Trajectory Planning With Shortest Path for Modified Uncalibrated Visual Servoing Based on Projective Homography

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.