Optimal Robust Two-Body Trajectory Design with Corrective Maneuvers

Abstract

The focus of this research is the optimization of impulsive transfer trajectories in the presence of stochastic effects. A trajectory design method is introduced that accounts for a normally distributed initial state dispersion and minimizes the sum of nominal impulsive plus trajectory correction maneuver (TCM) magnitude. Four main problems are presented. First, a deterministic optimal trajectory is developed; in the coplanar cases, the optimal solution is Hohmann transfer. For the second problem, an initial state dispersion and a target position dispersion constraint are introduced. It is shown to be possible to modify the nominal two-impulse trajectory to satisfy the dispersion constraint. In the third problem, a TCM is performed at the optimal point along the deterministic optimal trajectory, resulting in a more efficient method to influence the target position dispersion. Problem 4 is the development of a robust trajectory, where the nominal impulsive maneuvers and TCM are simultaneously optimized. The result is a different nominal trajectory and TCM that is less expensive than the total cost of problem 3. The optimal TCM is rapidly computed along each nominal trajectory using the numerically propagated state transition matrix history as a step inside the optimization algorithm.