This thesis presents the design of Kalman filter based attitude determination algorithms for a hypothetical LEO satellite and for a satellite attitude control test setup. For the hypothetical LEO satellite, an Extended Kalman Filter based attitude determination algorithms are formed with a multi-mode structure that employs the different sensor combinations and as well as online switching between these combinations depending on the sensor availability. The performance of these different attitude determination modes are investigated through Monte Carlo simulations. New attitude determination algorithms are prepared for the satellite attitude control test setup by considering the constraints on the selection of the suitable sensors. Here, performances of the Extended Kalman Filter and Unscented Kalman Filter are investigated. It is shown that robust and sufficiently accurate attitude estimation for the test setup is achievable by using the Unscented Kalman Filter.

In this thesis novel feedback attitude control algorithms and attitude estimation algorithms are developed for a three-axis stabilised spacecraft attitude control system. The spacecraft models considered include a rigid-body spacecraft equipped with (i) external control torque devices, and (ii) a redundant reaction wheel configuration. The attitude sensor suite comprises a three-axis magnetometer and three-axis rate gyroscope assembly. The quaternion parameters (also called Euler symmetric parameters), which globally avoid singularities but are subject to a unity-norm constraint, are selected as the primary attitude coordinates. There are four novel contributions presented in this thesis. The first novel contribution is the development of a robust control strategy for spacecraft attitude tracking maneuvers, in the presence of dynamic model uncertainty in the spacecraft inertia matrix, actuator magnitude constraints, bounded persistent external disturbances, and state estimation error. The novel component of this algorithm is the incorporation of state estimation error into the stability analysis. The proposed control law contains a parameter which is dynamically adjusted to ensure global asymptotic stability of the overall closedloop system, in the presence of these specific system non-idealities. A stability proof is presented which is based on Lyapunov's direct method, in conjunction with Barbalat's lemma. The control design approach also ensures minimum angular path maneuvers, since the attitude quaternion parameters are not unique. The second novel contribution is the development of a robust direct adaptive control strategy for spacecraft attitude tracking maneuvers, in the presence of dynamic model uncertainty in the spacecraft inertia matrix. The novel aspect of this algorithm is the incorporation of a composite parameter update strategy, which ensures global exponential convergence of the closed-loop system. A stability proof is presented which is based on Lyapunov's direct method, in conjunction with Barbalat's lemma. The exponential convergence results provided by this control strategy require persistently exciting reference trajectory commands. The control design approach also ensures minimum angular path maneuvers. The third novel contribution is the development of an optimal control strategy for spacecraft attitude maneuvers, based on a rigid body spacecraft model including a redundant reaction wheel assembly. The novel component of this strategy is the proposal of a performance index which represents the total electrical energy consumed by the reaction wheel over the maneuver interval. Pontraygin's minimum principle is applied to formulate the necessary conditions for optimality, in which the control torques are subject to timevarying magnitude constraints. The presence of singular sub-arcs in the statespace and their associated singular controls are investigated using Kelley's necessary condition. The two-point boundary-value problem (TPBVP) is formulated using Pontrayagin's minimum principle. The fourth novel contribution is an attitude estimation algorithm which estimates the spacecraft attitude parameters and sensor bias parameters from three-axis magnetometer and three-axis rate gyroscope measurement data. The novel aspect of this algorithm is the assumption that the state filtering probability density function (PDF) is Gaussian distributed. This Gaussian PDF assumption is also applied to the magnetometer measurement model. Propagation of the filtering PDF between sensor measurements is performed using the Fokker-Planck equation, and Bayes theorem incorporates measurement update information. The use of direction cosine matrix elements as the attitude coordinates avoids any singularity issues associated with the measurement update and estimation error covariance representation.

