Trajectory Modeling & Optimization for Future Space Systems

In this study six techniques for effectively modeling and analyzing the trajectories of future space systems are investigated. These techniques are grouped into methods for modeling trajectories by conversion to a mathematical programming problem, and methods for solving mathematical programming problems. The first group includes parallel shooting, high-order collocation and differential inclusion. Parallel shooting provides a general method of solving orbit transfer problems without path constraints whereas high-order collocation methods are very effective in solving problems with complex path constraints. Differential inclusion may be used to reduce the total problem size, potentially increasing the speed and robustness of a solution process. The second group includes sparse nonlinear programming, simulated annealing and genetic algorithms. Sparse nonlinear programming may be used to very rapidly find a locally optimizing solution. Simulated annealing and genetic algorithms may be used to find multiple regions where locally optimizing solutions exist, and are capable of solving problems with both discrete and continuous parameters. These six techniques will be studied keeping in mind the particular characteristics of advanced space systems employing high performance, low-thrust propulsion systems and multiple launches aboard a single launch vehicle.