1 A Survey on Formation Control of Small Satellites Guo-Ping Liu, Fellow, IEEE and Shijie Zhang Abstract -- This paper comprehensively reviews the state-of- the-art development in formation control of small satellites. Satellite formation flying, distributed satellite systems and fractionated satellite formation are discussed first. Various formation control architectures and methods of small satellites are then introduced, including the leader-following method, behaviour based method, virtual structure method, cyclic pursuit method, artificial potential function method, algebraic graph method, and non-contact force method. Coordinative control of multiple small satellites is also reviewed, covering coordinative control of satellite formation, coordinative attitude control of satellite formation, and coordinative coupled attitude and orbit control of satellite formation. The achievements and development trends of the formation control of small satellites are considered and analysed. Keywords: Satellite formation, small satellites, formation control, coordinative control. I. INTRODUCTION In the last century, human beings successfully entered into the space and made a great contribution to the progress of social civilization. At present, the space technology and applications have brought many changes in various fields. So far, more than four thousand satellites (artificial satellites) orbiting the earth have been launched and successfully applied to communications, navigation and positioning, meteorology, environmental and disaster monitoring, marine exploration and other fields [1]. Most of these achievements are based on a single satellite, which is the main force in applications of satellites. From the current development of space technology on the whole, the development of satellite technology leads to two different trends. One is the weight and size of a single satellite become heavier and larger, its structure and functions are more complex. The other is small satellites with multiple structures and their functions are relatively simple through coordination work to replace complexity of a single large satellite. Because of the complex technology, long development cycle and high cost, the development of large satellites is limited. On the other hand, with the development of new energy, new materials and new communication technology, the coordinated control system composed of many small satellites through the networking mode presents a booming trend [2]. Satellite formation flying is an important mode of multiple small satellites, in which each satellite remains in a stable close distance configuration, mutually maintains close connection and shares signal processing, information exchange, payload and other functions [3]. This mode is the main means of realizing the space-based interferometric synthetic aperture imaging, gravity field measurement, Guo-Ping Liu is with the School of Engineering, University of South Wales, Pontypridd CF37 1DL, UK. (e-mail: guoping.liu@southwales.ac. uk) Shijie Zhang is with School of Astronautics in Harbin Institute of Technology, Harbin 150001, China. (e-mail: sjzhang@hit.edu.cn) (Corresponding authors: Guo-Ping Liu and Shijie Zhang.) space optical virtual imaging applications etc. Since the 1990s, the concept of multi-satellite formation flying has conducted a number of space flight demonstrations and applications of satellite formation technology for astronomy, communications, meteorology, and environmental uses [4]. The advantages and significance of satellite formation technology and its applications have been validated. In recent years, with the development of space technology and space mission, satellite formation research category has been expanded. A traditional integrated satellite is decomposed into small payload modular satellites and small service modular satellites, which form a virtual space system via wireless ad hoc networks. In terms of requirements of task aggregation or separation, a separation-cluster satellite system is formed, which can effectively improve ability of dealing with uncertainty, enhance quick response ability, and reduce difficulty of entering the space. It is one of the most important directions of the development of international space technology. To make full use of satellite formation technology advantages, it greatly depends on coordinative control performance of the formation and distributed information fusion capability of each satellite, which is also necessary for the normal operation of the whole satellite formation. This is one of the key problems of satellite formation. Whether it is the coordinative control of satellite formation or the fusion of satellite information, it is necessary to realize information exchange between satellites through networks, which results in a networked satellite formation system. The cooperation of satellite formation forms a virtual satellite that replaces a single large satellite, achieves its equivalent functions and completes some tasks that cannot be done in a certain extent. The coordinative control system of the networked satellite formation is a distributed space system, which is composed of satellites that are independent each other, has local communication networks and realizes a common space mission [5]. The satellites share information via communication links on satellite networks and achieve consensus on the system target tasks through the principle of consistency. The satellite formation accomplishes control tasks of the whole system using common navigation and control through mutual coordination between individual satellites. Coordinative control methods and technologies of networked satellite formations will have a profound impact on space science and technology and its applications. It is fundamentally changing technical approaches of the existing satellite missions, which has incomparable advantages with existing satellites. The main points are as follows [6-9]: System cost reduction: Since the whole system completes a space mission through coordination of a number of small satellites, the design and manufacture of those small satellites can be done using standardized processes and the cost of production becomes lower. Due to the small size and light weight of the small satellites, their launch costs will be