Formalization and Analysis of Jacobian Matrix in Screw Theory and its Application in Kinematic Singularity
Sponsor
This work was supported by the National Natural Science Foundation of China (61472468,61572331,61602325,61373034),the National Key Technology Research and Development Program (2015BAF13B01),the International Cooperation Program on Science and Technology (2011DFG13000),the Project of Beijing Municipal Science & Technology Commission(Z141100002014001),the Project of Construction of Innovative Teams and Teacher Career Development for Universities and Colleges Under Beijing Municipality(No.IDHT20150507), and the Scientific Research Base Development Program of the Beijing Municipal Commission of Education(TJSHG201310028014).
Published In
2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
Document Type
Citation
Publication Date
12-2017
Abstract
Accurate specification and rigorous analysis of Jacobian matrix are indispensable to guarantee correct evaluation on the manipulator kinematics performance. In this paper, a formal analysis method of the Jacobian matrix in the screw theory is presented by using the higher-order logic theorem prover HOL4. Formalizations of twists and the forward kinematics are characterized with the product of exponential formula and the theory of functional matrices. To the best of our knowledge, this work is the first to formally reason about the spatial Jacobian using theorem proving. The formal modeling and analysis of a 3-DOF planar manipulator substantiate the effectiveness and applicability of the proposed approach to formally verify the kinematics properties of manipulator.
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DOI
10.1109/IROS.2017.8206115
Persistent Identifier
https://archives.pdx.edu/ds/psu/30659
Citation Details
Wu, A., Shi, Z., Yang, X., Guan, Y., Li, Y., & Song, X. (2017, September). Formalization and analysis of jacobian matrix in screw theory and its application in kinematic singularity. In 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (pp. 2835-2842). IEEE.
Description
©2017 IEEE