Abstract:

In order to solve the problem of inverse kinematics for general 6R robots,an algorithm with high accuracy based on symbolic preprocessing and matrix decomposition was proposed.Symbolic preprocessing was performed to obtain the coefficient matrixes of the inverse kinematics equations and avoid the accumulative errors of floating point computations.Singular value decomposition was adopted to ensure the rank stability of coefficient matrixes, eigendecompostion of matrixes and the method of selecting elements with the highest magnitude were applied to minimize the influence of accumulative errors on solving stability and accuracy.All these ensure that the algorithm can get 16 real solutions at most with any required accuracy.Experiments on general 6R robots and PUMA560 robots with small configuration perturbations verify the validity of the proposed algorithm.

Key words: inverse kinematics, symbolic processing, matrix decomposition, high accuracy

摘要：

为解决一般6R机器人的逆运动学问题，提出一种基于符号运算和矩阵分解的高精度逆运动学算法。采用符号运算求解逆运动学方程的系数矩阵，避免了大量中间过程的浮点数计算累积误差；通过矩阵奇异值分解优化方法提高消元矩阵的秩稳定性;将一元十六次方程求根问题转化为求解矩阵的特征值和特征向量问题，并选取较高数量级的相关元素求解关节变量，最大程度地减小数值计算累积误差的影响，提高了逆运动学算法的稳定性和精度，得到具有任意期望精度的最多16组实数逆运动学解。以一般6R机器人和有误差的PUMA560类型机器人作为求解实例，实验和仿真结果证明了算法的有效性。

关键词: 逆运动学, 符号运算, 矩阵分解, 高精度