Fuel-optimal control and guidance for low- and medium-thrust orbit transfer

This thesis presents new theoretical results which lead to new algorithms for the computation of fuel-optimal multiple-burn orbit transfers of low and medium thrust. Theoretical results introduced herein show how to add burns to an optimal trajectory and show that the traditional set of necessary conditions may be replaced with a much simpler set of equations. Numerical results are presented to demonstrate the utility of the theoretical results and the new algorithms. Two indirect methods from the literature are shown to be effective for the optimal orbit transfer problem with relatively small numbers of burns. Perturbations due to Earth's oblateness and atmospheric drag are considered. Example extremal solutions including these effects and computed by the aforementioned methods are presented. A new algorithm is presented which greatly eases the process of lowering cost by helping the numerical method to simply "jump" from an N-burn solution to an N + 1 burn solution, thereby lowering the cost of the transfer. Using this algorithm and the indirect methods mentioned above, the phenomena of multiple solutions is demonstrated for the optimal orbit transfer problem. A simple empirical guideline is proposed which chooses between two or more multiple solutions when using this algorithm. It is not claimed that the algorithm will obtain the globally optimal solution. Intuitively, one might want to think of an optimal multiple-burn transfer not as one large trajectory, but as a sequence of optimal one-burn transfers between transfer orbits that are optimally chosen. For ideal gravity, a strong relationship is shown to exist between these two problems. Based on this relationship, two new numerical methods are presented which iteratively compute optimal orbit transfers.