Embedded Optimization for Space Rider Reentry Module Parafoil GNC
Authors:   Sener Aeroespacial, Tres Cantos, Spain, Ramírez Jesús , Hewing Lukas , Cacciatore Francesco , Cardin Jorge , Lucrezia Michele 
Published: January 2024

The Space Rider Re-entry Module reusability concept includes using a guided parafoil during the descent and landing phase for a pinpoint touchdown without additional propellant use. The Space Rider landing shall comply with stringent requirements for what concerns vertical and lateral velocity at impact, to ensure a soft and safe landing.
In this frame, this paper addresses the very final part of the landing: a window of a few seconds in which the vehicle needs to reduce its vertical velocity below a threshold to meet the landing gear impact requirements. The manoeuvre to achieve this is known as the flare, typically consisting of a simultaneous full deflection of the parafoil winches to induce a momentary reduction in the vertical vehicle velocity. In this paper, we demonstrate that the execution of such a manoeuvre in a simple open-loop fashion leaves significant room for improvements and may indeed become incapable to meet touchdown requirements under system uncertainties and unfavourable wind conditions.
We then demonstrate major improvements in the landing performance by making use of a Model Predictive Control (MPC) scheme to actively control the parafoil in closed-loop to minimize the impact velocity. The optimization problem is formulated as a convex quadratic program which is subsequently solved by a tailored interior point solver developed in-house at SENER Aeroespacial. We give a sketch of the entire engineering pipeline, including a data-driven identification of low-complexity linear system models capturing the relevant dynamics for the flare execution. Furthermore, we outline a number of important design characteristics important for achieving the desired results, such as robustifying the formulation against uncertainties using a constraint-tightening scheme. Preliminary results under realistic wind conditions and system uncertainties show a reduction in failed cases from 61% with the baseline (open-loop) flare to below 5% with the MPC.
This predictive flare control scheme is accepted as part of the Scale Down Flight Tests (SDFT) to be performed in 2023 as part of the Space Rider GNC test campaign, taking the opportunity to demonstrate the potential of onboard optimization to improve mission performance. In order to comply with hardware and software requirements, the MPC has been fully developed using autocodable in-house tools with a significant focus on reducing the computational footprint to comply with hardware restrictions. No external toolboxes are used to ensure full visibility and control of the algorithms and allow computational optimization of the structure of the MPC Flare code. Along these lines, we make use of a condensed formulation together with a move-blocking scheme to reduce the number of optimization variables allowing for the use of robust and relatively simple solvers. The interior-point solver used for the optimization has been further tailored to exploit the problem structure and sparsity ensuring the solution of the optimization problem within a small fraction of the relevant sample times. The developed algorithms are supported by theoretical convergence guarantees and extensively tested on representative hardware empirically demonstrating their real-time reliability.
The MPC Flare and the optimization core end-to-end developed and tailored by SENER Aeroespacial will be proven in real flight within the Space Rider Reentry Module SDFT in 2023.