Optimization of mission design for constrained libration point space missions

Designing space missions to remain in the vicinity of an equilibrium point in a three-body system is both useful and more difficult than for a two-body system. Because of the rotation of the system, there is not just one point of equilibrium, but rather five points where the gravitational and centripetal accelerations exactly cancel. These points are called libration points (L1-L5). This work chooses an Earth-Sun L2 point mission, but is equally applicable to any libration point in any three-body system. This point is behind the Earth from the Sun and is useful because it is outside Earth's atmosphere and magnetosphere, but close enough for fast communications and maintenance missions. Also the telescope can point away from the light and heat interference of the Sun, Earth, and Moon simultaneously. The collinear points (Ll-L3) are unstable equilibriums, which makes trajectories near them quite sensitive to thrusting maneuvers or force perturbations by the full space environment. Trajectory and control history design about the unstable Sun-Earth L2 point will become increasingly complex as additional mechanical and scheduling constraints accompany scientific observation missions. Satisfying such constraints may be viewed as an optimization problem, with the objective of maximizing the mission goals. It then adds little further complexity to minimize fuel usage as part of the objective. Solving this design problem is an illustration of the power and ease of this alternative multiple-body mission design approach, which optimizes the whole trajectory and control design. In this thesis, the formulation of such an optimization problem is explained in several steps using increasingly complex dynamical and mission constraint models, and some resulting solutions for these steps are presented and discussed. The continuous time problem is first discretized using a pseudospectral method. The resulting finite dimensional problem is solved using a sequential quadratic programming algorithm. The design approach is discussed as a general mission optimization process, which can easily be used further into the design process and for more types of missions than the examples here, by applying it to a more realistically modeled and more highly constrained libration-point mission design.