Kinematics and Dynamics Hessian Matrixes of【推荐论文】 .doc
《Kinematics and Dynamics Hessian Matrixes of【推荐论文】 .doc》由会员分享,可在线阅读,更多相关《Kinematics and Dynamics Hessian Matrixes of【推荐论文】 .doc(19页珍藏版)》请在三一文库上搜索。
1、精品论文Kinematics and Dynamics Hessian Matrixes ofManipulators Based on Lie Bracket5ZHAO Tieshi1,2, GENG Mingchao1,2, LIU Xiao1,2, YUAN Feihu1,2(1. Parallel Robot and Mechatronic System Laboratory of Hebei Province,Yanshan University,066004;2. Key Laboratory of Advanced Forging & Stamping Technology an
2、d Science of Ministry ofNational Education,Yanshan University, 066004)10Abstract: The inertia forces and inertia coupling among the components of a manipulator must be considered in the design and control. However, as the traditional representations of accelerations haveno coordinate invariance, the
3、 corresponding inertia and Hessian matrices are not coordinate invariant, which causes the complication for analysis and control of kinemics and dynamics of a manipulator.Based on the investigation into the physical meaning of Lie bracket between two twists, the Lie bracket15representation of kinemi
4、cs Hessian matrix of the manipulator is deduced, the acceleration of the end-effector is expressed as linear-bilinear forms in this paper. Further, Newton-Eulers equations arerewritten as linear-bilinear forms, from which the dynamics Hessian matrix is deducted. The formulaeand Hessian matrixes are
5、proved to be coordinate invariant and convenient to program. An index of dynamics coupling based on dynamics Hessian matrixes is presented, and it is applied to a foldable20parallel manipulator, which demonstrates the convenience of the kinematics and dynamics Hessian matrices.Key words: Lie Bracket
6、, dynamics Hessian matrix, coupling index, parallel manipulator0Introduction25In robotic representation theories, Denavit and Hartenberg 1 notation for definition of spatial mechanisms and the homogeneous transformation of points introduced by Maxwell 2 are the most popular ones. Alternative methods
7、 with screw theory 3, Lie algebra 4 and dual quaternion 5 have been used. In kinematics, screw theory was employed with a great deal of contributions 6-7. The work was extended to the acceleration of an unconstrained rigid body and the end-effector of a30serial manipulator 8-10, where the accelerati
8、on of the end effector is in terms of the direction andmoment parts of the same screw coordinates. In addition, a linear-bilinear form with the influence coefficient matrices has been proposed to represent the acceleration of a manipulator 11.Besides, robotics researchers developed many of the most
9、efficient algorithms in dynamics, andLagrange and Newton-Eulers formulations are two main streams 12-14. However, both of them35become complex to analyze and calculate when applied to robot dynamics. Numerous formulations and recursive algorithms 15-16 have therefore been proposed that attempt to re
10、duce their symbolic and numerical complexity. A systemic theory of robotic mathematics based on homogeneous transformation and screw theory was presented 17, which enhanced the application of Lie groups and Lie algebra in robotics. Frank C. Park 18 investigated the modeling and40computational aspect
11、s of the (POE) product-of-exponentials formula for robot kinematics with Lie groups and Lie algebra; J. M. Rico and J. Gollardo 19 studied the application of Lie algebra to the mobility analysis of kinematic chains. The geometrical foundations 20 of robotics have been presented, in which a succinct
12、dynamics analysis using the derivatives of twist representing rigid body accelerations was given. The spatial operator algebraic formulation 21 of dynamics has been45developed by identifying structural similarities in an open chain dynamics. The formulations ofrobot dynamics with Lie groups and Lie
13、algebras 22-25 have drawn much attention, in which LieFoundations: National Science Foundation of China Grant(No.50975244)Brief author introduction:ZHAO Tieshi(1963-) is currently a professor with the Department of MechatronicsEngineering, Yanshan University. His research interests include parallel
14、mechanisms, stabilized platforms, sensor technology, and robotics technology. E-mail: - 19 -groups and Remannian geometry were used, link velocities and accelerations were expressed in terms of standard operations on the Lie algebra of SE(3). T.S. Zhao 26-27 study the dynamic and coupling actuation
15、of elastic underactuated manipulators based on Lie groups. However, as most50of dynamics formulae have no coordinate invariance, the analysis, design and control of manipulators are still complicated, especially for the analysis on the dynamic coupling performances. When kinematics and dynamics Hess
16、ian matrixes are involved, the design and analysisare more complicated for a serial or parallel manipulator.Based on the above work, this paper investigates the physical meaning of Lie bracket between55two twists. And then, the accelerations of the end-effector of manipulators are expressed as linea
17、r-bilinear forms, from which the kinemics Hessian matrixes are expressed as the Lie brackets of joint screws. Further, Newton-Eulers equations are rewritten as linear-bilinear forms, from which the dynamics Hessian matrix is deducted. The formulae and Hessian matrixes are proved to be coordinate inv
18、ariant and convenient to program. In the end, an index of dynamics coupling60based on dynamics Hessian matrixes is presented, and it is applied to a foldable parallel manipulator, which demonstrates the convenience of the kinematics and dynamics Hessian matrixes.1Kinematics Hessian Matrixes of Manip
19、ulators Based on LieBrackets65A Lie bracket is a linear operator, also a derivative operator 28-31. This section gives an investigation into the physical meaning of the Lie brackets between two twists, and then formulates acceleration mappings of manipulators with Jacobin and kinematics Hessian matr
20、ixes represented in Lie brackets.1.1Lie Bracket Representation of Acceleration70LetS = (s ; s 0 )andS = (s; s 0 )be two screws, the exponential mapping ofS with ai i ijjjimagnitude jiirepresents a rigid body motion of rigid body j with respect to i from time t=0 to t) s03 3 S j (t ) = exp(ji Si ) S
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 推荐论文 Kinematics and Dynamics Hessian Matrixes of【推荐论文】 of 推荐 论文
链接地址:https://www.31doc.com/p-3617894.html