In view of the classical visual servoing trajectory planning method which only considers the camera trajectory, this paper proposes one homography matrix based trajectory planning method for robot uncalibrated visual servoing. Taking the robot-end-effector frame as one generic case, eigenvalue decomposition is utilized to calculate the infinite homography matrix of the robot-end-effector trajectory, and then the image feature-point trajectories corresponding to the camera rotation is obtained, while the image feature-point trajectories corresponding to the camera translation is obtained by the homography matrix. According to the additional image corresponding to the robot-end-effector rotation, the relationship between the robot-end-effector rotation and the variation of the image feature-points is obtained, and then the expression of the image trajectories corresponding to the optimal robot-end-effector trajectories (the rotation trajectory of the minimum geodesic and the linear translation trajectory) are obtained. Finally, the optimal image trajectories of the uncalibrated visual servoing controller is modified to track the image trajectories. Simulation experiments show that, compared with the classical IBUVS method, the proposed trajectory planning method can obtain the shortest path of any frame and complete the robot visual servoing task with large initial pose deviation.

翻译：针对经典视觉伺服轨迹规划方法仅考虑相机轨迹的问题，本文提出一种基于单应性矩阵的机器人无标定视觉伺服轨迹规划方法。以机器人末端执行器坐标系为通用参考系，利用特征值分解计算机器人末端执行器轨迹的无穷远单应性矩阵，进而获得与相机旋转对应的图像特征点轨迹，同时通过单应性矩阵获取与相机平移对应的图像特征点轨迹。根据与机器人末端执行器旋转对应的附加图像，建立机器人末端执行器旋转与图像特征点变化之间的关系，从而得到最优机器人末端执行器轨迹（最小测地旋转轨迹与线性平移轨迹）对应的图像轨迹表达式。最终，修正无标定视觉伺服控制器的最优图像轨迹以跟踪这些图像轨迹。仿真实验表明，与经典IBUVS方法相比，本文提出的轨迹规划方法能够获得任意坐标架的最短路径，并在较大初始位姿偏差下完成机器人视觉伺服任务。