Landing a rocket on Earth is a key factor in enabling quicker and more cost-effective access to space. However, it poses significant challenges due to the highly uncertain environment. A robust, reliable, and real-time capable Guidance, Navigation, and Control (GNC) system is essential to guide the vehicle to the landing site while meeting terminal constraints and minimizing fuel consumption.. A 6-Degrees Of Freedom (DOF) flight simulator is developed, including accurate vehicle and environmental models such as variable Mass, Center of Mass and Inertia (MCI), winds, and detailed aerodynamics. Furthermore, not only thrust magnitude and engine deflections are used as controls, but also two sets of aerodynamic fins, as they are present in real rockets. Finally, initial condition dispersions and uncertainties in dynamics, navigation, and controls are included, to assess the robustness of the GNC strategy.
This study applies Meta Reinforcement Learning (meta-RL) to the terminal rocket landing problem. Through repeated interactions between an agent and its environment over multiple episodes, a Neural Network (NN) develops a policy that maps observed states to control actions. Unlike traditional methods, meta-RL leverages both current and past observations to output the optimal action, enhancing the robustness of the policy. Recurrent Neural Networks (RNNs) like Long-Short Term Memory (LSTM), are commonly used in meta-RL for their ability to handle sequential data. However, this thesis investigates also the use of attention-based Gated Transformer XL (GTrXL) networks, which are promising to improve the solution accuracy.
This research confirms this hypothesis, demonstrating that the GTrXL-based policy significantly outperforms the LSTM-based one. This policy is also less sensitive to internal hyperparameters, provided that the NN has a sufficient number of weights and biases to capture all the relevant features. The results indicate that incorporating complex vehicle and environmental models, along with dispersed initial conditions, aerodynamic and wind uncertainties, navigation and control errors, and actuator deflection rate constraints into the training process, yields a robust GTrXL-based policy. This guidance policy is able to meet terminal constraints on position, horizontal velocity, vertical angle, and angular rates in 1000/1000 simulations. The only exception is the vertical velocity which is exceeded on average by only 2-3 m/s. Including a thrust rate constraint mitigates this issue, reducing the average violation to 1 m/s. Finally, developing a terminal patch to increase the thrust magnitude in the last few meters before touchdown completely eliminates the vertical velocity issue, producing a 100% success rate, with all the Monte Carlo runs meeting all the terminal constraints. Moreover, the NN produces a solution in about 6 ms, showing great potential for its real-time use. The results are consistently superior to those of a conventional Guidance and Control (G&C) strategy where a Linear Quadratic Regulator (LQR) controller tracks an optimal trajectory, consuming only 6% more fuel.
Recommendations for future works include improving the reward function to better handle the vertical velocity constraint, and penalizing control effort to have smoother Thrust Vector Control (TVC) and fins control profiles. It is also suggested to expand the simulation scenario, including the unpowered aerodynamic descent.

One of the biggest trade-offs in aviation is between a vehicle’s ability to take-off and land vertically and its efficiency in cruising flight. The recent drive for electric vehicles creates space to consider new solutions to this trade-off. Tilt wing aircraft offer significant advantages in vertical take-off and landing (VTOL) operations due to their versatile design. One of the difficulties in designing configurations with little historical data is that they are difficult to predict. The challenge of formulating a flight dynamics model valid through the transition phase from vertical to horizontal flight is undertaken in this study. This research aims to investigate the tilt wing aircraft behaviour through the wing tilt transition, as well as the stability characteristics. A six degree of freedom model implemented on the Canadair CL-84 Dynavert compares favourably to flight test data, albeit with low-fidelity especially around hovering flight. The likely cause is the simple rotor to wing slipstream interference modelled. The stability characteristics reveal large spikes in positive stability of the longitudinal derivative Cmu and Cmw due to the behaviour of the wings and the slipstream effect on the horizontal tail, with normalized values up to 5.5 and 150 respectively. Some unstable flight configurations are found within the flight envelope at 41 degrees and 28 degrees due to wing stall.

