La thèse porte sur le développement des techniques non linéaires robustes de stabilisation et commande des systèmes avec perturbations de model. D’abord, on introduit les concepts de base de stabilité et stabilisabilité robuste dans le contexte des systèmes non linéaires. Ensuite, on présente une méthodologie de stabilisation par retour d’état en présence d’incertitudes qui ne sont pas dans l’image de la commande («unmatched»). L’approche récursive du «backstepping» permet de compenser les perturbations «unmatched» et de construire une fonction de Lyapunov contrôlée robuste, utilisable pour le calcul ultérieur d’un compensateur des incertitudes dans l’image de la commande («matched»). Le contrôleur obtenu est appelé «recursive Lyapunov redesign». Ensuite, on introduit la technique de stabilisation par «Immersion & Invariance» comme outil pour rendre un donné contrôleur non linéaire, robuste par rapport à dynamiques non modelées. La première technique de contrôle non linéaire robuste proposée est appliquée au projet d’un autopilote pour un missile air-air et au développement d’une loi de commande d’attitude pour un satellite avec appendices flexibles. L’efficacité du «recursive Lyapunov redesign» est mis en évidence dans le deux cas d’étude considérés. En parallèle, on propose une méthode systématique de calcul des termes incertains basée sur un modèle déterministe d’incertitude. La partie finale du travail de thèse est relative à la stabilisation des systèmes sous échantillonnage. En particulier, on reformule, dans le contexte digital, la technique d’Immersion et Invariance. En premier lieu, on propose des solutions constructives en temps continu dans le cas d’une classe spéciale des systèmes en forme triangulaire «feedback form», au moyen de «backstepping» et d’arguments de domination non linéaire. L’implantation numérique est basée sur une loi multi-échelles, dont l’existence est garantie pour la classe des systèmes considérée. Le contrôleur digital assure la propriété d’attractivité et des trajectoires bornées. La loi de commande, calculée par approximation finie d’un développement asymptotique, est validée en simulation de deux exemples académiques et deux systèmes physiques, le pendule inversé sur un chariot et le satellite rigide. / The dissertation deals with the problems of stabilization and control of nonlinear systems with deterministic model uncertainties. First, in the context of uncertain systems analysis, we introduce and explain the basic concepts of robust stability and stabilizability. Then, we propose a method of stabilization via state-feedback in presence of unmatched uncertainties in the dynamics. The recursive backstepping approach allows to compensate the uncertain terms acting outside the control span and to construct a robust control Lyapunov function, which is exploited in the subsequent design of a compensator for the matched uncertainties. The obtained controller is called recursive Lyapunov redesign. Next, we introduce the stabilization technique through Immersion \& Invariance (I\&I) as a tool to improve the robustness of a given nonlinear controller with respect to unmodeled dynamics. The recursive Lyapunov redesign is then applied to the attitude stabilization of a spacecraft with flexible appendages and to the autopilot design of an asymmetric air-to-air missile. Contextually, we develop a systematic method to rapidly evaluate the aerodynamic perturbation terms exploiting the deterministic model of the uncertainty. The effectiveness of the proposed controller is highlighted through several simulations in the second case-study considered. In the final part of the work, the technique of I\& I is reformulated in the digital setting in the case of a special class of systems in feedback form, for which constructive continuous-time solutions exist, by means of backstepping and nonlinear domination arguments. The sampled-data implementation is based on a multi-rate control solution, whose existence is guaranteed for the class of systems considered. The digital controller guarantees, under sampling, the properties of manifold attractivity and trajectory boundedness. The control law, computed by finite approximation of a series expansion, is finally validated through numerical simulations in two academic examples and in two case-studies, namely the cart-pendulum system and the rigid spacecraft.

Spacecraft missions such as spacecraft docking and formation flying require high precision relative position and attitude data. Although Global Positioining Systems can provide this capability near the earth, deep space missions require the use of alternative technologies. One such technology is the vision-based navigation (VISNAV) sensor system developed at Texas A&M University. VISNAV comprises an electro-optical sensor combined with light sources or beacons. This patented sensor has an analog detector in the focal plane with a rise time of a few microseconds. Accuracies better than one part in 2000 of the field of view have been obtained. This research presents a new approach involving simultaneous activation of beacons with frequency division multiplexing as part of the VISNAV sensor system. In addition, it discusses the synchronous demodulation process using digital heterodyning and decimating filter banks on a low-power fixed point DSP, which improves the accuracy of the sensor measurements and the reliability of the system. This research also presents an optimal and computationally efficient six-degree-of-freedom estimation algorithm using a new measurement model based on the attitude representation of Modified Rodrigues Parameters.

