# Swing Analysis and Control Research of the Space Tethered Combination in the Maneuver Process
## 1 Introduction  
With the increase of human aerospace activities, space debris problems become more and more pronounced. The space debris environment is seriously threatening the development of aerospace projects [1]. Especially in geostationary earth orbit (GEO), it has important military value and a strategic position in communication, navigation, meteorology and investigation. However, these orbital resources are quite limited. There is no extra energy to deorbit the space debris from GEO, so the space debris, which will be the cataloguing targets, increases steadily, with a rate of 30 per year. The severity and frequency of the disintegration events will increase with the mass and cross section area of the orbiting objects. Based on this situation, the active removal technology of non-cooperative targets, such as space debris, has become one of the hotspots in the field of space research [2; 3; 4]. In order to meet the requirements of non-cooperative target capture tasks, the concept of flexible capture has gradually entered human vision, which covers the target with flexible structures (e.g., net, cloth), and forms a reliable combination with the mission spacecraft through a flexible tether. In recent years, many research teams have carried out a number of projects on flexible capture. The typical space flexible capture projects include the ROGER (Robotic Geostationary Orbit Restorer) of the ESA (European Space Agency) [5], the electric debris removal device EDDE (Electro Dynamic Debris Eliminator) of the American Star Company [6; 7], the asteroid capture program ARM (Asteroid Retrieval Mission) of NASA [8; 9], the Furoshiki satellite project of Japan [10; 11] and so on. However, whatever the flexible capture system, in the maneuver process for the space tethered combination after target capture, the physical phenomena of collision, swing, tumbling and recombination betweenthe flexible capture system and the targets can easily occur in a very weak gravity field, which will affect the measurement, and control and communication with the capturing platform. Hence, the above-mentioned problems must be analyzed and controlled. There are some discussions on the maneuver dynamics and control of the space tethered combination, and the feedback tension control [12, 13], optimal control [14], predictive control [15] input-shaping control [16, 17] that are applied to the space tethered combination. In recent years, some research on the swing analysis and control of the space tethered combination has been conducted. [PERSON] studied the dynamics of deorbiting large space debris by means of a tethered space-tug under the action of a space tug thruster [18, 19]. [PERSON] developed a sophisticated mathematical model, taking into account the system's orbital motion, the relative motion of two spacecraft and spacecraft attitude motion, and the possible risks, such as tether slack, spacecraft collision, tether rupture, tether-tug intertwist and the destabilizing of the tug's attitude [20]. [PERSON] established the general nonlinear dynamics of the tethered combination system in the post-capture phase with the consideration of the attitudes of two spacecrafts and the quadratic nonlinear elasticity of the tether, and analyzed the inter resonance phenomenon of a simplified model [21]. [PERSON] analyzed the librational and vibrational characteristics of the tethered system, and designed a sliding mode controller in the orbital plane [22, 23]. [PERSON] designed a tether tension control law for use during orbital transfer via the small-gain theorem, which can suppress the swing of the space tethered combination [24]. However, the out-of-plane motion was not taken into account, and the validity of the swing control strategies were not tested in the above research. In this paper, we focus on the analysis and controller design of the swing. The purpose of this paper is to find some simple methods that are easy to implement in engineering.