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为促进一般6R机器人运动学逆解的应用,提出了一种四元数矩阵和对偶四元数矩阵算法,该算法把四元数应用于平面旋转的特殊情况,把旋转角度的正弦、余弦改写为矩阵形式,可以导出平面四元数的2个矩阵形式的基,建立了四元数矩阵形式的串联6R机械手运动学方程,再通过线性消元和2次应用分次字典序Groebner基消去5个变元,最后采用Dixon结式进行消元,得到没有增根的一元16次方程。这种算法得出的结果通过与过去得出的6R机器人逆解算法进行对比,表明所提出的算法可行性和正确性。
In order to promote the application of general inverse kinematics of 6R robot, a quaternion matrix and dual quaternion matrix algorithm are proposed. The algorithm applies quaternion to the special case of plane rotation, and rewrites the sine and cosine of rotation angle In the form of matrix, we can derive two matrixes of quaternion in the form of matrix. The equations of kinematics of tandem 6R manipulators in the form of quaternion matrix are established. By using linear elimination and two times of application, A variable, the final use of Dixon knot elimination, get no rooted 16 yuan equation. The result obtained by this algorithm is compared with the 6R robot inverse solution algorithm which was obtained in the past, which shows the feasibility and correctness of the proposed algorithm.