Optimal spacecraft trajectories via higher order differential inclusions

Higher order differential inclusion (HODI) is a new modeling technique that is applied to the modeling and optimization of spacecraft trajectories. The spacecraft equations-of-motion are mathematically manipulated into differential constraints that remove explicit appearance of the control variables (e.g., thrust direction and magnitude) from the problem statement. These constraints are transformed into a nonlinear programming problem by using higher order approximations of the derivatives of the states. In this work, the new method is first applied to a simple example to illustrate the technique and then to a three-dimensional, propellant-minimizing, Low-Earth-Orbit to Geosynchronous-Earth-Orbit spacecraft transfer problem. Comparisons are made with results obtained using an established modeling technique.