一般6R机器人的高精度逆运动学优化算法

Optimized Inverse Kinematics Algorithm with High Accuracy for General 6R Robots

为提高一般6R机器人逆运动学算法的精度和效率,提出一种基于符号运算和矩阵分解的优化算法。对6个基础逆运动学方程作变换,采用符号运算预处理得到14个逆运动学方程,避免大量浮点数计算累积误差。利用其中6个方程与关节变量3无关的特点,将目标矩阵从24阶降低到16阶,包含的关节变量从3个增加到4个。把一元16次方程求根问题转换为矩阵特征分解问题,并选取较高数量级的相关数据元素计算关节变量,进一步提高了算法精度。以一般6R机器人为例,求解结果表明,提出的算法能够得到具有任意期望精度的最多16组实数逆运动学解。

In order to improve the accuracy and efficiency of the inverse kinematics algorithm for general 6R robots, an optimized algorithm was proposed based on symbolic processing and matrix decomposition. The 6 basic inverse kinematics equations were transformed, and symbolic preprocessing was applied to gain 14 inverse kinematics equations without any accumulative errors caused by float point computations. By exploiting the characteristic that 6 equations among them were independent on joint variable 3, the order of the target matrix was reduced from 24 to 16, as while as the number of the included joint variables was increased from 3 to 4. The problem of solving a polynomial of degree 16 was optimized to decomposing a matrix of order 16, and elements with the higher magnitude were selected for calculating the joint variables, so the accuracy was enhanced in a further step. Experiments on general 6R robots show that, the proposed inverse kinematics algorithm can seek 16 real solutions at most with any required accuracy.