基于向量内积的机器人实时逆解算法

Real-time Inverse Kinematics Algorithm Based on Vector Dot Product

为提高6R机器人逆运动学求解算法的实时性,提出了一种基于向量内积变换的实时高效逆运动学求解算法。将复杂的矩阵方程转换为含有6个未知关节变量的10个纯代数逆运动学方程,并在方程的简化过程中引入符号运算预处理,避免了大量浮点运算带来累积误差。通过相关方程的优化线性组合,有效避免了5、6两关节变量求解时产生增根的情况,大幅提高了逆解算法的效率。试验结果表明,同等求解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0.014 ms,能满足机器人的在线控制要求。

In order to improve the real-time performance of inverse kinematics for 6R robots, a real-time and efficient algorithm based on vector dot product was proposed. The complex matrix equations were transformed to 10 pure algebraic equations containing 6 unknown joint variables, and symbolic preprocessing was applied in simplifying equations without any error accumulations caused by floatingpoint calculations. The production of extraneous roots in the solving process of the 5th and 6th joint variables was avoided by optimizing the linear combinations of related equations, which greatly improved the efficiency of the algorithm. Experiments on a 6R robot show that, the proposed algorithm has a stronger real-time performance than those of others to get the same precision solutions, the average time for gaining 8 accurate closed-form solutions is only 0. 014 ms, and it can be applied efficiently in the practical on-line robot control.