Time Optimal Drag-Based Targeted De-Orbiting for Low Earth Orbit

Abstract

Controlled de-orbiting plays a crucial role in any space mission to ensure landing of a satellite or capsule in the desired location and preventing damage to people and property on the ground caused by debris. The necessary orbital energy reduction from the initial conditions to the re-entry interface can be achieved using a de-orbit burn or exploiting drag modulation as a control mechanism. The current work perfectly fits in this scenario, proposing a novel algorithm to generate minimum-time optimal trajectories for a satellite ballistic de-orbiting from a Low Earth Orbit (LEO) to the atmospheric re-entry interface. The formulation is written in terms of modified equinoctial orbital parameters, particularly suitable for trajectory analysis and optimization, even in cases of oscillatory problems with large time scales as in the de-orbiting problem. The optimization problem is solved with the MATLAB software GPOPS-II using a hp adaptive Gaussian quadrature orthogonal collocation method. It is formulated as a single-stage optimization problem considering the exposed surface as a control variable. The cost function to be minimized is the final time, while the imposition of an event constraint on the altitude at the de-orbit point ensures its value is in an acceptable range. A novel class of solutions is defined for the algorithm implementation to guarantee the desired values of latitude and longitude. It has been used to generate high-precision optimal trajectories and corresponding control variable laws in different conditions. The identification of a common trend of solutions along an infinite-shaped pattern allowed the possibility to model a wide range of missions, involving different initial conditions and satellites. A subsequent Monte Carlo analysis showed the algorithm validity and robustness with a successful outcome on 500 cases and an error less of 0.5% for most of them.