Trajectory optimization has proven to be a powerful tool in solving a wide variety of optimal control problems in the aerospace field. However, in many cases, numerical complexities prevent the analysis of optimal trajectories for high-fidelity models, particularly due to the inherent difficulty of transcribing high-order dynamic systems. This research project proposes a methodology incorporating reduced-order modeling that retains the most critical dynamic characteristics from a full-order model while allowing the resulting simplification to be manageable for a trajectory optimization solver. The study applies this methodology to evaluate optimal landing trajectories for the UNIFIER19 C7A, a hybrid-electric aircraft equipped with a distributed electric propulsion system that was previously developed under the UNIFIER19 project. Results show that the reduced-order models generated for the aircraft can be used to generate flyable trajectories, verified by tracking the resulting landing approach paths using the base high-fidelity model. It is envisioned that this methodology will also be applicable to other aircraft models and mission phases.

Urban Air Mobility (UAM) has seen remarkable growth over the past decade, especially considering the delivery of goods. Notably, the delivery of medical supplies via Unmanned Aerial Vehicles (UAVs) has emerged as a promising application, which is driven by its societal benefits and has been demonstrated successfully in rural environments. However, expanding these operations to urban areas presents a unique set of challenges, such as high traffic density and the need for online path planning of UAVs. Effective path planning and coordination are of utmost importance to allow for safe and efficient delivery operations in urban environments. Currently, path planning of UAVs is relatively unexplored, and for drone delivery models the trajectories of UAVs are often oversimplified. This research aims to fill the research gap by developing and evaluating an online path planning and coordination mechanism in 3D for a cooperative fleet of autonomous UAVs delivering medical supplies. The Rotterdam Area is selected as a use case, but the model can be adapted to other cities. Utilising an agent-based model formulation, this paper formulates a novel approach for multi-agent pathfinding in 3D and real-world environments, where the travelled paths of UAVs in drone delivery models are computed by taking into account the urban environment and kinematics of UAVs. Windowed Cooperative Safe Interval Path Planning (WC-SIPP) is used as a path planning and coordination mechanism, where kinematic constraints of UAVs and safety separation distances between UAVs are incorporated. Experimental studies show the capability of the algorithm to plan UAVs in different multi-layer urban environments. We establish that including more than one vertical layer is beneficial for UAVs to avoid conflicts by allowing them to change altitudes during flight. Additionally, we show that an increase in the number of layers does not lead to an increase in the delivery time of packages. However, an increase in available layers does come with a decrease in computational performance. Besides, the proposed method is able to plan the trajectories of UAVs and ensure safety separation between UAVs within a dynamic environment, where up to 20 unexpected obstacles are introduced into the environment. Furthermore, we demonstrated that for our operation model, assigning prioritisation based on either mission type or package request time did not influence the delivery time of packages.

The concept of Distributed Electric Propulsion (DEP) aircraft holds great promise in achieving the goals outlined in Flightpath 2050. This involves utilizing electricity to power propellers and enhancing overall flight performance through interactions between the wings and propellers. This thesis investigates the stability and control aspects of DEP aircraft compared to conventional aircraft. A tool is proposed to estimate the minimum horizontal tail and aileron size for different configurations, considering propeller effects. Analyzing three configurations (turboprop excluding propeller effects, turboprop including propeller effects, and DEP including propeller effects), propellers are found to destabilize the aircraft but enhance take-off rotation and provide additional damping during roll. The DEP aircraft exhibits a 19% smaller normalized horizontal tail size than the turboprop (with propeller effects), attributed to lower propeller destabilizing moments and a shorter fuselage. Despite a lower roll requirement, the DEP aircraft needs the same normalized aileron size due to larger rolling moment of inertia. A sensitivity analysis suggests a T-Tail is optimal for DEP aircraft stability, and adjusting battery placement and reserve fuel improves overall performance.

Inaccuracies in robotic arms can significantly hinder their performance in tasks where precision is critical. This thesis focuses on the kinematic calibration and elasticity compensation of a 6 degrees of freedom robotic arm integrated into the Lunar Rover Mini, developed in collaboration with the Robotics and Mechatronics Institute of the German Aerospace Center (DLR), Wessling. The arm, constructed using 3D-printed components and driven by affordable RC servo motors, experiences notable inaccuracies in end-effector positioning due to joint flexibility and structural deformation, especially under load. This research aims to enhance the arm's accuracy through a model-based calibration approach that compensates for both elastic deformations and geometric misalignments, addressing the absence of feedback sensors. This cost-effective approach, which requires only 3D measurements of the end-effector's position, has resulted in an approximately 80% reduction in the robotic arm's average position error, proving advanced robotic technologies can be more accessible for educational and research applications.

