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.
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]. Journal of Shanghai Jiaotong University(Science), 2024
, 29(3)
: 450
-456
.
DOI: 10.1007/s12204-023-2661-4
[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.
