Open-Source Visualization of Reusable Rockets Motion: Approaching Simulink - FlightGear Co-simulation

This paper shows how to approach effective visualization of the motion of reusable rocketsby combining Simulink / Matlab modeling with the capabilities of FlightGear, a state-of-the-artopen-source tool typically used for aircraft simulation in the gaming community. We describethe entire open-source toolchain and the steps needed for the coupling of the involved software,with detailed code provided as Appendices. Finally, We propose a concrete example, associatedwith the application to the motion of reusable rockets

Costate Convergence with Legendre-Lobatto Collocation for Trajectory Optimization

This paper introduces a new method of discretization that collocates both endpoints of the domain and enables the complete convergence of the costate variables associated with the Hamilton boundary-value problem. This is achieved through the inclusion of an \emph{exceptional sample} to the roots of the Legendre-Lobatto polynomial, thus promoting the associated differentiation matrix to be full-rank. We study the location of the new sample such that the differentiation matrix is the most robust to perturbations and we prove that this location is also the choice that mitigates the Runge phenomenon associated with polynomial interpolation. Two benchmark problems are successfully implemented in support of our theoretical findings. The new method is observed to converge exponentially with the number of discretization points used

Physical Modeling and Simulation of Reusable Rockets for GNC Verification and Validation

Reusable rockets must rely on well-designed Guidance, Navigation and Control (GNC) algorithms. Because they are tested and verified in closed-loop, high-fidelity simulators, emphasizing the strategy to achieve such advanced models is of paramount importance. A wide spectrum of complex dynamic behaviors and their cross-couplings must be captured to achieve sufficiently representative simulations, hence a better assessment of the GNC performance and robustness. This paper focuses on of the main aspects related to the physical (acausal) modeling of reusable rockets, and the integration of these models into a suitable simulation framework oriented towards GNC Validation and Verification (V&V). Firstly, the modeling challenges and the need for physical multibody models are explained. Then, the Vertical Landing Vehicles Library (VLVLib), a Modelica-based library for the physical modeling and simulation of reusable rocket dynamics, is introduced. The VLVLib is built on specific principles that enable quick adaptations to vehicle changes and the introduction of new features during the design process, thereby enhancing project efficiency and reducing costs. Throughout the paper, we explain how these features allow for the rapid development of complex vehicle simulation models by adjusting the selected dynamic effects or changing their fidelity levels. Since the GNC algorithms are normally tested in Simulink®, we show how simulation models with a desired fidelity level can be developed, embedded and simulated within the Simulink® environment. Secondly, this work details the modeling aspects of four relevant vehicle dynamics: propellant sloshing, Thrust Vector Control (TVC), landing legs deployment and touchdown. The CALLISTO reusable rocket is taken as study case: representative simulation results are shown and analyzed to highlight the impact of the higher-fidelity models in comparison with a rigid-body model assumption

An Instantaneous Impact Point Guidance for Rocket with Aerodynamics Control

This paper aims to propose a new guidance algorithm for a rocket with aerodynamics control for launch operations, based on the concept of the instantaneous impact point (IIP). In this study, the rocket with aerodynamics control is considered with the purpose of reducing dispersion of the impact point after separation of the rocket for safety reasons. Since a very limited aerodynamic maneuverability is typically allowed for the rocket due to the structural limit, a guidance algorithm producing a huge acceleration demand is not desirable. Based on this aspect, the proposed guidance algorithm is derived directly from the underlying principle of the guidance process: forming the collision geometry towards a target point. To be more specific, the collision-ballistic-trajectory where the instantaneous impact point becomes the target point, and the corresponding heading error are first determined using a rapid ballistic trajectory prediction technique. Here, the trajectory prediction method is based on the partial closed-form solutions of the ballistic trajectory equations considering aerodynamic drag and gravity. And then, the proposed guidance algorithm works to nullify the heading error in a finite time, governed by the optimal error dynamics. The key feature of the proposed guidance algorithm lies in its simple implementation and exact collision geometry nature. Hence, the proposed method allows achieving the collision course with minimal guidance command, and it is a desirable property for the guidance algorithm of the rocket with the aerodynamics control. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed guidance algorithm

Robust Control for Reusable Rockets via Structured H-infinity Synthesis

This paper discusses the problem of synthesizing robust controllers for reusable rocketsduring the aerodynamic descent phase. Emphasis is given to a well-established subset ofmethods, specifically robust control techniques based on theH∞concept. A thoroughdescription of how this family of methods can be used for the descent phase of reusablerockets is provided, together with a comparison of the full- and structured-version ofH∞methods. The methodology, the problem faced and the performance that can be obtainedare discussed. Some results are shown for CALLISTO, a reusable rocket demonstratorjointly developed by DLR, JAXA, and CNE

Apollo 11 Reloaded: Optimization-based Trajectory Reconstruction

This paper wants to be a tribute to the Apollo 11 mission, that celebrated its 50th anniversary in 2019. By using modern methods based on numerical optimization we reconstruct critical phases of the original mission, and more specifically the ascent of the Saturn V, the translunar injection maneuver that allowed the crew to leave the Earth’s sphere of influence, and the Moon landing sequence, starting from the powered descent initiation. Results were computed by employing pseudospectral methods, and show good agreement with the original post-flight reports released by NASA after the successful completion of the mission