robot system modeling with complex constraints.

Key words: industrial robot, constraint relationship, kinematic influence coefficients method, Jacobian matrix, Hessian matrix

中图分类号:

徐亚茹1,2，李克鸿1,2，商新娜2，金晓明1,2，刘荣3，张建成1,2. 基于影响系数法的机器人动力学方程约束关系建立[J]. J Shanghai Jiaotong Univ Sci, 2024, 29(3): 450-456.

XU Yaru(徐亚茹), LI Kehong(李克鸿), SHANG Xinna（商新娜）, JIN Xiaoming(金晓明), LIU Rong(刘荣), ZHANG Jiancheng（张建成）. Establishment of Constraint Relation of Robot Dynamics Equation Based on Kinematic Influence Coefficients Method[J]. J Shanghai Jiaotong Univ Sci, 2024, 29(3): 450-456.

参考文献

[1] ZHANG L B, WANG J C, CHEN J L, et al. Dynamic modeling for a 6-DOF robot manipulator based on a centrosymmetric static friction model and whale genetic optimization algorithm [J]. Advances in Engineering Software, 2019, 135: 102684.
[2] MIRTAHERI S M, ZOHOOR H. Efficient formulation of the Gibbs-Appell equations for constrained multibody systems [J]. Multibody System Dynamics, 2021, 53(3): 303-325.
[3] WANG X Y, GE T, YANG K, et al. Dynamic modeling of underwater self-reconfigurable robot with kane’s method [J]. Journal of Shanghai Jiao Tong University, 2013, 47(12): 1874-1880 (in Chinese).
[4] ZHANG X L, CHEN Z Y, XU S P, et al. Udwadia–Kalaba approach for three link manipulator dynamics with motion constraints [J]. IEEE Access, 2019, 7: 49240-49250.
[5] LIU J A, LIU R. Simple method to the dynamic modeling of industrial robot subject to constraint [J]. Advances in Mechanical Engineering, 2016, 8(4): 168781401664651.
[6] GUO M, CHEN E R, YAN M Q. The neural network terminal sliding mode control for the 3-RRC parallel robot [J]. Advances in Mechanical Engineering, 2022, 14(3): 168781322210878.
[7] LYU G Z, RONG L. Violation elimination of nominal models for manipulators constructed with Udwadia– Kalaba equation [J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44: 2305.
[8] HAN J, ZHANG K, DONG F F. Robust constraintfollowing servo control for flexible for flexible manipulator based on Udwadia-Kalaba [J]. Journal of Hefei University of Technology (Natural Science), 2020, 43(5): 577-583 (in Chinese).
[9] QIN F F, ZHAO H, ZHEN S C, et al. Adaptive robust control for lower limb rehabilitation robot with uncertainty based on Udwadia–Kalaba approach [J]. Advanced Robotics, 2020, 34(15): 1012-1022.
[10] SHI H, LIANG Y B, LIU Z H. An approach to the dynamic modeling and sliding mode control of the constrained robot [J]. Advances in Mechanical Engineering, 2017, 9(2): 168781401769047.
[11] LYU G Z, LIU R. Determination of stability correction parameters for dynamic equations of constrained multibody systems [J]. Mathematical Problems in Engineering, 2018, 2018: 1-10.
[12] LEAL-NARANJO J A, WANG M F, PAREDESROJAS J C, et al. Design and kinematic analysis of a new 3-DOF spherical parallel manipulator for a prosthetic wrist [J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2019, 42(1): 1-12.
[13] RAO C Y, XU L M, CHEN Q H, et al. Dynamic modeling and performance evaluation of a 2UPR-PRU parallel kinematic machine based on screw theory [J]. Journal of Mechanical Science and Technology, 2021, 35(6): 2369-2381.
[14] CHAI X X, WANG M, XU L M, et al. Dynamic modeling and analysis of a 2PRU-UPR parallel robot based on screw theory [J]. IEEE Access, 2020, 8: 78868-78878.
[15] RIOS O. Method of influence coefficients for kinematic and dynamic modeling of robotic systems [J]. IEEE Transactions on Robotics, 2016, 32(1): 236-245.
[16] HUANG Z, WANG J, FANG Y F. Analysis of instantaneous motions of deficient-rank 3-RPS parallel manipulators [J]. Mechanism and Machine Theory, 2002, 37(2): 229-240.
[17] XU Y R, LIU R. Dynamic modeling of SCARA robot based on Udwadia–Kalaba theory [J]. Advances in Mechanical Engineering, 2017, 9(10): 168781401772845.

基于影响系数法的机器人动力学方程约束关系建立

Establishment of Constraint Relation of Robot Dynamics Equation Based on Kinematic Influence Coefficients Method

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