Actuator Constrained Optimal Formation Keeping Near the Libration Points

Spacecraft formations that evolve near the libration points of the Sun-Earth/Moon system are one option commonly considered for space-based interferometry applications. Although precision tracking is often envisioned as a requirement, earlier studies have already revealed that the dynamically sensitive nature of this region of space presents a number of unique challenges in this respect. For instance, physical hardware limitations, specifically related to the on-board actuators, can limit the attainable tracking accuracy. The goal of this investigation is to devise a numerical process that allows the designer to identify the maximum tracking accuracy achievable in the presence of actuator (e.g., thruster) constraints. This is accomplished through the application of direct optimization methods. A problem formulation is presented that effectively treats, within a nonlinear programming framework, problems with state and control discontinuities and problems involving temporally continuous but spatially discrete control variables. The results of this investigation lay the algorithmic foundation for future explorations involving multiple independent actuators each with its own set of constraints and switching dependencies.