Ball valves are a critical component in a plethora of liquid propellant propulsion systems. The Spanish company PLD Space is considering the usage of these valves in their new series of KER-LOX liquid propellant rocket engines, the TEPREL-C & TEPREL-C Vacuum engines. These will be operating on-board the Miura 5 launch vehicle. The purpose of this research is to re-design and analyze an unoptimized ball valve design, as to make it suitable for cryogenic service while minimizing its mass. The secondary objective of the research is to inquire into the aspects of ball valve operation. This includes investigating the required operating torque of a ball valve and the achievable flow factor as a function of a ball valve's opening angle. The results of this thesis are scripts which can estimate the torque and flow factor values, a methodology to mass-optimize a ball valve, and a re-designed ball valve suitable for cryogenic service.

While the space industry expands rapidly and space exploration becomes ever more relevant, this thesis aims to automate the design of Multiple Gravity-Assist (MGA) transfers using low-thrust propulsion. In particular, during the preliminary design phase of space missions, the combinatorial complexity of MGA sequencing is large and current optimisation approaches require extensive experience and can take days to simulate. Therefore, a novel optimisation approach is developed -- called the Recursive Target Body Approach -- that uses the hodographic-shaping low-thrust trajectory representation together with a combination of tree-search methods to automate the optimisation of MGA sequences. The approach gradually constructs the expected optimal MGA sequence by recursively evaluating the optimality of subsequent gravity-assist targets. Moreover, the approach includes novel figures of merit as well as parallelisation concepts to increase the robustness and accelerate the convergence. An Earth-Jupiter transfer with a maximum of three gravity assists is considered as a reference problem. Extensive tuning improved the quality of the MGA trajectory representations substantially and as a result, a robust low-thrust trajectory optimisation could be ensured. A distinct group of highly fit MGA sequences is consistently found that can be passed to a higher-fidelity method. In conclusion, the Recursive Target Body Approach can automatically and reliably be used for the preliminary optimisation of low-thrust MGA trajectories.

Now that a rocky planet is confirmed to orbit in the habitable zone of our closest stellar neighbor Proxima Centauri, the interest in visiting that system is growing; especially since Breakthrough Starshot proposed a fly-through mission of the Alpha Centauri system by sending a swarm of laser-driven photon sails. While many engineering problems still need to be solved for such a mission to succeed, research has shown that futuristic, theoretical photon-sail configurations can reach the Alpha Centauri system within 75-80 years while also getting captured in a bound orbit about one of the binary stars. This paper investigates trajectories from the binary star system towards planet Proxima b. A mission to Proxima b is scientifically grounded since measurements or pictures could help us better comprehend the evolution of rocky planets and potential life-formation in our Universe. The classical Lagrange points in the binary system (AC-A/AC-B) and the system Proxima Centauri-Proxima b (AC-C/Proxima b) are used to find possible trajectories towards Proxima b. The transfer is divided into a departure phase from AC-A/AC-B and an arrival phase to AC-C/Proxima b. Heteroclinic connections are then exploited using a patched restricted three-body problem method to connect the two phases. A grid search is applied on the optimization parameters to explore the design space, after which a genetic algorithm is applied to further optimize the link, focusing on minimization of the position, velocity, and time error at linkage. Futuristic sail configurations are used, including double-sided reflective sails and lightness numbers up to ß = 1779. The design space exploration shows that a double-sided sail provides little improvement over a one-sided sail, mainly due to the constant sail attitude along the trajectories. Results from the genetic algorithm show that a transfer from the L2-point in the AC-A/AC-B system to the L1-point in the AC-C/Proxima b can be accomplished with a transfer time of 235 years for the one-sided graphene-based sail with a surface of 315x315 m^2 carrying a payload of 10 grams. A transfer from the L2-point in the AC-A/AC-B system to the L3-point in the AC-C/Proxima b, with a smaller one-sided graphene-based sail (75x75 m^2, carrying a payload of 10 grams), results in a transfer time of 1025 years. For both sail configurations, the position error at linkage is kept below 1% of the total travel distance, the velocity error below 1% of the velocity at linkage, and the time error below 1% of the total transfer time.

