ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

Trajectory optimization of spacecraft has been an active research field for many years. Many solvers are based on local optimizers (gradient based, heuristic methods) therefore lacking the guarantee of finding the global optimum within finite time. A novel optimization algorithm is introduced based on interval analysis which does provide this guarantee. Moreover, all optimal solutions in the solution set will be found. State parameterization is used to transfer the infinite dimensional trajectory optimization problem into a finite dimensional, static optimization problem. By using state parameterization instead of the commonly used control parameterization one can prevent explicit integration of the dynamics. Instead the dynamics are used to derive the control trajectories based on the state trajectories via the equations of motion. Preventing explicit integration reduces the computational load significantly. The proposed solver (optimization and parameterization) is validated using three examples: the orbit transfer problem (Hohmann transfer), rendezvous and docking problem (using Hill-Clohessy-Wiltshire equations), and formation flying with large inter-satellite distances. The results demonstrate that the proposed solver can indeed produce guaranteed optimal trajectories for linear and non-linear complex problems.