# Angular Trajectory Design for MR-SPS Using Bezier Shaping Approach
## 1 Introduction  
With the increasing demand for energy and the depletion of non-renewable energy, the world is facing a serious energy crisis. As a kind of abundant clean and renewable energy, the rational utilization of solar energy is of great significance to solve the energy crisis and environmental problems. Solar power satellite (SPS) also called space power station or space solar power satellite (SSPS) first proposed by [PERSON] in 1968 [1] is a class of large-scale on-orbit servicing spacecraft that can collect solar energy in space and transmit electrical energy in the form of microwave to the earth. A typical SPS consists of three main parts: the solar collector uses the solar arrays to receive the sunlight and convert the solar energy into electric energy, some SPSs are equipped with concentrators such as lenses or concave mirror to converge the sunlight; the conversion device converts the electric energy into microwave or laser; the antenna or laser transmitter transmits the microwave or laser to the ground, in which the rectenna of the receiving station receives the microwave or laser and converts it into electric energy which can be injected to power supply system. Over the past couple of decades, the United States, Europe, Japan, and China have put forward a variety of construction schemes for SPSs. Since [PERSON] first proposed the idea of building a SPS in geostationary orbit (GEO), in 1970s, NASA continued to explore the feasibility and key technologies of SPS and proposed the 1979 SPS reference system [2]. In 1990s, NASA successively proposed a series of SPS configurations, including Sun Tower, Solar Disc, Abacus and Integrated Symmetrical Concentrated system (ISC) [3]. In 2011, [PERSON] came up with the solar power satellite via arbitrarily large-phased array (SPS-ALPHA) [4]. ESA put forward the Sail Tower SPS, which effectively reduced the system mass but could not achieve sustainable energy supply [5]. JAXA began the study of SPS in 1990 and several configurations were given, for example, JAXA 2001, JAXA 2002, and Tethered SPS [6], etc. Tethered SPS has smaller mass and can supply energy continuously. China has carried out research on SPS since 2015 based on two types of SPS concept: Multirotary-joint Solar Power satellite (MR-SPS) by CAST [7] and Space Solar Power Station via Orb-shape Membrane Energy Gathering Array (SSPS-OMEGA) by Xidian University [8]. The core task of a SPS is to collect as much solar energy as possible and transmit it to the ground accurately. To accomplish the above goal, attitude of an SPS is supposed to be adjusted so that the solar collector tracks the sun and at the same time, the antenna or laser transmitter points to the rectenna in the ground accurately. Due to its large mass and inertia, large torque is required for attitude control of a SPS, which means more actuators and fuel need to be carried and further increases the mass of the system. In order to reduce fuel consumption and mass, some research has been done. [9] proposed a novel quasi-Sun-pointing attitude in Sun-frozen orbit. Although about 3% electricity must be given up, little control effort is required to deal with the solar radiation pressure and gravity-gradient torque. Refs. [10; 11] developed an integrated orbit, attitude, and structural control system architecture for very large SSPS in GEO. A low-bandwidth attitude control system was proposed utilizing cyclic-disturbance accommodating control to provide precision pointing of the Abacus platform in the presence of dynamic modeling uncertainties and external disturbances. Moreover, the configuration of the actuators and the propellants required were also analyzed in detail. In [12; 13], a detailed study of solar power satellites' orbit dynamics was performed, and a direct comparison between the attitude dynamics of SPS in GLP orbit and in GEO was made. When both attitude and orbit control are considered, fuel consumption is less in GLP compared to in GEO.