The Kinematic and Dynamic Modeling and Numerical Calculation of Robots with Complex Mechanisms Based on Lie Group Theory
The kinematic and dynamic models of robots with complex mechanisms such as the closed-chain mechanism and the branch mechanism are often very complex and difficult to be calculated. Aiming at this issue, in this paper, the pose of the component in robots is represented by the Euclidean group and its...
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| Veröffentlicht in: | Mathematical problems in engineering 2021-10, Vol.2021, p.1-34 |
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| creator | Ma, Lu-Han Zhong, Yong-Bo Wang, Gong-Dong Li, Nan |
| description | The kinematic and dynamic models of robots with complex mechanisms such as the closed-chain mechanism and the branch mechanism are often very complex and difficult to be calculated. Aiming at this issue, in this paper, the pose of the component in robots is represented by the Euclidean group and its subgroups with the proposed method. The component’s velocity is derived using the relationship between the Lie group and Lie algebra, and the acceleration and Jacobian matrix are then derived on this basis. The Lagrange equation is expressed by the obtained kinematic parameter expressions. Establishing the model with this method can obtain clear physical meaning and make the expressions uniform and easy to program, which is convenient for computer-aided calculation and parameterization. Calculating by the properties of the Lie group can reduce the calculation and model complexity, especially for calculating the velocity and acceleration, which reduces the calculation error and eases the calculation. Therefore, the proposed modeling and calculation method of kinematics and dynamics of robots is especially suitable for robots with complex mechanisms. As an example, the kinematic and dynamic model of the manipulator developed in our laboratory is established and a working process of it is numerically calculated. Then, the results of the numerical calculation are compared with the results of virtual prototype simulation in ADAMS to verify the correctness. |
| doi_str_mv | 10.1155/2021/6014256 |
| format | Article |
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Aiming at this issue, in this paper, the pose of the component in robots is represented by the Euclidean group and its subgroups with the proposed method. The component’s velocity is derived using the relationship between the Lie group and Lie algebra, and the acceleration and Jacobian matrix are then derived on this basis. The Lagrange equation is expressed by the obtained kinematic parameter expressions. Establishing the model with this method can obtain clear physical meaning and make the expressions uniform and easy to program, which is convenient for computer-aided calculation and parameterization. Calculating by the properties of the Lie group can reduce the calculation and model complexity, especially for calculating the velocity and acceleration, which reduces the calculation error and eases the calculation. Therefore, the proposed modeling and calculation method of kinematics and dynamics of robots is especially suitable for robots with complex mechanisms. As an example, the kinematic and dynamic model of the manipulator developed in our laboratory is established and a working process of it is numerically calculated. Then, the results of the numerical calculation are compared with the results of virtual prototype simulation in ADAMS to verify the correctness.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2021/6014256</identifier><language>eng</language><publisher>New York: Hindawi</publisher><subject>Acceleration ; Algebra ; Chain branching ; Complexity ; Dynamic models ; Engineering ; Euler-Lagrange equation ; Group theory ; Jacobi matrix method ; Jacobian matrix ; Kinematics ; Lie groups ; Parameterization ; Robots ; Subgroups ; Velocity ; Virtual prototyping</subject><ispartof>Mathematical problems in engineering, 2021-10, Vol.2021, p.1-34</ispartof><rights>Copyright © 2021 Lu-Han Ma et al.</rights><rights>Copyright © 2021 Lu-Han Ma et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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Aiming at this issue, in this paper, the pose of the component in robots is represented by the Euclidean group and its subgroups with the proposed method. The component’s velocity is derived using the relationship between the Lie group and Lie algebra, and the acceleration and Jacobian matrix are then derived on this basis. The Lagrange equation is expressed by the obtained kinematic parameter expressions. Establishing the model with this method can obtain clear physical meaning and make the expressions uniform and easy to program, which is convenient for computer-aided calculation and parameterization. Calculating by the properties of the Lie group can reduce the calculation and model complexity, especially for calculating the velocity and acceleration, which reduces the calculation error and eases the calculation. Therefore, the proposed modeling and calculation method of kinematics and dynamics of robots is especially suitable for robots with complex mechanisms. As an example, the kinematic and dynamic model of the manipulator developed in our laboratory is established and a working process of it is numerically calculated. 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| subjects | Acceleration Algebra Chain branching Complexity Dynamic models Engineering Euler-Lagrange equation Group theory Jacobi matrix method Jacobian matrix Kinematics Lie groups Parameterization Robots Subgroups Velocity Virtual prototyping |
| title | The Kinematic and Dynamic Modeling and Numerical Calculation of Robots with Complex Mechanisms Based on Lie Group Theory |
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