In this paper, an Inverse Kinematics (IK) algorithm combining the analytical method and the numerical one is proposed to solve the IK problem of a 7-DOF spraying robot with 4R 3-DOF non-spherical wrist. Firstly, the 7-DOF spraying robot is transformed into a 7-DOF robot with 3R spherical wrist and the arm angle is used as the redundancy parameter. The approximate IK solution is calculated analytically using offset angle method by means of approximation. Secondly, the approximate solution is taken as the initial value of the iterative algorithm and by updating the joint angles through the damped least-square method with augmented Jacobian matrix, the final exact solution is obtained after a few iterations. Three simulation experiments show that the proposed algorithm not only has high computational efficiency and accuracy, but also can obtain multiple solutions and show the self-motion characteristics of the 7-DOF robot. The novel algorithm may be implemented in real-time control of the 7-DOF spraying robot.

本文提出了一种结合分析方法和数值方法的运动学（IK）逆向算法，解决了具有4R 3-DOF非球腕的7自由度喷涂机器人的IK问题。首先，将7自由度喷涂机器人转变为具有3R球形腕部的7自由度机器人，并将手臂角度用作冗余参数。IK近似解是通过偏移角方法通过近似分析得出的。其次，将近似解作为迭代算法的初始值，并通过阻尼最小二乘法用增强的雅可比矩阵更新关节角度，经过几次迭代得到最终的精确解。三个仿真实验表明，该算法不仅具有较高的计算效率和准确性，而且还可以获得多种解决方案，并展示了7自由度机器人的自运动特性。该新颖算法可以在7自由度喷涂机器人的实时控制中实现。