Uncertainty Dispersion Analysis and Optimal Control of Atmospheric Re-Entry

Abstract

In this study, the atmospheric re-entry onto Earth and Mars is analysed concerning uncertainties. These uncertainties can arise in the modelling and the initial entry angle and velocity during the re-entry leading to hazards and malfunctions influencing the mission success. Therefore, the temporal evolution of uncertainties throughout the re-entry, descent and landing is examined using the Stochastic Liouville Equation.

This equation yields probability density functions depending on the states of the system dynamics and the time. From this a most probable trajectory together with 1-sigma and 3-sigma error bars can be estimated giving an impression on the influence of uncertainties. Furthermore, the covariance matrices are deduced from the probability density functions generating landing dispersions at the end time of the re-entry.

Beside ballistic trajectories also optimal trajectories for manoeuvrable re-entry vehicles are analysed. In this case, the re-entry vehicle is controllable in its flight path angle and the trajectories are optimized concerning the descent time.