Thesis (M.S.)--Air Force Institute of Technology, 2003. / Title from title screen (viewed July 1, 2004). "March 2003." Vita. "AFIT/GCA/ENV/03-04." "ADA415257"--URL. Includes bibliographical references (p. 71-74). Also issued in paper format.

Preliminary interplanetary trajectory designs frequently use simplified two-body orbital mechanics and linked conics methodology to model the complex trajectories in multi-body systems. Incorporating gravity assists provides highly efficient interplanetary trajectories, enabling otherwise infeasible spacecraft missions. Future missions may employ powered gravity assists, using a propulsive maneuver during the flyby, improving the overall trajectory performance. This dissertation provides a complete description and analysis of a new interplanetary trajectory design tool known as TRACT (TRAjectory Configuration Tool). TRACT is capable of modeling complex interplanetary trajectories, including multiple ballistic and/or powered gravity assists, deep space maneuvers, parking orbits, and other common maneuvers. TRACT utilizes an adaptable architecture of modular boundary value problem (BVP) algorithms for all trajectory segments. A bi-level optimization scheme is employed to reduce the number of optimization variables, simplifying the user provided trajectory information. The standardized optimization parameter set allows for easy use of TRACT with a variety of optimization algorithms and mission constraints. The dissertation also details new research in powered gravity assists. A review of literature on optimal powered gravity assists is presented, where many optimal solutions found are infeasible for realistic spacecraft missions. The need was identified for a mission feasible optimal powered gravity assist algorithm using only a single impulsive maneuver. The solution space was analyzed and a complete characterization was developed for solution types of the optimal single-impulse powered gravity assist. Using newfound solution space characteristics, an efficient and reliable optimal single-impulse powered gravity assist BVP algorithm was formulated. The mission constraints were strictly enforced, such as maintaining the closest approach above a minimum radius and below a maximum radius. An extension of the optimal powered gravity assist research is the development of a gravity assist BVP algorithm that utilizes an asymptote ΔV correction maneuver to produce ballistic gravity assist trajectory solutions. The efficient algorithm is tested with real interplanetary mission trajectory parameters and successfully converges upon ballistic gravity assists with improved performance compared to traditional methods. A hybrid approach is also presented, using the asymptote maneuver algorithm together with traditional gravity assist constraints to reach ballistic trajectory solutions more reliably, while improving computational performance.

Spacecraft missions such as spacecraft docking and formation flying require high precision relative position and attitude data. Although Global Positioining Systems can provide this capability near the earth, deep space missions require the use of alternative technologies. One such technology is the vision-based navigation (VISNAV) sensor system developed at Texas A&M University. VISNAV comprises an electro-optical sensor combined with light sources or beacons. This patented sensor has an analog detector in the focal plane with a rise time of a few microseconds. Accuracies better than one part in 2000 of the field of view have been obtained. This research presents a new approach involving simultaneous activation of beacons with frequency division multiplexing as part of the VISNAV sensor system. In addition, it discusses the synchronous demodulation process using digital heterodyning and decimating filter banks on a low-power fixed point DSP, which improves the accuracy of the sensor measurements and the reliability of the system. This research also presents an optimal and computationally efficient six-degree-of-freedom estimation algorithm using a new measurement model based on the attitude representation of Modified Rodrigues Parameters.

Thesis (Master of Military Studies)-Marine Corps Command and Staff College, 2008. / Title from title page of PDF document (viewed on: Feb 2, 2010). Includes bibliographical references.

