On-board Trajectory Computation for Mars Atmospheric Entry Based on Parametric Sensitivity Analysis of Optimal Control Problems

This thesis develops a precision guidance algorithm for the entry of a small capsule into the atmosphere of Mars. The entry problem is treated as nonlinear optimal control problem and the thesis focuses on developing a suboptimal feedback law. Therefore parametric sensitivity analysis of optimal control problems is combined with dynamic programming. This approach enables a real-time capable, locally suboptimal feedback scheme. The optimal control problem is initially considered in open loop fashion. To synthesize the feedback law, the optimal control problem is embedded into a family of neighboring problems, which are described by a parameter vector. The optimal solution for a nominal set of parameters is determined using direct optimization methods. In addition the directional derivatives (sensitivities) of the optimal solution with respect to the parameters are computed. Knowledge of the nominal solution and the sensitivities allows, under certain conditions, to apply Taylor series expansion to approximate the optimal solution for disturbed parameters almost instantly. Additional correction steps can be applied to improve the optimality of the solution and to eliminate errors in the constraints. To transfer this strategy to the closed loop system, the computation of the sensitivities is performed with respect to different initial conditions. Determining the perturbation direction and interpolating between sensitivities of neighboring initial conditions allows the approximation of the extremal field in a neighborhood of the nominal trajectory. This constitutes a locally suboptimal feedback law. The proposed strategy is applied to the atmospheric entry problem. The developed algorithm is part of the main control loop, i.e. optimal controls and trajectories are computed at a fixed rate, taking into account the current state and parameters. This approach is combined with a trajectory tracking controller based on the aerodynamic drag. The performance and the strengthsa and weaknesses of this two degree of freedom guidance system are analyzed using Monte Carlo simulation. Finally the real-time capability of the proposed algorithm is demonstrated in a flight representative processor-in-the-loop environment

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

Sensor fault detection and isolation for electro-mechanical actuators in a reusable launch vehicle TVC system

This paper introduces a model-based Fault Detection and Isolation (FDI) approach for a Reusable Launch Vehicle (RLV) Thrust Vector Control (TVC) system operated by Electro-Mechanical Actuators (EMAs). The focus is on the sensors required for the EMA embedded control system to track the on-board computer control commands. The nullspace FDI method is considered and applied to detect and isolate additive faults affecting the mentioned sensors. A detailed formulation of the problem and the EMA-based TVC system modelling for FDI synthesis is provided, including the mechanical load exerted by the rocket nozzle. The FDI synthesis framework is introduced and the application of the nullspace-based strategy is described, including considerations about isolability of the faults. Vehicle-induced loads can potentially disrupt the fault detection process, therefore they are included in the problem formulation to achieve decoupling from the residual generator output and not incur into false alarms. The generator performance is then assessed in fault-free and faulty scenarios using a high-fidelity TVC physical model, and successively benchmarked at the example of an RLV mission scenario

Design of a Control Allocation Solution for the Winged Reusable Launch Vehicle ReFEx

This paper presents a control allocation solution for the technology demonstrator mission ReFEx, which focuses on a vertical takeoff and horizontal landing strategy with autonomous navigation, online guidance, and controlled flight throughout the mission. The trajectory for the demonstration flight is aimed as one for a winged launch vehicle first stage: maintaining stability and control of the vehicle while reaching a predefined target. During the atmospheric phase the vehicle is stabilized by using an active aerodynamic control system which transforms inputs from the guidance and navigation systems into control commands for the individual actuators. In that sense, the control allocation subsystem translates commanded moments into commanded aerodynamic surface deflections. Due to the effect of modeling uncertainties, navigation errors, and underactuated regions, this subsystem needs to be robustified. The algorithm proposed in this paper addresses this challenge via a combination of the deflections required to trim the vehicle together with delta-deflections that aim at converging iteratively to the commanded moments. The combination of these two contributions is able to respond fast to state changes, compensate for modeling uncertainties and navigation errors, and provide a safe mode for the underactuated regions. The performance of the system is studied using a high-fidelity simulator

ReFEx: Reusability Flight Experiment - Flight Safety Analysis

The German Aerospace Center project ReFEx aims to demonstrate autonomous GNC capabilities for aerodynamically controlled RLVs, its launch is scheduled for 2024 in Australia. This paper covers the flight safety analysis required by the Australian Space Agency (ASA). Monte Carlo campaigns results are used to assert that the flight termination system is capable of destabilizing the vehicle, to define impact probabilities for different ground areas, which are then use to calculate the risk of human injury for offnominal trajectories of the reentry segment. The results show that the requirements of the ASA are fulfilled with margin

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

CALLISTO: towards reusability of a rocket stage: current status

JAXA, CNES and DLR have decided to cooperate to develop and fly a scaled reusable VTVL rocket stage called CALLISTO (Cooperative Action Leading to Launcher Innovation in Stage Toss - back Operations). This vehicle is paving the way for future reusable launch vehicles in Europe and in Japan. During phase B important progress in term of methods and operation philosophy specific to RLV have been made. Amongst other progresses, that will ease the development of future operational VTVL, in the domain of aerodynamic modelling, GNC landing leg deployment but also flight domain definitions are presented. These are concrete results which can at least partly be useful for other RLV projects