Speaker
Description
As the Low Earth Orbit (LEO) satellite population increases, methods for computation of space debris re-entry footprints are an increasingly important part of assessing the impact of a spacecraft on humanity. Unfortunately, methods for forward and backward propagation of uncertainty and state estimation in uncontrolled re-entry struggle with a great deal of the common complicating factors on uncertainty propagation. Re-entry dynamics exhibit a strong dependence on attitude, so are thus high-dimensional, and are strongly non-linear and therefore also feature significant non-Gaussianity. The simulators applied to such problems also carry significant computational expense. Hence the feasible methods in this domain must make sacrifices in terms of physical or statistical accuracy, according to the well-known bias-variance tradeoff. The common preferred choice is to be statistically conservative through use of Monte Carlo campaigns.
Here an alternate approach is proposed that is computationally efficient and maximally conservative in terms of problem uncertainty due to the sacrifice of statistical information. Based upon the concept of reachable sets from control theory, a methodology is introduced that propagates the bounds of a volume of reachable space in the state space of the problem. By requirement of an aerodynamic model where aerodynamic coefficient ratios can be predicted based upon attitude, i.e. panel codes, and assumption that all uncertainties can be bounded by intervals the number of necessary samples for an absolute worst case debris footprint can be drastically reduced.
By selecting angle-of-attack, angle-of-sideslip pairs on the wind frame 2-sphere, attitude states can be found that result in aerodynamic forces that maximise reachability. Combining the state parameters with the uncertainty space and applying specific assumptions on re-entry models, a bounding box on the reachable set can be propagated.
This method is applied to a re-entry case of an upper stage with uncertainty in terms of initial state, atmospheric conditions and modelling assumptions and compared to a conventional Monte Carlo propagation. Finally, consideration is given to inverse problems and backward set propagation.