Performing crucial activities for space exploration, e.g., debris removal and on-orbit servicing, systems for Rendezvous and Proximity Operations (RPO) are required to be autonomous and scalable. Within this context, learning-based relative navigation has gained significant traction due to the latest advancements in AI and the cost-effectiveness of monocular cameras.

This thesis introduces a pose estimation system composed of an Object Detection (OD) and a Keypoint Detection (KD) network for keypoint extraction, coupled with a pose solver, and trained purely on synthetic images. When applying realistic data augmentations, the system achieves a reduction in KD error by 80%, further improved by training on photorealistic images. After an architecture optimization step, the final system consistently meets the inference time requirements on the Myriad X edge processor. This proves the feasibility of developing RPO systems with artificial data, showcasing a scalable approach, while complying with the limitations of onboard hardware.

CubeSat missions have been deployed to cislunar space and beyond, paving the way for the next significant advancement: a dedicated CubeSat mission to explore a planet near Earth. To contribute to this goal, the German Aerospace Center (DLR) has developed radiation-hardened small satellite technologies, including communications, power and onboard computer subsystems. This study presents a stand-alone Mars exploration mission using the CubeSat standard that will demonstrate DLR’s in-house technologies. This mission will perform an independent transfer to the Red Planet, achieve orbital insertion, and conduct measurements on its lower atmosphere and gravity field. A system concept has been created by integrating the in-house technologies, investigating the necessary Commercial-Off-The-Shelf (COTS) components, and performing the mission analysis to assess the feasibility of the mission. The resulting 12U CubeSat has a 20.8 kg wet mass, 6.3 km/s low-thrust maneuvering capability and can generate up to 90 W of power at Mars. The proof-of-concept mission is planned for a 4-year duration.