A considerable number of Very Long Baseline Interferometry (VLBI) surveys have been conducted in the northern hemisphere and very few in the southern hemisphere mostly because of a lack of telescopes and therefore adequate baseline coverage. Thus there is a deficit of calibrator sources in the southern hemisphere. Further, some of the most interesting astronomical objects eg. the galactic centre and the nearest galaxies (the small and large Magellanic Clouds) lie in the southern hemisphere and these require high resolution studies. With a major expansion of radio astronomy observing capability on its way in the southern hemisphere (with the two SKA (Square Kilometre Array) precursors, meerKAT (Karoo Array Telescope) and ASKAP (Australian SKA Pathfinder), leading to the SKA itself) it is clear that interferometry and VLBI in the southern hemisphere need a dense network of calibration sources at different resolutions and a range of frequencies. This work seeks to help redress this problem by presenting an analysis of 31 southern sources to help fill the gaps in the southern hemisphere calibrator distribution. We have developed a multi-parameter method of classifying these sources as calibrators. From our sample of 31 sources, we have 2 class A sources (Excellent calibrators), 16 class B sources (Good calibrators), 9 class C sources (Poor calibrators) and 4 class D sources (Unsuitable calibrators).

This dissertation addresses novel techniques in determining gyroless micro-satellite attitude and attitude rate. The main objective of this thesis is to explore the possibility of using commercially available low cost micro-light star sensor as a stand-alone sensor for micro-satellite attitude as well as attitude rate determination. The objective is achieved by developing accurate and computationally efficient algorithms for the realization of onboard operation of a low fidelity star sensor. All the algorithms developed here are tested with the measurement noise presented in the catalog of the sensor array STAR-1000. A novel accurate second order sliding mode observer (SOSMO) is designed for discrete time uncertain linear multi-output system. Our design procedure is effective for both matched and unmatched bounded uncertain ties and/or disturbances. The bound on uncertainties and/or disturbances is assumed to be unknown. This problem is addressed in this work using the second order multiple sliding modes approach. Second order sliding manifold and corresponding sliding condition for discrete time system is defined similar on the lines of continuous counterpart. Our design is not restricted to a particular class of uncertain (matched) discrete time system. Moreover, it can handle multiple outputs unlike single out-put systems. The observer design is achieved by driving the state observation error and its first order finite difference to the vicinity of the equilibrium point (0,0) in a finite steps and maintaining them in the neighborhood thereafter. The estimation synthesis is based on Quasi Sliding Mode (QSM) design. The problem of designing sliding mode observer for a linear system subjected to unknown inputs requires observer matching condition. This condition is needed to ensure that the state estimation error is a asymptotically stable and is independent of the unknown input during the sliding motion. In the absence of a matching condition, asymptotic stability of the reduced order error dynamics on the sliding surface is not guaranteed. However, unknown bounded inputs guarantee bounded error on state estimation. The QSM design guarantees an ultimate error bound by incorporating Boundary Layer (BL) in its design procedure. The observer achieves one order of magnitude improvement in estimation accuracy than the conventional sliding mode observer (SMO) design for an unknown input. The observer estimation errors, satisfying the given stability conditions, converge to an ultimate finite bound (with in the specified BL) of O(T2), where T Is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The robustness of the proposed observer with respect to measurement noise is also analyzed. The design algorithm is very simple to apply and is implemented for two examples with different classes of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results show the robustness with respect to the measurement noise for SOSMO. Second order sliding mode observer gain can be calculated off-line and the same gain can work for large band of disturbance as long as the disturbance acting on the continuous time system is bounded and smooth. The SOSMO is simpler to implement on board compared to the other traditional nonlinear filters like Pseudo-Linear-Kalman-filter(PLKF); Extended Kalman Filter(EKF). Moreover, SMO possesses an automatic adaptation property same as optimal state estimator(like Kalman filter) with respect to the intensity of the measurement noise. The SMO rejects the noisy measurements automatically, in response to the increased noise intensity. The dynamic performance of the observer on the sliding surface can be altered and no knowledge of noise statistics is required. It is shown that the SOSMO performs more accurately than the PLKF in application to micro-satellite angular rate estimation since PLKF is not an optimal filter. A new method for estimation of satellite angular rates through derivative approach is proposed. The method is based on optic flow of star image patterns formed on a star sensor. The satellite angular rates are derived directly from the 2D-coordinates of star images. Our algorithm is computationally efficient and requires less memory allocation compared to the existing vector derivative approaches, where there is also no need for star identification. The angular rates are computed using least square solution method, based on the measurement equation obtained by optic flow of star images. These estimates are then fed into discrete time second order sliding mode observer (SOSMO). The performance of angular rate estimation by SOSMO is compared with the discrete time First order SMO and PLKF. The SOSMO gives the best estimates as compared to the other two schemes in estimating micro-satellite angular rates in all three axes. The improvement in accuracy is one order of magnitude (around1.7984 x 10−5 rad/ sec,8.9987 x 10−6 rad/ sec and1.4222 x 10−5 rad/ sec in three body axes respectively) in terms of standard deviation in steady state estimation error. A new method and algorithm is presented to determine star camera parameters along with satellite attitude with high precision even if these parameters change during long on-orbit operation. Star camera parameters and attitude need to be determined independent of each other as they both can change. An efficient, closed form solution method is developed to estimate star camera parameters (like focal length, principal point offset), lens distortions (like radial distortion) and attitude. The method is based on a two step procedure. In the first step, all parameters (except lens distortion) are estimated using a distortion free camera model. In the second step, lens distortion coefficient is estimated by linear least squares (LS) method. Here the derived camera parameters in first step are used in the camera model that incorporates distortion. However, this method requires identification of observed stars with the catalogue stars. But, on-orbit star identification is difficult as it utilizes the values of camera calibrating parameters that can change in orbit(detector and optical element alignment get change in orbit due to solar pressure or sudden temperature change) from the ground calibrated value. This difficulty is overcome by employing a camera self-calibration technique which only requires four observed stars in three consecutive image frames. Star camera parameters along with lens (radial and decentering) distortion coefficients are determined by camera self calibration technique. Finally Kalman filter is used to refine the estimated data obtained from the LS based method to improve the level of accuracy. We consider the true values of camera parameters as (u0,v0) = (512.75,511.25) pixel, f = 50.5mm; The ground calibrated values of those parameters are (u0,v0) =( 512,512) pixel, f = 50mm; Worst case radial distortion coefficient affecting the star camera lens is considered to be k1 =5 x 10−3 .Our proposed method of attitude determination achieves accuracy of the order of magnitude around 6.2288 x 10−5 rad,3.3712 x 10−5 radand5.8205 x 10−5 rad in attitude angles φ,θ and ψ. Attitude estimation by existing methods in the literature diverges from the true value since they utilize the ground calibrated values of camera parameters instead of true values. To summarize, we developed a formal theory of discrete time Second Order Sliding Mode Observer for uncertain multi-output system. Our methods achieve the desired accuracy while estimating satellite attitude and attitude rate using low fidelity star sensor data. Our methods require lower on-board processing requirement and less memory allocation; thus are suitable for micro-satellite applications. Thus, the objective of using low fidelity star sensor as stand-alone sensor in micro-satellite application is achieved.

