Trajectory Design of a Spacecraft Formation for Space-Based Solar Power Using Sequential Convex Programming

The concept of collecting solar power in space and transmitting it to the Earth using microwaves has been studied by numerous researchers in the past. The Space Solar Power Initiative (SSPI) at Caltech is a collaborative project to bring about the scientific and technological innovations necessary for enabling a space-based solar power system. The proposed system comprises an array of ultra-light, membrane-like deployable modules with high efficiency photovoltaic (PV) concentrators and microwave transmission antennas embedded in the structure. Each module is 60m x 60m in size and in the final configuration, hundreds of these modules span a 3km x 3km array in a geosynchronous orbit. As this formation goes around the Earth, the orientation and position of each module has to be changed so as to optimize the angle made by the photovoltaic surface with respect to the sun and by the antenna surface with respect to the receiving station on Earth. In order to achieve high antenna array efficiency, the modules have to remain in a tight formation with an edge-to-edge distance on the order of a few meters. In addition, the modules also have to avoid collisions and maintain a planar configuration to avoid the possibility of both PV and RF shadowing. In this paper, we present the trajectory design that achieves the dual goal of minimizing the propellant usage and maximizing the power delivered to the ground station, while meeting the various orbital constraints. The optimal control problem is solved using sequential convex programming for a 4 x 4 formation and the results obtained show that it is possible to maintain the formation for 11 years in a geo-synchronous orbit with relatively small amounts of propellant. This serves as a critical achievement in the path towards realizing the objective of space-based solar power.