基于分块矩阵的6R机器人实时逆解算法

为提高6R机器人逆运动学求解的强实时性,提出了一种基于分块矩阵相乘来求解逆运动学的方法。将复杂的6个矩阵方程转换为含有6个未知变量的8个纯代数方程来进行求解,并在方程简化过程中引用符号运算预处理,避免了大量浮点运算带来累积误差。通过方程组的优化,可避免第3关节变量求解中产生增根的情况。试验结果表明,在同等精度要求下,该逆解算法相比于其他算法具有更强的实时性,得到精确的8组封闭解平均仅需0.009 7 ms,能够满足机器人的在线控制要求。

Real-time inverse kinematics algorithm for 6R robot based on block matrix

A new algorithm is proposed based on block matrix in order to improve the real-time performance of inverse kinematics for 6R robots.The 6 complex matrix equations are transformed to the 8 pure algebraic equations with 6 unknown joint variables,and symbolic preprocessing is applied in simplifying equations without any error accumulations due to floating-point calculations.The production of extraneous roots in the solving process of the third joint variable is avoided by optimizing the linear combinations of related equations.The results of experiments show that the proposed algorithm has a stronger real-time performance than the others with the same precision solutions.The average time for gaining 8 accurate closed-form solutions is only 0.009 7 ms.The precision solution of proposed algorithm can satisfy the requirement of robot on-line control.