<div>Since as early as the 1920s, dinitrogen tetroxide (N2O4) has been regarded as a promising oxidizer in rocket propulsion systems. In more recent times, its predecessor, mixed oxides of nitrogen (MON), remains a top contender among oxidizers, due to its unique characteristics such as low freezing temperature and compatibility with common spacecraft materials. Today, these N2O4-based oxidizers are the preferred choice in many upper stages, launch escape systems, reaction control systems, liquid apogee engines, and in-space primary propulsion systems. N2O4-based oxidizers are a key factor in rocket propulsion, and thoroughly understanding their history, development, characteristics, synthesis, and composition analysis are crucial for space exploration today and into the future.<br><br></div><div>To fully understand and predict the physical properties of a MON sample, it is important to measure and quantify its chemical composition. The recommended method for MON composition analysis, as prescribed by the Department of Defense’s Defense Specification (MIL-SPEC) document on N2O4, involves the oxidation of NO and dinitrogen trioxide (N2O3) in the MON sample to determine their amounts. An equation unofficially called the “MIL-SPEC equation” is then used to determine the amount of NO needed to mix with N2O4 to synthesize that particular MON sample. However, no explanation is given as to how the equation was derived, or its significance.<br><br></div><div>This thesis aims to collect and organize key information on the synthesis, handling, and composition analysis of MON propellant. First, the history of development of N2O4-based oxidizers was researched, and current and future uses of N2O4 and MON propellants were identified. Then a method for synthesis and composition analysis was devised and tested. Water contamination was expected of skewing the results, so the process of water contamination was examined analytically. Then a detailed derivation of the MIL-SPEC equation was conducted, to fully understand its mechanics. An attempt was then made to reverse-engineer an unexplained numerical value in the equation, labeled by the author as the “solubility factor”. Several derivations were provided with varying degrees of complexity, producing alternative solubility factors of varying accuracies. Finally, experimental data was applied to these derived, hypothetical solubility factors and the MIL-SPEC solubility factor, with the intent of determining whether improvements could be made to the MON composition determination process.<br><br></div><div>The results suggest that the MIL-SPEC equation is sufficient for providing a relatively accurate measurement of the composition of a MON sample, while also being easy to implement, both in taking the necessary measurements and in conducting the numerical calculation. However, some minor adjustments to the equation could produce consistently more accurate composition measurements without adding any more difficulty or complication.</div>