RLV development can be considered as the modern step towards mission design due to financial and strategic decisions. In the past, reusability has been addressed however the level of maturity of the technology, both in terms of hardware and software was not yet reached. There are several aspects to developing a RLV, and these can be categorized into optimization of the LV, optimization of the trajectory, and cost analysis. TO be able to determine the feasibility of the mission, it is not just necessary to develop a suitable configuration, but to also determine the physical feasibility of the trajectory. Several methods exist of which convex optimization is selected. This class of algorithms have risen in popularity in the regime of powered descent guidance, and present a desirable trade-off between performance and computational cost. An already existing algorithm, DESCENDO, for a two-staged vehicle CALLISTO purposed for a mission to a geo-synchronous orbit, is taken as reference. The algorithm is rewritten in YALMIP allowing it to perform more efficiently by saving computation time through creation of multiple controllers based on a discretized burn schedule. A potential candidate for reusability in the future is selected, which is a VEGA variant, considered as a two-staged vehicle with set requirements on the mission and configuration. Through closed-loop simulations, the feasibility of RTLS for a particular mission of this VEGA variant can be studied. The disciplines involved in the study include the launch vehicle optimization, engine sizing, preliminary ascent & descent, and 3-DoF simulations. Previous research at TU Delft on RLV has included the work Rozenmeijer, Vandamme, Van Kesteren, Miranda, and Contant, graduate students of the TU Delft Aerospace Engineering faculty. The work relied on the usage of the TUDAT C++ software environment and based its feasibility or reusability of operations through a cost-analysis. A shift in direction is taken away from cost-analysis to examine at a greater detail the physical feasibility of the trajectory for a nominal candidate RLV. This is done by examining the influence of simulator to guidance algorithm dynamics and guidance algorithm parameters. Moreover, a nominal payload class between 100 and 500 kg is selected to determine the configuration of the vehicle ideal for this mission. To be able to determine feasibility of RTLS, three metrics are considered, which are the final landing velocity, final landing position, and maximumdynamic pressure. The study performs higher fidelity analysis only on the return phase, and as such the starting conditions for descent are determined through a preliminary design process by considering a drag-less ascent. This returns a starting altitude of around 26-30 km, with similar values for starting downrange position, and varying conditions of initial mass and velocity. For the preliminary descent, it is found that the metric of dynamic pressure does not reach more than around 60% of the limit imposed by the VEGA-C, which is similar for other VEGA variants. This coincides with research done with the CALLISTO vehicle. All in all, the best cases for these metrics and one included as an overall best case where candidates for the 400 kg payload class. The selection criteria for best cases of the preliminary descent involved the dynamic pressure, final velocity, and required propellant mass for descent. Moreover, the vehicle optimization results showed that this contained the most variation of vehicle characteristics, and as such it was deemed as a desirable class to work with for its flexibility in design. The best case burnt mass result was selected as the best case velocity required extensive propellant mass to burn for only a less than 7 m/s difference in result, which would not be indicative of what the convex algorithm could achieve due to dynamics involved in the preliminary experiment. This nominal candidate is then tested for various variations of controller tuning parameters combinations, burn schedules, and simulator/guidance frequencies. The results showed a clear desirable region for the final time of just between 300 and 310 seconds for return, favouring shorter burns. The solution envelope for the burn schedule showed gaps in zones of feasibility as well as optimality, suggesting some performance issues with the algorithm due to it failing to find solutions. Nevertheless this envelope is well defined and several feasible solutions existed. The influence of parameter tuning and simulator frequency was studied. It was determined that no set of guidance parameters could give an advantage over the other, but that some values did favour feasibility more. This is somewhat in contrast to the selection of frequencies, as despite the fact there was also a large difference for higher frequency ratios between the Q3 to Q4 and Q0 to Q2, there is a noticeably trend that higher ratios are favoured. Moreover, a local optimal ratio of frequency of 10-1 was also found, and being the same ratio used for the other experiments as well as the CALLISTO study, provides more evidence that this effect is intended. The uncertainties studied are for the initial state variations, errors in reading of position and velocities, and process time delays. It was noted that almost all the errors in the initial state variations shared similar distributions for ranges of values of the metrics. The overall majority returned feasible as well as the large minority of this returned optimal. Of little to no significance was the processing time delay, of which the overwhelming majority returned optimal results, and the rest where outliers whose process time factor where beyond the 3σ limit imposed in the creation of normal random variables. The largest errors arose from the real-time uncertainty in the velocities and position, modelled after pseudo-range errors. Although results showed a high density in the feasible and optimal regions for metrics of final time and position, there was also a high density past the feasible regions. It can be considered that the feasibility of RTLS operations for such a VEGA vehicle is restricted by such errors as expected, but nevertheless results are promising in what can be the main steps to lead to an error analysis study by the use of state estimation techniques and testing various modifications made to the SOCP problem to improve performance.

With the increasing number of wind farm projects, a growing interest is seen towards the extension of wind turbine durability and the optimisation of energy production. A promising technology in this direction, is the use of lidars for remote sensing of wind fields and particularly for lidar-assisted control of wind turbines. Many investigations have been carried out to study the performance of lidars for measuring global wind statistics and test out lidar-assisted control strategies. However there appears to be less research efforts towards identifying and characterising localised and specific flow structures within the wind field, which is the aspect of focus in this study.

Whilst the main objective is to detect flow structures, this study also dives into the lidar measurement process. A striking feature of this process is the extensive data processing procedure applied to reduce noise and provide a final output in the form of the line-of-sight velocity. As this consists on relatively large data reduction and condensing steps, the question therefore arises, is useful information lost during this process?

To investigate the different stages of the lidar measurement process, a continuous wave lidar emulator was developed and served as the main tool for simulating lidar operation under controlled conditions. The first part of the investigation was performed on the Lamb-Oseen vortex, and was aimed at finding traces of the vortex within the lidar outputs. Besides, the line-of-sight velocity output, the Doppler spectrum was also analysed in a statistical sense with the use of moments. Three main indicators of the presence of the vortex were identified in the velocity envelope and the variations of the Doppler spectrum standard deviation and skewness across the vortex core. Tests were performed to see the effects of varying conditions (core size, noise, line-of-sight effects, etc.) on these patterns. From these sensitivity tests, a possible approach at characterising the vortex position, core radius and circulation was formulated. Further testing was then performed by adapting the methods used to a LES simulated wind turbine tip vortices.

