Worst-case analysis is one of the most important elements in the verifica-tion and validation process used to ensure the reliable operation of safety-critical systems for defence, aerospace and space applications. In this the-sis, an optimization-based worst-case analysis framework is developed forspace applications. The proposed framework has been applied and success-fully validated on a number of European Space Agency funded researchprojects in the areas of flexible satellites, hypersonic re-entry vehicles, andautonomous rendezvous systems. Firstly, the problem of analyzing the robustness of an Attitude and OrbitalControl Systems (AOCS) for a flexible scientific satellite with a large num-ber of uncertainties is considered. The analysis employs a detailed simula-tion model of a flexible satellite and multivariable controller, together witha number of frequency and time domain performance criteria which arecommonly used by the space industry to verify correct functionality of full-authority multivariable satellite control systems. Second, the flying qualitiesanalysis of a re-entry vehicle is investigated for a number of complex sce-narios involving different types of uncertainties and disturbances. Specificmethods are utilized to deal with analysis problems involving probabilisticuncertainties, physically correlated uncertainties and highly dynamical dis-turbances. In another study, an integrated analytical/optimization-basedanalysis framework is proposed for the robustness analysis of AOCS fora telecoms satellite with flexible appendages. We develop detailed LinearFractional Transformation (LFT)-based models of the uncertainties presentin a modern telecom satellite and apply µ-analysis to these models in or-der to generate robustness guarantees. We validate these models and re-sults by cross-checking them against worst-case analysis results producedby global optimization algorithms applied to the original system model. Fi-nally, the optimization-based framework developed in this thesis is employedto analyze the robustness of the Guidance, Navigation and Control (GNC)system for autonomous spacecraft. This study considers the autonomousrendezvous problem over the terminal flight phase in the presence of a largenumber of realistic parametric uncertainties and a number of safety criteriarelated to the capture specification. An integrated analytical/optimization-based approach was also developed for this problem so that the computa-tional cost of simulation-based analyses can be reduced, through leveragingresults from robust control tools such asµ-analysis. The main contributions of the thesis are (a) to provide convincing demon-strations of the usefulness of optimization-based worst-case analysis on anumber of different space applications, each of which involves highly com-plex simulators developed by leading industrial companies from the Euro-pean Space sector, and (b) to show how optimization-based analysis meth-ods may be combined with analytical tools from robust control theory tocreate a more integrated, efficient and reliable verification and validationprocess for space applications.

This thesis concerns the development of path planning algorithms for unmanned aerial vehicles (UAVs) to avoid obstacles in two- (2D) and three-dimensional (3D) urban environments based on the visibility graph (VG) method. As VG uses all nodes (vertices) in the environments, it is computationally expensive. The proposed 2D path planning algorithms, on the contrary, select a relatively smaller number of vertices using the so-called base line (BL), thus they are computationally efficient. The computational efficiency of the proposed algorithms is further improved by limiting the BL’s length, which results in an even smaller number of vertices. Simulation results have proven that the proposed 2D path planning algorithms are much faster in comparison with the VG and hence are suitable for real time path planning applications. While vertices can be explicitly defined in 2D environments using VG, it is difficult to determine them in 3D as they are infinite in number at each obstacle’s border edge. This issue is tackled by using the so-called plane rotation approach in the proposed 3D path planning algorithms where the vertices are the intersection points between a plane rotated by certain angles and obstacles edges. In order to ensure that the 3D path planning algorithms are computationally efficient, the proposed 2D path planning algorithms are applied into them. In addition, a software package using Matlab for 2D and 3D path planning has also been developed. The package is designed to be easy to use as well as user-friendly with step-by-step instructions.