This thesis describes the design, implementation and analysis for a preliminary study for DLR's MASCOT lander's next mission to Small Solar System Bodies (SSSB). MASCOT (Mobile Asteroid Surface Scout) is a nano-lander that flew aboard Hayabusa2 (JAXA) to an asteroid, Ryugu. It is a passive nano-spacecraft that can only be deployed ballistically from a hovering spacecraft. Current research focusses on optimizing similar close-approach missions for deploying landers or small cubesats into periodic orbits but does not provide solutions with semi-autonomous small landers deployed from farther distances. This study aims to overcome this short-coming by proposing novel yet simple Guidance, Navigation and Control (GNC) and Propulsion systems for MASCOT. Due to its independent functioning and customisable anatomy, MASCOT can be adapted for several mission scenarios. In this thesis, a particular case-study is modelled for the HERA (ESA) mission. The first phase of the study involves the design of a landing trajectory to the moon of the Didymos binary asteroid system. For a preliminary analysis, the system - Didymain (primary body), Didymoon (secondary body) and MASCOT (third body) - are modelled as a Planar Circular Restricted Three Body Problem (PCR3BP). The numerical integration methodology used for the trajectory is the variable-step Dormand–Prince (Runge Kutta) ODE-4,5 (Ordinary Differential Equation) solver. The model is built in MATLAB-Simulink (2019a) and refined iteratively by conducting a Monte Carlo analysis using the Sensitivity Analysis Tool. Two models - a thruster-controlled system and an alternative hybrid propulsion system of solar sails and thrusters - are simulated and proven to be feasible. The results show that the stable manifold near Lagrange 2 points proposed by Tardivel et. al. for ballistic landings can still be exploited for distant deployments if a single impulse retro-burn is done at an altitude of 65 m to 210 m above ground with error margins of 50 m in position, 5 cm/s in velocity and 0.1 rad in attitude. The next phase is the conceptual design of a MASCOT-variant with GNC abilities. Based on the constraints and requirements of the flown spacecraft, novel GNC and Propulsion systems are chosen. To identify the overriding factors in using commercial-off-the-shelf (COTS) for MASCOT, a market survey is conducted and the manufacturers of short-listed products are consulted. The final phase of the study is to analyse the proposed equipment in terms of parameter scope and capability-oriented trade-offs. Two traceability matrices, one for devised solutions and system and another for solutions versus capabilities, are constructed. The final proposed system is coherent with the given mass, volume and power constraints. A distant deployment of MASCOT-like landers for in-situ observation is suggested as an advantageous and risk-reducing addition to large spacecraft missions to unknown micro-gravity target bodies. Lastly, the implications of this study and the unique advantages of an enhanced MASCOT lander are explored for currently planned SSSB missions ranging from multiple rendezvous, fly-by or sample-return missions. Concluding, this study lays the foundation for future work on advanced GNC concepts for unconventional spacecraft topology for the highly integrated small landers. / <p>This thesis is submitted as per the requirements for the Spacemaster (Round 13) dual master's degree under the Erasmus Mundus Joint Master's Degree Programme. </p> / MASCOT team, DLR