Reusability Flight Experiment Guidance: Trajectory Correction After Ascent

This paper presents the design and implementation of a guidance algorithm for the re-entry vehicle ReFEx (Reusability Flight Experiment). This algorithm aims at correcting for the dispersion in position and velocity after separation from the launcher, by updating the trajectory. The need for this update is driven by the expected divergence from the nominal trajectory at separation, due to the use of an unguided launcher. The transcription of the problem into an optimal control problem is used as a baseline for verification purposes. This algorithm consists of a simplification of the optimal control problem, reducing the profiles of the control variables to a finite set of control parameters. Combining this problem reduction with a function that propagates the trajectory from the initial state, this approach is able to transform the problem into an unconstrained optimization problem. This paper shows that this simplification is able to find solutions of similar quality to the full optimal control approach. The resulting algorithm is proven real-time capable by deploying it into a hardware equivalent of the on-board computer. In addition, a strategy to diverge during flight to an alternative target if the nominal one cannot be reached is appended to the algorithm.