螺旋理论中雅可比矩阵的形式化、分析及其在运动奇异性中的应用

2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Pub Date : 2017-09-01 DOI:10.1109/IROS.2017.8206115

Aixuan Wu, Zhiping Shi, Xiumei Yang, Yong Guan, Yongdong Li, Xiaoyu Song

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引用次数: 2

摘要

准确的雅可比矩阵规范和严谨的雅可比矩阵分析是正确评价机械臂运动学性能的必要条件。本文利用高阶逻辑定理证明器HOL4，给出了螺旋理论中雅可比矩阵的形式化分析方法。扭曲的形式化和正运动学用指数公式和泛函矩阵理论的乘积来表征。据我们所知，这项工作是第一个使用定理证明对空间雅可比矩阵进行正式推理的工作。通过对一个三自由度平面机械臂的形式化建模和分析，验证了该方法对机械臂运动学特性形式化验证的有效性和适用性。

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Formalization and analysis of jacobian matrix in screw theory and its application in kinematic singularity

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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2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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