Thesis (MEng) Stellenbosch University, 2014 / ENGLISH ABSTRACT: An Attitude Determination and Control System (ADCS) demonstrator and testing platform was required for satellite engineering students. The ADCS demonstrator and testing platform will allow students to develop insight into the concepts and challenges of ADCS design and implementation. The existing model nano-satellite EyasSAT was used as a design platform for a new ADCS demonstrator. A new ADCS module (ADCS_V2) was developed to replace the existing EyasSAT ADCS module. The new module allows for three-axis ADCS and the demonstration of the ADCS on an air bearing platform. The air bearing allows full freedom of movement for yaw rotations with limited pitch and roll rotations. The actuators and sensors required for the ADCS were developed and integrated into EyasSAT. In addition a new PCB was designed to form the ADCS_V2 module. Attitude determination algorithms and attitude control algorithms were implemented and tested using MATLAB Simulink simulations. These algorithms were then implemented on the ADCS_V2 module. The ADCS was tested using Hardware In the Loop (HIL) techniques and an air bearing. The yaw attitude of EyasSAT could be controlled within 0.4 degrees accuracy with all the sensors active. In order to stabilize the air bearing platform, the pitch and roll angles were rate controlled. The pitch and roll rates were damped to within 6 mrad/s. / AFRIKAANSE OPSOMMING: ’n Oriëntasiebepaling en Beheerstelsel (OBBS) demonstrasie en toets platform was benodig vir satellietingenieurswese studente. Die nuwe OBBS sal studente toelaat om insig te ontwikkel met betreking tot die idees en uitdagings wat verband hou met die ontwikkeling en implementering van ’n OBBS. Die huidige nano-sateliet model EyasSAT was gebruik as ’n ontwerpsbasis vir die nuwe OBBS. Die nuwe OBBS was ontwikkel om die huidige module van EyasSAT te vervang. Die nuwe OBBS laat oriëntasiebepaling en -beheer in drie asse toe. Die nuwe OBBS en EyasSAT kan die werking van ’n OBBS demonstreer op ’n luglaerplatform. Die luglaer laat vrye rotasie om die gierhoek toe terwyl die rol- en stygings-as beperk word. Die aktueerders en sensors wat benodig word vir die OBBS is ontwikkel en geïntegreer in EyasSAT saam met ’n nuwe gedrukte stroombaanbord om die nuwe OBBS te vorm. Orientasiebepaling en orientasiebeheer algoritmes is geïmplementeer en getoets met die hulp van MATLAB Simulink simulasies. Die algoritmes was op die OBBS module geïmplementeer en getoets deur gebruik te maak van HIL tegnieke en praktiese toetse op die luglaer. Die rotasie hoek van EyasSAT kan met ’n akkuraatheid van 0.4 grade beheer word indien al die sensors gebruik word. Die rol en stygingshoeksnelheid was gekanselleer om die luglaer stabiel te hou. Die hoeksnelheid van die twee asse kon tot kleiner as 6 mrad/s beheer word.

The problematics of precise pointing and more specifically an attitude control is present sincethe first days of flight and Aerospace engineering. The precise attitude control is a matter ofnecessity for a great variety of applications. In the air, planes or unmanned aerial vehicles needto be able to orient precisely. In Space, a telescope or a satellite relies on the attitude control toreach the stars or survey the Earth. The attitude control can be based on various principles, pre-calculated variables, and measurements. It is common to use the gyroscope, Sun/Star/horizonsensors for attitude determination. While those technologies are well established in the indus-try, the rise in a computational power and efficiency in recent years enabled processing of aninfinitely more rich source of information - the vision. In this Thesis, a visual system is used forthe attitude determination and is blended together with a control algorithm to form a VisionBased Attitude Control system.A demonstrator is designed, build and programmed for the purpose of Vision Based AttitudeControl. It is based on the principle of Visual servoing, a method that links image measure-ments to the attitude control, in a form of a set of joint velocities. The intermittent steps arethe image acquisition and processing, feature detection, feature tracking and the computationof joint velocities in a closed loop control scheme. The system is then evaluated in a barrage ofpartial experiments.The results show, that the used detection algorithms, Shi&Tomasi and Harris, performequally well in feature detection and are able to provide a high amount of features for tracking.The pyramidal implementation of the Lucas&Kanade tracking algorithm proves to be a capablemethod for a reliable feature tracking, invariant to rotation and scale change. To further evaluatethe Visual servoing a complete demonstrator is tested. The demonstrator shows the capabilityof Visual Servoing for the purpose of Vision Based Attitude Control. An improvement in thehardware and implementation is recommended and planned to push the system beyond thedemonstrator stage into an applicable system.

<div>Autonomous transportation is a research field that has gained huge interest in recent years, with autonomous electric or hydrogen cars coming ever closer to seeing everyday use. Not just cars are subject to autonomous research though, the field of aviation is also being explored for fully autonomous flight. One very important aspect for making autonomous flight a reality is attitude control, the control of roll, pitch, and sometimes yaw. Traditional approaches for automated attitude control use PID (proportional-integral-derivative) controllers, which use hand-tuned parameters to fulfill the task. In this work, however, the use of Reinforcement Learning algorithms for attitude control will be explored. With the surge of more and more powerful artificial neural networks, which have proven to be universally usable function approximators, Deep Reinforcement Learning also becomes an intriguing option. </div><div>A software toolkit will be developed and used to allow for the use of multiple flight simulators to train agents with Reinforcement Learning as well as Deep Reinforcement Learning. Experiments will be run using different hyperparamters, algorithms, state representations, and reward functions to explore possible options for autonomous attitude control using Reinforcement Learning.</div>

