一种高精度求解多轴机器人逆运动学的方法

提升多轴机器人逆运动学的求解精度与速度是保证机器人轨迹规划与实时控制性能的基础，也是机器人领域密切关注的难题。提出一种高精度、高效率地求解3至6R串链机器人逆运动学的方法。首先，将用于描述机器人位置与姿态的旋转变换阵与单位四元数采用半角正切的形式表达，建立与关节角度无冗余的机器人位姿方程。其次，分析Dixon结式求解多元高阶多项式的方法，将其应用于求取3R与一般6R机器人的逆运动学解析解。利用多项式环的特性处理矩阵，能够有效避免计算奇异性的产生。通过分析以矢量表达的Dixon矩阵，消去矩阵中的一些无效项，降低矩阵的阶数，避免阶次组合爆炸问题的发生。仿真实例表明，任意可达姿态下，6R机器人的逆运动学解一般能达到8组，这一多解的性能提升机器人的灵巧度。一般6R机器人逆解的单次计算时间不高于4ms，位置及姿态误差(相对)均小于10^-15，验证所提出的逆解方法的实时性和精密性。本文所做工作为精密操作机器人的运动学研究提供了理论依据。

A High-precision Method for Solving the Inverse Kinematics of Multi-axis Robots

Improving the accuracy and speed of the inverse kinematics of multi axis robots is the basis of improving the performance of trajectory planning and real-time control of robots, and it is also a difficult problem in the robot field. A high-precision and efficient method for solving the inverse kinematics of 3 to 6 degrees of freedom serial robot is presented in the paper. Firstly, the rotation transformation matrix and unit quaternion used to describe the position and attitude of the robot are expressed in the form of the tangent of half angles, and the position equation is established without redundancy of joint angles. Secondly, the Dixon resultant method for solving multivariate high-order polynomials is analyzed and applied to solve the inverse kinematics of 3R robots and general 6R robots. Using the characteristics of polynomial ring to process the matrix can effectively avoid the occurrence of computational singularity. By analyzing the Dixon matrix expressed in vector, some invalid terms in the matrix are eliminated, the size of the matrix is reduced, and the occurrence of order combination explosion problem is reduced. The simulation example shows that the inverse kinematic solution of 6R robot can generally reach 8 groups, and this performance improves the dexterity of robots. The single calculation time is not more than 4 ms, and the position and attitude errors (relative) are less than 10^?15. The efficiency and precision of the proposed inverse kinematics method are verified. The work of this paper provides a theoretical basis for the kinematics research of precision manipulator.