In order to improve the robustness and optimize trajectory of projective homography-based uncalibrated visual servoing (PHUVS) proposed in our previous work, an analytical expression of optimal trajectory for camera in projective homography space is proposed in this article, which is totally free of camera parameters and is corresponding to camera’s shortest path in the 3-D space with straight path in translation and minimal geodesic in rotation. The projective homography is computed without scale ambiguity in both planning and tracking stages. The PHUVS controller is modified correspondingly to track the planned trajectory in projective homography space while maintaining superior characteristic of PHUVS under uncalibrated scenario. The simulations and experiments’ results reveal the effectiveness and necessity of the proposed trajectory optimization method in the existence of large initial errors. Note to Practitioners —The state-of-the-art visual-guided robotic technology in industry usually requires system calibration, which is often costly, vulnerable, and challenging for ordinary workers. In our previous work, we offered an uncalibrated visual servo method based on projective homography named projective homography-based uncalibrated visual servoing (PHUVS), which is suitable for plug and play application for eye-in-hand robot visual servo tasks. However, PHUVS suffers from some defects, including undesirable 3-D space motion and local convergence. In this article, we proposed the trajectory planning method along with a modified PHUVS controller to improve the original one from the disadvantages mentioned earlier. This planning method is also calibration-free. With pure image information, a straight-line path in translational motion along with minimal geodesic in rotary motion can be achieved. This approach is capable of extending the range of applications for uncalibrated visual servo technology in robotic tasks, such as assembling, painting, and robotic machining.

中文翻译：

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基于投影同形论的修正非标定视觉伺服的最短路径轨迹规划

为了提高我们先前工作中提出的基于投影单应性的非标定视觉伺服（PHUVS）的鲁棒性并优化其轨迹，本文提出了投影单应性空间中相机最优轨迹的解析表达式，该表达式完全没有相机参数，并且对应于相机在3-D空间中的最短路径，其中平移路径为平直路径，旋转轴为最小测地线。在计划和跟踪阶段都计算出投影单应性而没有尺度模糊性。相应地修改了PHUVS控制器，以在投影单应性空间中跟踪计划轨迹，同时在未校准的情况下保持PHUVS的卓越特性。执业者注意 —行业中最先进的视觉引导机器人技术通常需要系统校准，这通常成本高昂，脆弱且对普通工人来说具有挑战性。在我们之前的工作中，我们提供了一种基于射影单应性的非标定视觉伺服方法，称为基于射影单应性的非标定视觉伺服（PHUVS），它适用于即插即用应用，用于手边机器人视觉伺服任务。但是，PHUVS存在一些缺陷，包括不希望的3D空间运动和局部会聚。在本文中，我们提出了一种轨迹规划方法以及改进的PHUVS控制器，以克服前面提到的缺点改进原始方法。此计划方法也无需校准。有了纯图像信息，可以实现平移运动中的直线路径以及旋转运动中的最小测地线。这种方法能够扩展未经校准的视觉伺服技术在机器人任务（例如装配，喷涂和机器人加工）中的应用范围。