Optimization of a tetrahedral satellite formation

Two fundamental approaches can be applied to satellite-formation mission design: active control, where satellites exert forces with their thrusters to maintain a constant or periodic geometry for all or part of each orbit, and natural, where satellite orbits are designed to naturally assemble a geometry for all or part of each orbit to within a tolerance defined from scientific requirements. An actively controlled formation can be labeled virtual rigid body (VRB) because geometry is precisely maintained as if the satellites were rigidly connected. This work describes a hierarchical optimization method for minimizing mission design computational complexity and applies this method to the design of VRB, natural-orbit, and multi-impulse solutions for a tetrahedron formation applicable to the proposed magnetospheric multiscale mission. Cost is defined in terms of total fuel per second of observation and tetrahedron geometric quality factor. Although both natural-orbit and active solutions are feasible, the active solutions substantially increase average data quality and observation time per orbit at minimum fuel cost, and the multi-impulse solution does not require thruster use during data collection periods.