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.