A growing interest in distributed systems of small satellites has recently emerged due to their ability to perform a variety of new mission types, increasing technical capability, and reduced time and cost for development. However, the lack of available and dedicated small launch services currently restricts the establishment of these systems in orbit. Secondary payload launch opportunities and alternative deployment strategies can address the issue of access-to-orbit and support the delivery of the constellation to the correct orbit configuration following launch. Of these deployment strategies, the method of indirect plane separation, which utilises the natural precession of Earth orbits, is particularly applicable to the deployment of small satellite constellations due to the potential to significantly reduce propulsive requirements, albeit at the cost of increased deployment time. A review of satellite constellation design revealed that existing methods and tools are not suitable for the analysis of small satellite constellations and are not equipped to investigate alternative deployment strategies, despite the potential benefits of improved access-to-orbit, reduced system complexity, and reduced cost. To address the identified gaps in the design process, a methodology in which the analysis of small satellite constellation deployment is integrated into the system design framework is presented in this thesis. The corresponding system design-space is subsequently explored using a numerical optimisation method, which aids the identification of effective system designs and promotes the understanding of relationships between the design variables and output objectives. The primary objectives of this methodology are to ensure that the different opportunities for deployment of small satellite constellations are thoroughly examined during the design process and to support the development of improved mission and system designs. The presented methodology is demonstrated using a reduced order framework comprised of an analysis for the deployment of small satellite constellations, preliminary vehicle and propulsion system sizing processes, and system cost estimating relationships. Using this simplified mission design framework, the design space-exploration of three small satellite constellation mission case-studies is performed by application of a multiobjective genetic algorithm. Objectives of time-to-deploy, system mass, and system cost are used to direct the optimisation process and search for the most effective solutions in the system design-space. In order to perform the analysis of constellation deployment by the process of indirect plane separation, a simulation method using a semi-analytical propagation technique and time-varying atmospheric density model was developed and verified by comparison to the actual deployment of the FORMOSAT-3/COSMIC mission. The results of the case-studies presented illustrate the ability of the developed methodology to support the design process for satellite constellations and enable the identification of promising and improved system architectures for further development. Moreover, through the enumeration and quantification of the system design-space and tradespace, the methodology is shown to support the identification of relationships and trends between the design variables and selected output objectives, increasing the knowledge available to the system design team during the design process.

Space missions increasingly require sophisticated guidance, navigation and control algorithms, the development of which is reliant on verification and validation (V&V) techniques to ensure mission safety and success. A crucial element of V&V is the assessment of control system robust performance in the presence of uncertainty. In addition to estimating average performance under uncertainty, it is critical to determine the worst case performance. Industrial V&V approaches typically employ mu-analysis in the early control design stages, and Monte Carlo simulations on high-fidelity full engineering simulators at advanced stages of the design cycle. While highly capable, such techniques present a critical gap between pessimistic worst case estimates found using analytical methods, and the optimistic outlook often presented by Monte Carlo runs. Conservative worst case estimates are problematic because they can demand a controller redesign procedure, which is not justified if the poor performance is unlikely to occur. Gaining insight into the probability associated with the worst case performance is valuable in bridging this gap. It should be noted that due to the complexity of industrial-scale systems, V&V techniques are required to be capable of efficiently analysing non-linear models in the presence of significant uncertainty. As well, they must be computationally tractable. It is desirable that such techniques demand little engineering effort before each analysis, to be applied widely in industrial systems. Motivated by these factors, this thesis proposes and develops an efficient algorithm, based on the cross entropy simulation method. The proposed algorithm efficiently estimates the probabilities associated with various performance levels, from nominal performance up to degraded performance values, resulting in a curve of probabilities associated with various performance values. Such a curve is termed the probability profile of performance (PPoP), and is introduced as a tool that offers insight into a control system's performance, principally the probability associated with the worst case performance. The cross entropy-based robust performance analysis is implemented here on various industrial systems in European Space Agency-funded research projects. The implementation on autonomous rendezvous and docking models for the Mars Sample Return mission constitutes the core of the thesis. The proposed technique is implemented on high-fidelity models of the Vega launcher, as well as on a generic long coasting launcher upper stage. In summary, this thesis (a) develops an algorithm based on the cross entropy simulation method to estimate the probability associated with the worst case, (b) proposes the cross entropy-based PPoP tool to gain insight into system performance, (c) presents results of the robust performance analysis of three space industry systems using the proposed technique in conjunction with existing methods, and (d) proposes an integrated template for conducting robust performance analysis of linearised aerospace systems.