Dynamics of the Space Tug System with a Short Tether

Hindawi Publishing Corporation International Journal of Aerospace Engineering Volume 2015, Article ID 740253, 16 pages http://dx.doi.org/10.1155/2015/740253 Research Article Dynamics of the Space Tug System with a Short Tether Jiafu Liu,1 Naigang Cui,2 Fan Shen,2 and Siyuan Rong2 1 Shenyang Aerospace University, Shenyang 110136, China Harbin Institute of Technology, Harbin 150001, China 2 Correspondence should be addressed to Jiafu Liu; Received 25 February 2015; Revised 12 June 2015; Accepted 2 July 2015 Academic Editor: Paul Williams Copyright © 2015 Jiafu Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The dynamics of the space tug system with a short tether similar to the ROGER system during deorbiting is presented. The kinematical characteristic of this system is significantly different from the traditional tethered system as the tether is tensional and tensionless alternately during the deorbiting process. The dynamics obtained based on the methods for the traditional tethered system is not suitable for the space tug system. Therefore, a novel method for deriving dynamics for the deorbiting system similar to the ROGER system is proposed by adopting the orbital coordinates of the two spacecraft and the Euler angles of ROGER spacecraft as the generalized coordinates instead of in- and out-plane librations and the length of the tether and so forth. Then, the librations of the system are equivalently obtained using the orbital positions of the two spacecraft. At last, the geostationary orbit (GEO) and the orbit whose apogee is 300 km above GEO are chosen as the initial and target orbits, respectively, to perform the numerical simulations. The simulation results indicate that the dynamics can describe the characteristic of the tether-net system conveniently and accurately, and the deorbiting results are deeply affected by the initial conditions and parameters. 1. Introduction The number of flying objects including the controlled spacecraft and the space debris (including the abandoned spacecraft) in the low earth orbit (LEO) and the geostationary orbit (GEO) increases sharply because of the frequent human space activities [1–3]. It is reported by ESA that, at the end of 2008, there were 1186 objects in GEO and only 32% were controlled spacecraft. The collision risks will be posed by the uncontrolled spacecraft and space debris mentioned above. Therefore, it is necessary to monitor and clear the abandoned spacecraft and space debris. The RObotic GEostationary Orbit Restorer (ROGER) concept was proposed by ESA. The researchers not only focused on the economic consideration and future business application but also focused on the orbital monitoring and clearance of the abandoned spacecraft [4, 5]. To make use of the space electrodynamic tethered system to deorbit spacecraft has been studied in [6, 7], which utilizes the motion of the conductive tether relative to the magnetic field of the earth to produce electrodynamic forces. It is also proposed that the abandoned spacecraft can be deorbited by the solar radiation pressure experienced by the sailcraft attached to the spacecraft. The sailcraft is initially folded and will be deployed when the spacecraft is spent. The feasibility of the solar radiation pressure based deorbiting approach has been demonstrated by the NanoSail-D project within NASA. Moreover, the cubeSail project in Surrey [8] and the project using solar pressure in Strathclyde [9] are also performed to study the spacecraft deorbiting approach by solar pressure. It is a practical method by using the space robots to capture the noncooperative spacecraft or to deorbit the abandoned spacecraft. The method can also be used in the space missions such as spacecraft repair and fuel charges [10, 11]. The space tether based deorbiting system is the most comprehensively studied one among the methods mentioned above, including the ROGER system and the space electrodynamic tethered system. The monitoring for the current orbit and forecasting for the future orbit are studied in the ROGER project [5]. The feasibility of the GEO service is also discussed from the view of economic and technical aspects. The ROGER spacecraft approaches, captures, and transports the abandoned spacecraft into the graveyard orbit. The configuration of the 2 International Journal of Aerospace Engineering ROGER system including the ROGER spacecraft and the subsystem used for capturing the abandoned spacecraft is studied and developed in ESA. The technical details of the ROGER system mainly focus on the grappling equipment, attitude and orbit control devices and so forth. Moreover, the guidance, navigation, and control elements are also focused on [4]. The typical electrodynamic tethered system for deorbiting is MXER, which utilizes the electrodynamic force to deorbit the spacecraft. The system design is presented in [12, 13]. The studies concerning space tethered system mainly focus on tether models [14, 15], tether vibrations [16–19], in-plane and out-plane librations [20–26], attitude motions [19, 27–30], and orbital motions [31–33]. The bead model is adopted to establish the dynamical equations in [14, 15]. Input Shaping method is adopted to reduce the initial vibrations of the electrodynamic tether system in [34]. The stability of inplane and out-plane librations of the electrodynamic tethered system in inclined and elliptic orbits with high eccentricity is studied in [25, 26], and the chaotic librations can be stabilized to the periodic motion by delayed feedback control. The attitude control of the main satellite can be performed by the offset scheme [27]. The vibration of the tether can also be suppressed by the offset scheme [19]. There are a large number of literatures concerning with space tethered system, however, few concerning with the system design and dynamics for the space tug system similar to the ROGER system during deorbiting. It seems that the configurations of the tethered systems in [35, 36] are analogous to the ROGER system; however, there exist differences between them. The paper is organized as follows. Firstly, the configuration that the ROGER spacecraft in front of the abandoned one is adopted, the reference frames and coordinate transformations are presented. Secondly, the conclusion that the traditional dynamic modeling strategy for the tethered system is not suitable for the space tug system similar to the ROGER system in this paper is presented. Thirdly, the dynamic model for the space short-tether system during deorbiting is presented. The attitude motion of the ROGER spacecraft, the orbital motion of the two spacecraft, the librations of the system, and the elasticity of the tether are all considered. Finally, the effectiveness of the dynamic model is verified by numerical simu (...truncated)