## 1 Introduction  
Operating an ultra-high-caliber optical system in high space orbit is one of the key goals of the Chinese space industry and will help scientists to make more detailed observations of the universe [1]. However, it is impossible to transport it to space as a whole or install such a large space system manually in space. Large space structure construction through on-orbit services (OOS) may be the best solution [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13]. OOS missions also include visual inspection, fuel refueling and satellite repair and are of increasing interest to the space industry because of their high economical potential and strategic benefits. There are many interesting challenges in the development and operation of space robots for OOS missions, such as motion estimation and the prediction of target objects, multi-physics modeling and the simulation of space manipulators, practical dynamic parameter identification, dexterous and efficient manipulation, time delay and sensor errors in feedback controls, compliance and intelligent controls, multi-arm coordinated controls and operations, among others [5; 6; 7]. A visual servo is also an important technology for manipulators for OOS missions [8; 9; 10; 11; 12; 13]. It uses the image information captured by a camera to position or track space manipulators. This paper mainly considers the uncalibrated visual servo strategy for a hyper-redundant manipulator with a hand-eye system to realize the alignment of both static and dynamic assembly objects when the desired image features are known. Joint flexibility is a problem in space manipulators that may cause vibration. Joint flexibility is ignored in the research presented in this paper; the details of the joint flexibility problem can be found in [14]. The traditional visual servo relies on the accurate calibration of the internal camera parameters and the hand-eye relationship and determines the pose of the manipulator based on the current image information and calibrated system parameters [13; 15; 16; 17; 18]. Various parameters of a robotic vision system are likely to change in the complex and harsh space environment, which will have a serious impact on the accuracy of the visual servo. Moreover, frequent system recalibration will greatly increase the cost and workload, and its feasibility is quite low [19; 20; 21; 22]. For these reasons, research into uncalibrated visual servos is very significant. The term \"uncalibrated\" mainly means that the internal and external parameters of a camera are unknown. Compared with the position-based visual servo and hybrid visual servo, which both require 3-D reconstruction and are highly sensitive to calibration error, an image-based visual servo is more applicable to this uncalibrated situation [21; 22]. An image-based uncalibrated visual servo (IBUVS) uses image information such as the pixel coordinates of target feature points to construct task functions directly and design a controller based on the image Jacobian, which is estimated online in each control period [23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38]. In actual application, some image features may be missing owing to motion blur, inconspicuous background contrast and the occlusion of the visual field, causing the visual servo task to fail. In addition, image transmission noise and the resulting image processing errors also impact the accuracy of visual servos. To solve these problems, researchers have proposed an uncalibrated visual servo based on projective homography (PHUVS) [23]. This method solves the homography matrix by matching as many feature points as possible and uses the elements of the homography matrix to construct the task function. The homography matrix can be solved as long as there are no less than four pairs of matched feature points. Therefore, the visual servo will not be interrupted even if some feature points are lost. In addition, the PHUVS has a certain compensatory effect on image noise.