Les travaux présentés dans ce mémoire constituent une contribution à la conception de méthodes systématiques pour l’analyse et la commande de systèmes périodiques et incertains. Une partie importante de cette thèse est également consacrée au contrôle d’attitude de satellites dont la dynamique se prête naturellement à une représentation sous forme de modèles périodiques soumis à des incertitudes. La première partie propose une présentation unifiée des résultats d’analyse et de synthèse de modèles périodiques et incertains à temps-discret via des méthodes basées sur des inégalités linéaires matricielles (LMI) et en s’appuyant sur la théorie de Lyapunov. Par la suite, l’accent est mis sur une nouvelle classe de correcteurs périodiques à mémoire pour lesquels l’entrée de commande est construite en utilisant l’historique des états du système conservés en mémoire. Des exemples numériques démontrent que ces nouveaux degrés de liberté permettent de repousser les limites des performances robustes. La seconde partie s’intéresse aux aspects de périodicité et de robustesse du contrôle d’attitude de satellite rencontrés notamment lors de l’utilisation des magnéto-coupleurs. Ces actionneurs s’appuient sur le champ géomagnétique variant périodiquement le long de l’orbite du satellite. Différentes stratégies de commande sont mises en œuvre et comparées entre elles avec le souci constant de tenir compte des principales limitations des actionneurs. Cette démarche conduit à une nouvelle loi de commande périodique régulant le moment cinétique des roues à réactions sans perturber le contrôle d’attitude dont l’effort de commande est réparti sur l’ensemble des actionneurs. / This manuscript reviews contributions to the development of systematic methods for analysis and control of periodic uncertain systems. An important part of this thesis is also dedicated to the design of attitude control systems for satellites whose dynamics is naturally represented as a periodic model subject to uncertainties. The first part is devoted to the developpement of a unifying presentation of the analysis and synthesis results of periodic, uncertain and discrete-time models via methods relying on linear matrix inequalities (LMI) and based on Lyapunov theory. Subsequently, the focus is on a new class of periodic control laws with memory for which the control input is constructed using history of the states of the system kept in memory. Numerical experiments show that these new degrees of freedom can outperformed the existing results. The second part deals with periodic and robustness aspects of attitude control of a satellite using magnetorquers. These actuators use the geomagnetic field that varies periodically along the orbital trajectory. Different control strategies are implemented and compared with one another with the constant concern of taking the main limitations of the actuators into account. This approach leads to a new control law regulating the momentum of the reaction wheels without disturbing attitude control for which the control effort is shared by all actuators.

Star trackers are essential instruments commonly used on satellites. They provide precise measurement of the orientation of a satellite and are part of the attitude control system. For cubesats star trackers need to be small, consume low power and preferably cheap to manufacture. In this thesis work the electronics for a miniature star tracker has been developed. A star detection algorithm has been implemented in hardware logic, tested and verified. A platform for continued work is presented and future improvements of the current implementation are discussed. / Stjärnkameror är vanligt förekommande instrument på satelliter. De tillhandahåller information om satellitens orientering med mycket hög precision och är en viktig del i satellitens reglersystem. För kubsatelliter måste dessa vara små, strömsnåla och helst billiga att tillverka. I detta examensarbete har elektroniken för en sådan stjärnkamera utvecklats. En algoritm som detekterar stjärnor har implementerats i hårdvara, testats och verifierats. En hårdvaruplattform som fortsatt arbete kan utgå ifrån har skapats och förslag på förbättringar diskuteras.

