Design and Development of R2M2 – a Multi-Physics Modeling Tool for Reusable Launch Vehicles
Authors:   German Aerospace Center (DLR), Wessling , Germany, Gäßler Björn , Evrim Briese Lâle , Acquatella Paul , Simplício Pedro , Bennani Samir , Casasco Massimo 
Published: January 2024

Launcher guidance and control (G&C) design is a very demanding process, most notably because mission requirements are known to compete against each other and strong couplings between different disciplines exist. These effects become even more impactful when it comes to reusable launch vehicles, many of which are currently under development. The main task of the G&C system is to generate and follow a trajectory to fulfil mission objectives. This is achieved using various actuator types, which typically include the main engine(s), thrust vector control (TVC), aerodynamic control surfaces and cold-gas thrusters of a reaction control system‎(RCS).

The motion of these actuators introduces excitations of flexible modes and perturbations through the launchers’ structure which cannot be easily modelled since the mechanical properties are highly time-varying due to the propellant being burnt to generate thrust. External perturbations from aerodynamics or wind reinforce these effects. Furthermore, actuators and other subsystems are subject to faults and failures having multiple potential origins. All of these perturbations must be handled by the G&C system.

In the current industrial approach, these multi-physics effects are tackled by separate teams using their own tools while G&C design is usually based on low-fidelity models that simplify the interactions between disciplines. The adoption of multi-physics acausal modelling approaches such as MODELICA and MATLAB Simscape is believed to enable a more efficient and accurate modelling of the multi-disciplinary interactions.

This motivates the development of a dedicated multi-physics simulator for multi-actuated vertical take-off vertical landing (VTVL) vehicles based on MathWorks’ Simulink/Simscape. Setting up simulators is a crucial and time-consuming activity in GNC design. The openly distributable Rapid Reusable Launcher Simulation via Multi-physics Modeling (R2M2) tool is a multi-physics simulator framework that aims at reducing this modeling effort and enabling users to quickly and easily set up simulations of VTVL vehicles by only defining the required model parameters. This helps users to save time and resources and enables them to focus their research and development efforts on the GNC system.

On the other hand, R2M2 provides the simulation environment to rapidly evaluate GNC approaches. In addition to simplifying the setup process, the R2M2 tool is also highly adaptable and able to simulate a wide range of VTVL mission scenarios, including different vehicle and actuator configurations and environmental conditions. Automated Monte Carlo routines are also provided to facilitate the investigation of the effects of wind disturbances and uncertain parameters.

The tool is capable of modeling external influences such as gravitational and aerodynamic effects, as well as internal dynamics from time-varying and moving masses. Modeling of variable-mass dynamics is an essential component for launch vehicle simulations. Mass properties of launch vehicles are changing mainly due to the propulsion causing the ejection of combustion products through the engines’ nozzles. The varying mass influences not only the vehicle’s properties such as the center of mass and moments of inertia but also generates additional forces and moments for instance due to Coriolis effects [R1] [R2]. In addition, the tool can consider common actuator failure cases including the jamming of TVC actuators and aerodynamic control surfaces and degraded engine performance. Future implementations may extend the tool to being capable to consider sloshing effects and structural flexibility.

This paper describes the design of the R2M2 tool and provides an overview of its functionalities and applications. The implementation within MathWorks’ physical simulation environments Simscape and Simscape Multibody is shown for all relevant subsystems and physical effects. Challenges and drawbacks using Simscape for flight mechanics modeling are addressed. These main challenges arise from limited Simscape functionalities and its closed-source nature when the interaction of variable mass dynamics and physical effects specific to aerospace applications, such as aerodynamic forces and moments, have to be modeled. Possible solutions and work-arounds, as implemented in the tool, are shown.

A benchmark scenario of a two staged launch vehicle ascent is implemented to verify the desired functionality of the R2M2 tool. To enable trajectory tracking the benchmark vehicle is configured with an engine cluster of five throtteable main engines, thrust vector control (TVC), aerodynamic control surfaces (fins) and a reaction control system‎(RCS). A preliminary controller and control allocation design is shown which enables stable flight on the vehicle’s ascent trajectory. The benchmark implementation offers the potential for synthesis and assessment of more sophisticated RLV guidance and control algorithms to improve the overall system performance and robustness.

[R1] F. O. Eke; Dynamics of Variable Mass Systems. Technical Report CR-1998-208246, National Aeronautics and Space Administration (NASA); 1999

[R2] B. Gäßler, L.E. Briese, P. Acquatella, P. Simplício, S. Bennani, M. Casasco; Variable-Mass Dynamics Implementation in Multi-Physics Environment for Reusable Launcher Simulations; 9th EUROPEAN CONFERENCE FOR AERONAUTICS AND AEROSPACE SCIENCES (EUCASS), 2022, Lille