In all tests performed, it is clear that the most detrimental obstacle to reliable vortex detection arises from the surrounding flow field which distorts the structure of the vortex and hence the regularity of the patterns identified within the lidar measurement process. An additional barrier are measurement process noise sources which tend to damp the signal rather than distort it, thus weakening but preserving the general shape of the identified features.

Applicability of the detection method developed is possible, but challenging in real operating conditions, due to the noisy background wind field and the ignorance of the approximate vortex location in the wind inflow. However, with continued and improved future studies, the approach shown may result in a suitable way of determining wake regions from the detection of tip vortices, thus providing a valuable input for wind turbine control and wind farm power optimisation.

Single-Stage-To-Orbit (SSTO) launch vehicles are capable of reaching orbit while being potentially fully reusable. A technology capable of enabling SSTO access to space is the air-breathing engine, which has a high specific impulse and low thrust-over-weight (T/W) ratio compared to conventional rocket engines. This necessitates the use of a Horizontal Take-off and Horizontal Landing (HTHL) launch vehicle with a lifting surface, which enables banking maneuvers that can manipulate the orbital Right Ascension of the Ascending Node (RAAN) that the space plane achieves. This means that the space plane is capable of advancing or delaying its time of launch, while still achieving a similar orbital RAAN. This effectively increases the launch window even if a precise orbit insertion is necessary.

This thesis answers the question what the fuel-optimal ascent trajectory is for a space plane that would extend its launch window. In order to answer this question, the full six DoF equations of motion have been defined to simulate the ascent trajectory of a space plane. Additionally, a robust Guidance and Control system is developed that can use the nonlinear translational and rotational equations of motion.

For several launch times, ranging from two hours earlier to two hours later than the nominal launch time, the ascent trajectory has been optimized that included a banking maneuver. It was found that at the cost of propellant, it is possible to have a launch time delayed are advanced by as much as two hours, which means that the space plane can manipulate the RAAN by ± 30 degrees. The extra propellant cost can be related to increased drag losses during the banking maneuver.

The number of space objects has largely increased in the recent years, becoming a considerable threat to the present and future of satellite operations and human spaceflight. This introduces a need to accurately compute the risk of collision between satellites and space debris. Current methodologies are limited by the type of encounter and the vehicle shape, usually simplified by a sphere. These assumptions rely mainly on linearization of the dynamics and simplification of the uncertainty distribution as a Gaussian function. Developing a collision probability calculation method that overcomes these limitations and provides high-accuracy results is the topic of this work. The methodology developed follows a hybrid combination of trajectory propagation and statistical methods for uncertainty propagation. With the propagation method covariance information of the satellite position and velocity will be available. Finally, the method is adapted to any satellite geometry by developing a numerical quadrature technique based on a combination of spheres to model the real body shape. The combination of these methodologies to compute the collision probability has been verified with a set of test cases by means of a Monte Carlo simulation and compared to alternative algorithms. It is found that the method improves the accuracy in calculating the collision probability by more than 70% with respect to conventional alternatives. Regarding real-life scenarios, the Cosmos-2251/Iridium-33 and the Chang Zheng-4C/Cosmos-2004 encounters are simulated. In both cases, the time of encounter and collision risk have been correctly estimated with the developed method. Finally, in view of the recent destruction of satellite Cosmos-1408 as a result of an anti-satellite missile test, a screening of its resulting debris threatening the International Space Station (ISS) is performed. During a two-week period, ten close encounters were detected, one of which posed a significant risk to the ISS. When applying the method considering the real shape of the ISS, the collision probability decreases by two orders of magnitude, proving the significance of this approach to correctly estimate the risk and guide space operations.

