Continuation Methods and Non-Linear/Non-Gaussian Estimation for Flight Dynamics

We propose herein to augment current NASA spaceflight dynamics programs with algorithms and software from three domains. First, we use parameter continuation methods to assist in computation of trajectories in complicated dynamical situations. Numerical parameter continuation methods have been used extensively to compute a menagerie of structures in dynamical systems including fixed points, periodic orbits, simple bifurcations and invariant manifolds. Perhaps more important for the current work, such methods have already proven their worth in flight dynamics problems, especially those having to do with the complicated dynamics near libration points. Second, we propose to use Continuous Mechanics and Optimal Control (CMOC). Algorithms based the CMOC formalism promises to support optimal trajectory design using both discrete and continuous control. Third, we propose to use advanced filtering techniques and representations of probability density functions to appropriately compute and manage the uncertainty in the trajectories. While advanced methods for understanding and leveraging the underlying dynamics are clearly necessary for effective mission design, planning, and analysis, we contend that they do not suffice. In particular, they do not, in and of themselves, address the issue of uncertainty.Herein we discuss methods that balance the accuracy of the uncertainty representation against computational tractability.