Abstract: 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.

Key words: multi-axis robot, inverse kinematics, analytical solution, high precision, Dixon resultant, multivariate polynomial