Successive convexification-based fuel-optimal high-altitude guidance of the RETALT reusable launcher
Authors:   Deimos Engineering and Systems, Tres Cantos, Madrid, Spain, Spada Fabio , Ghignoni Pietro , Botelho Afonso , De Zaiacomo Gabriele , Rosa Paulo 
Published: January 2024

The last decade witnessed the major boost in space services since the beginning of space commercial activities. Development of reusable launchers has played a fundamental role in such advancement: cuts in refurbishment costs have indeed positively impacted on the financial needs to access stable operational orbits. In this context, the EU and ESA have made increasing efforts to achieve the goal of making launcher reusability the state of the art in Europe. One such effort is RETALT (Retro Propulsion-Assisted Landing Technologies) a Horizon 2020 project that allowed to increase the TRL of key technologies that will enable retro propulsion-assisted launcher reusability in Europe (Marwege, et al., 2022). In particular, one of the enabling technologies for launchers’ recovery through vertical landing is indeed GNC. Reliable and performing GNC algorithms are necessary to perform terminal manoeuvres autonomously and precisely within a limited available time horizon. In RETALT, a GNC solution was developed and brought to TRL3, assessing its performance considering uncertainties and dispersions on the vehicle and environmental models (Ghignoni, et al., 2022). On the other hand, dispersions at stage separation, i.e. the beginning of the re-entry arc, heavily impact on booster trajectory, and, if not properly managed, prevent the rocket from being able to reach the landing site.
Leveraging on the work done in RETALT, Deimos continued improving the GNC solution for reusable launchers, aiming at increasing the knowledge of the problem and the robustness of the algorithms. This paper focuses on the high-altitude guidance solution for the downrange landing (DRL) of the first stage of RETALT1, a two-stage-to-orbit (TSTO) launcher studied within RETALT. The DRL mission foresees an initial ballistic arc and two distinct burns connected by an aerodynamic phase. A high-altitude firing (re-entry burn) aims at reducing aerothermal loads, while the terminal landing burn guarantees a soft pinpoint landing on a floating barge.
The first aim of the work is combining state-of-the-art indirect and direct techniques to design a re-entry burn guidance capable of handling stage separation dispersions, while guaranteeing compliance with mass, online guidance and attitude requirements. Indirect methods are used in an offline fashion: the free-final time Hamiltonian boundary value problem stemming from the first-order optimality necessary conditions of the fuel-optimal 3DoF optimal entry guidance problem is solved at first. This is done for a finite number of sample points drawn from the dispersed initial conditions and a grid of ignition heights. A lookup table mapping initial conditions to optimal ignition height is thus obtained and used to schedule the beginning of the firing. Convex direct methods are used onboard, and a continuation technique is adopted to obtain a guidance profile compatible with attitude constraints: the 3DoF dynamics problem is solved first; its solution is then fed to a second iteration embedding nonlinear attitude kinematics and satisfying attitude rate limitations.
The second aim of the work is validating the guidance algorithm in a high-fidelity simulation environment. The DEIMOS-proprietary RETALT Functional Engineering Simulator (RETALT-FES) is used for such purpose; it includes detailed vehicle configurations and mission scenario models contributing to simulate a real-life scenario with GNC algorithms in the loop. In the full-length paper the algorithm will be then proved capable of handling such further dispersions.
The full proposed strategy, therefore, presents itself as a mid-ground with respect to uncertainties handling: the most relevant ones, i.e. the ones associated with separation conditions, are included within the guidance scheme, while the remaining ones are contained with the standard feedback-based control strategies.
Bibliography
Ghignoni, P. et al., 2022. RETALT: Recovery GNC for the Retro-Propulsive Vertical Landing of an Orbital Launch Vehicle. Bruges, HiSST2022.
Marwege, A. et al., 2022. RETALT: review of technologies and overview of design changes. CEAS Space Journal.