Design of ReFEx Guidance: Periodic On-Board Trajectory Updates

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 accumulating effect of modeling uncertainties and control and navigation errors, by periodically updating the trajectory so that it leads from the most recent estimated state to the target. The need for these trajectory modifications is driven by strict requirements in accuracy. The algorithm consists in a simplification of the optimal control problem. First of all, the control variables are expressed as a function of a set of parameters. These parameters, which definitions are critical as they define the solution space, define both the short term behaviour and the overall profile of the control variables. By combining this parameterization with a function that propagates the trajectory while accounting for constraints, the original optimal control problem can be transformed into a non-linear unconstrained optimization problem. As solving this problem completely would take excessive execution time, a trade-off was conducted between the maximum number of iterations allowed and the frequency of the trajectory updates. This paper shows that this algorithm compensates for the errors throughout the trajectory, reaching the target with the required accuracy. Due to the target being located a certain altitude, there are several additional requirements related to the touch-down. Additional corrections of the control variable profiles are made in order to avoid no-landing zones, particularly lakes, and to minimize the vertical impact velocity, via a flare maneuver.