Accommodating measurement uncertainty in the optimization of space flight trajectories

Equality constraints in trajectory optimization are typically handled as exact in space flight optimization. Frequently, however, the constraints are not known exactly, perhaps due to measurement uncertainty. In this paper, it is shown how this inexactness can be accommodated in a natural way by solving the deterministic optimization problem as a maximum a posteriori estimation problem. An example illustrating the approach is given in which an optimal two-impulse Lambert control law is developed which maintains a satellite in a desired Earth orbit. By accommodating uncertainty in this manner, the approach might improve cost performance, facilitate implementation, and reveal new relationships.