Description: Flying spacecraft in formations presents several advantages over traditional single spacecraft missions. Smaller, inexpensive spacecraft can be used to complete complex tasks and provide more flexibility when investigating unknown environments. Currently, large fuel costs required for formation maintenance significantly reduce the lifetime of multi-spacecraft operations. Simplifying assumptions made when designing formation control algorithms cause controllers to constantly adjust for modeling errors. This project aims to remedy this problem by using an innovative means to encapsulate complex spacecraft dynamics and use this formulation to design formations and develop control policies. This research will use the geometric description of a torus to represent the motion of spacecraft around its primary. Almost all bounded motion can be described using torus angles. That is, a set of torus angles maps to a position and velocity for an orbiting spacecraft. This allows us to unify motion in a diverse set of complicated dynamics by utilizing this description. Representing motion with tori is also advantageous as the trajectories of the torus angles are typically much simpler than the corresponding motion in Cartesian space. Hence, by using toroidal manifolds to capture spacecraft motion, more fuel-efficient control can be performed while still preserving simplicity in the algorithms. Previous work in designing passive formations on tori will be leveraged. Passive formations allow nature to bound spacecraft motion and therefore don’t require fuel to maintain their structure. These formations require exact placement of spacecraft on to their respective tori, but due to uncertainty in the environment, this is not feasible from an open-loop prospective. Control laws will be developed to drive spacecraft to these passive formations, allowing nature to perform most of the formation maintenance.

Benefits: Flying spacecraft in formations presents several advantages over traditional single spacecraft missions. Smaller, inexpensive spacecraft can be used to complete complex tasks and provide more flexibility when investigating unknown environments. Currently, large fuel costs required for formation maintenance significantly reduce the lifetime of multi-spacecraft operations. Simplifying assumptions made when designing formation control algorithms cause controllers to constantly adjust for modeling errors.