This thesis provides insights to what is peculiar about a solar sail attitude and orbit control system and provides the assessment, in the form of a feasibility study, of the effectiveness of sail tip vanes as a control hardware to escape the Earth sphere of influence. The demonstrator aims to prove the technology for the Sunshade project, a constellation of solar sails located at the Lagrangian point L1 to obscure part of the solar radiation directed towards earth. Solar sailing poses a few fundamental challenges to spaceflight and it is a yet-to-be-proven branch of space engineering. Other tentative design exist but there is no standard to follow or off-the-shelf component that can be straightforward used. Moreover the scalability to the final project has to be accounted for in every step of the project.&lt;/p&gt;&lt;p&gt;The project is divided in a preliminary dimensioning, followed by a Simulink® based simulation which tests preliminary decisions. The simulation, performed on an orbit on the ecliptic plane, integrates models of Earth’s eclipse and environmental disturbance torques.  The escape time for a 100 m solar sail is found to be 1215 days, with a nonlinear PD control algorithm and sail tip vanes as the only control hardware. Attention is also posed on the consequence of a simplified sail film deformation in terms of centre of pressure to centre of mass off-set. / I detta examensarbete studeras vad som är speciellt med solsegels system för attityd- och bankontroll och ger en bedömning, i form av en möjlighetsstudie, av effektiviteten hos flöjlar som sätts på seglets hörn som kontrollhårdvara för att lämna jordens inflytelsesfär. Demonstratorn syftar till att bevisa tekniken för Sunshade-projektet, en konstellation av solsegel belägen vid lagrangepunkten L1 för att skugga en del av solstrålningen riktad mot jorden. Solsegling innebär några grundläggande utmaningar för rymdfärden och det är en ännu inte bevisad gren av rymdteknik. Annan preliminär design finns, men det finns ingen standard att följa eller standardkomponenter som enkelt kan användas. Dessutom måste skalbarheten till det slutliga projektet redovisas i varje steg i projektet.Projektet är uppdelat i en preliminär dimensionering, följt av en Simulink-baserad simulering som testar preliminära beslut. Simuleringen, utförd på en omloppsbana påekliptikan, integrerar modeller av jordens skugga och störningar av vridmoment från ett antal källor.Flykttiden för ett 100m solsegel blir 1215 dagar, med en icke-linjär PD kontrollalgoritm och segelhörnsflöjlar som den enda styrhårdvaran. Dessutom studeras förskjutningen av tryckcentrum i förhållande till masscentrum under en förenklad modell av segeldeformation.

In this thesis, a simulation harness is constructed in Simulink for the purpose of validating the Attitude Determination and Control System (ADCS) on the APTAS student CubeSat in support of the upcoming flight readiness review. The simulation results are used to verify the compliance of a subset of the requirements for the ADCS, detailed in table 1. Calibration of the onboard sun sensor array, which is used to find the sun vector for the attitude determination, is performed using a break-out board of sun sensors tested in a sun simulator. The data gathered from this test is used to model the sun sensor system in the simulation and in flight software. The results show that the sun sensor system is able to find the sun vector with an average error angle of 5.4 degrees, though the error angle may spike up to 18 degrees in operation. It is found that the complete ADCS is able to guide the spacecraft toward the desired nadir-facing attitude, though not with the accuracy specified in the requirements. The spacecraft is able to detumble much better than required. All deficiencies found in the ADCS software have been corrected. These changes arelisted in appendix B. It is concluded that, despite its flaws, the ADCS software is flight ready. / Project APTAS

[pt] Quadrirrotores são veículos aéreos que possuem quatro rotores fixos e orientados na direção vertical. Devido à sua simplicidade mecânica frente aos helicópteros tradicionais, os mesmos têm se tornado cada vez mais populares nos meios de pesquisa, militares e, mais recentemente, industriais. Essa topologia de veículo data do início do século XX mas o desenvolvimento em escala só foi possível após a recente evolução e miniaturização dos sistemas eletrônicos embarcados, dos motores elétricos e das baterias. A movimentação desses veículos no espaço é possível graças à sua inclinação em relação ao solo e, para tal, é imprescindível obter e controlar corretamente a atitude do mesmo. As unidades de medidas inerciais (IMU) surgiram como uma solução para esse problema. Através da fusão dos dados obtidos com os sensores presentes nessas centrais (acelerômetros, girômetros e magnetômetro) é possível estimar a atitude do veículo. O presente trabalho apresenta soluções tanto para a estimativa quanto para o controle de atitude de quadrirrotor. Os modelos matemáticos desenvolvidos são validados em simulações numéricas e em testes experimentais. O objetivo é que as soluções propostas apresentem resultados positivos para que possam ser empregadas nos quadrirrotores em escala. / [en] Quadrotors are vehicles that have four fixed rotors in the vertical direction. Due to its mechanical simplicity compared to traditional helicopters, these vehicles have become increasingly popular in the research, military and, more recently, industrial fields. This type of vehicle first appeared in the early twentieth century, but the development of small-scale models was only possible after the recent evolution and miniaturization of embedded electronics, electric motors and batteries. A Quadrotor can fly in any direction by changing its inclination relative to the ground, so it is essential to calculate and properly adjust its attitude. The inertial measurement units (IMU) emerged as one solution to this problem. By merging the IMU sensors data, it is possible to estimate the vehicle s attitude. This dissertation presents solutions for both the estimation and the control of the vehicle s attitude. The developed mathematical models are validated with numerical simulations and experimental tests. The goal is that the presented solutions give enough good results so they can be used in small-scale Quadrotors.