Optimising spacecraft reorientation manoeuvres with respect to time, energy and propellant is essential for achieving a high mission performance. Solving this reorientation problem in real time and onboard is considered to be a promising opportunity to achieve further efficiency improvements in space missions. However, the nonlinear programming (NLP) methods that are currently used are too slow for onboard implementation. Therefore, in this study, a sequential convex programming (SCP)-based optimisation algorithm was developed to solve the spacecraft reorientation problem in real time. Several features are implemented and proposed to improve the algorithm performance compared to existing studies, amongst others: an alternative transcription technique, a method to reduce inter-nodal constraint violations and an improved initialisation strategy. Furthermore, an extensive Monte Carlo campaign was conducted to thoroughly assess the performance of the SCP algorithm. While showing similar performance in terms of robustness and optimality, the median computational efficiency of the SCP algorithm was found to be up to a factor 6.1 higher than a state-of-the-art NLP benchmark algorithm. All results considered, it can be concluded that SCP-based optimisation algorithms are a promising candidate for solving the spacecraft reorientation problem onboard.

Re-entry mission design remains an active field of study to safely return space missions back to Earth. With the developments in on-board computers, mission design and especially optimization of these missions has been performed numerically at an increasing rate at the cost of computing power. Analytical second-order methods have previously been shown to provide accurate results for mission design with less computational effort, but have not been applied to mission optimization. The analytical method was tested and shown to provide good results for a range of initial conditions. During optimization, restrictions arising from their derivation show that fundamental problems remain for application in mission optimization as the entry state cannot be freely defined. Additionally, two new optimization algorithms have been tested for re-entry mission optimization, a variable chromosome length algorithm and the Multi-objective Hypervolume-based Ant Colony Optimizer, both are found to provide results similar to the MOEA/D algorithm.

Safe Curriculum Learning constitutes a collection of methods that aim at enabling Rein- forcement Learning (RL) algorithms on complex systems and tasks whilst considering the safety and efficiency aspect of the learning process. On the one hand, curricular reinforce- ment learning approaches divide the task into more gradual complexity stages to promote learning efficiency. On the other, safe learning provides a framework to consider a system’s safety during the learning process. The latter’s contribution is significant on safety-critical systems, such as transport vehicles where stringent (safety) requirements apply. This pa- per proposes a black box safe curriculum learning architecture applicable to systems with unknown dynamics. It only requires knowledge of the state and action spaces’ orders for a given task and system. By adding system identification capabilities to existing safe cur- riculum learning paradigms, the proposed architecture successfully ensures safe learning proceedings of tracking tasks without requiring initial knowledge of internal system dynam- ics. More specifically, a model estimate is generated online to complement safety filters that rely on uncertain models for their safety guarantees. This research explicitly targets linearised systems with decoupled dynamics in the experiments provided in this article as proof of concept. The paradigm is initially verified on a mass-spring-damper system. After that, the architecture is applied to a quadrotor where it is able to successfully track the system’s four degrees of freedom independently, namely attitude angles and altitude. The RL agent is able to safely learn an optimal policy that can track an independent reference on each degree of freedom.

RANS simulation are one of the most used tools for aerodynamic analysis. The advantage of RANS simulations is the reduced computational cost compared to other methods such as LES or DNS. This is because by solving the RANS equations one only solves for the mean flow. However, this reduction in computational cost comes at the price of uncertainty. During the derivation of the RANS equations a closure problem is introduced. The turbulence models that solve this closure model of the Reynolds stress introduce the largest level of uncertainty. In this research symbolic regression is used to augment the k-ω-SST turbulence models with corrections directly inferred from high fidelity data sources such as DES, LES or DNS. This model is augmented with a correction to the anisotropic part of the Reynolds stress and a direct correction to the turbulence production. These correction fields are calculated through the so called frozen approach, where the k- and ω-transport equations are solved using the frozen mean flow values from the high fidelity data. Symbolic regression with Pope's eddy viscosity hypothesis as a basis is used to find models for these correction fields. With these correction models the k-ω-SST is extended to a non-linear turbulence model for the prediction of the eddy viscosity. Elastic net regression forms the basis of the machine learning method and is used to promote sparsity of the correction models. The sparsity is needed for stability and to keep the computational efficiency of the RANS method. This symbolic regression method is named SpaRTA and has been successfully applied to 2D cases in literature. In this work that is extended to 3 fully 3D cases, namely a wall mounted cube, an infinite circular cylinder and an idealised rotating wheel on a road surface. This study has shown the applicability of the SpaRTA methodology to these cases, resulting in models that have the extrapolating capabilities to improve the results on all 3 test geometries.