Design of ReFEx Guidance: Trajectory Correction after Ascent

Abstract

This paper presents the design and implementation of a guidance algorithm for the re-entry vehicle ReFEx. This algorithm aims at correcting for the dispersion in position and velocity after separation from the launcher, by generating an updated trajectory leading from the estimated state to the target. The need for this trajectory update is driven by the huge uncertainty regarding the state at the end of the ascent phase, as ReFEx will be launched with an unguided rocket. The transcription of the problem into an optimal control problem is used as a baseline to verify the algorithm proposed. This algorithm consists of a simplification of the optimal control problem, reducing the profiles of the control variables to a set of control parameters. Defining this set of parameters is not trivial as it limits the solution space. 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 as the full optimal control approach. The results also show that the uncertainty of the state at separation is excessively high to guarantee reaching the nominal target. Therefore, a strategy to define the convergence envelope to the nominal target is developed. This approach, which is also used to define the alternative target, is based in regularized logistic regression.