Analytic Gradient Computation for Bounded-Impulse Trajectory Models Using Two-Sided Shooting.

Many optimization methods require accurate partial derivative information in order to ensure efficient, robust, and accurate convergence. In this paper, analytic methods are developed for computing complex partial derivatives of two bounded-impulse trajectory models: the multiple gravity-assist low-thrust and the multiple gravity-assist with n deep-space maneuvers using shooting transcriptions. Particular attention is paid to the match point defect constraint present in these models due to its complex functional dependencies, and the gradient computations presented are extended to allow for the computation of trajectory path constraints. A comet sample return mission design problem is solved that underscores the benefits of implementing analytic gradient equations for these trajectory models. The computational efficiency of the techniques presented is compared against other methods available for computing partial derivative information, including automatic differentiation and the method of finite differences.

An Automated Solution of the Low-Thrust Interplanetary Trajectory Problem.

Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. In addition, a time-history of control variables must be chosen that defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated, which can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a hybrid optimal control problem. The method is demonstrated on hypothetical missions to Mercury, the main asteroid belt, and Pluto.