This research analyzes and demonstrates the local position determination problem on Earth using a novel instrument, the Compass Star Tracker. Special focus is given to the theoretical development of the mathematics of local position determination, the design and fabrication of a proof-of-concept instrument, an error source analysis, and the experimental tests used to validate the position determination concepts. Star sensors are typically used as attitude determination instruments on spacecraft orbiting Earth. In this capacity, the star sensor determines the orientation of the spacecraft using digital images of the stars. This research utilizes the basic functionality of the star sensor in a new way; the orientation information from the star image is used to determine a user's latitude and longitude coordinates on Earth. This concept is valuable because it allows users to determine their position autonomously. The fundamental concepts that enable local position determination were originally published in Drs. Samaan, Mortari, and Junkins (AAS 04-007). This research improves upon that work by eliminating the zenith-orientation constraint and providing several crucial theoretical corrections. In addition to the position determination mathematics, this research provides analysis of the theoretical and practical error sources associated with the position determination problem. This research also details the design, fabrication, and experimental test program of a proof-of-concept Compass Star Tracker. Together, the theoretical development, error analysis, instrument design, and test program serve as validation of the the position determination concept. This work is intended as the first of many steps toward eventual deployment of autonomous position determination sensors on the Moon and Mars.

Studies aimed at the development of indigenous low cost star tracker and gyroless attitude and angular rate estimation is presented in the thesis. This study is required for the realization of low cost micro satellites. A target specification of determining the attitude with accuracy (3σ) of 0.05 degrees and attitude rate with accuracy (3σ) in the range of 50rad/sec at a rate of 10 samples/second in all the axes is set as a goal for the study. Different sensor arrays available in the market are evaluated on the basis of their noise characteristics, resolution of the analog-to-digital converter (ADC) present and ability to work in low light conditions, for possible use in the hardware realization of star tracker. STAR1000 APS CMOS array, manufactured by Cypress Semiconductors, qualified these performance criteria, is used for the simulation study. An algorithm is presented for scanning the sensor array, detection of star image and retrieving the information concerning the photoelectron counts corresponding to a star image. The exact designation of the center of the star image becomes crucial as it has direct implications on the accuracy of the estimated attitude. Various algorithms concerning the centroid estimation of a defocused star image on the sensor array to subpixel accuracy are studied and Gaussian Weighed Center of Gravity algorithm is adapted with some modifications and an accuracy of 0.039 pixels is obtained in both horizontal and vertical direction of the array. A one-to-one relationship is established between the stars obtained in the field-of-view (FOV) of the star tracker with the stars present in the star catalog resident in the star tracker through star identification algorithm. A star identification algorithm which relies on the interstar angles and brightness of the stars is developed in this thesis. The interstar angles of the stars visible in the FOV of the star sensor is recorded, compared with the inter-star angles made by the stars selected in the catalog, based on initial brightness match with stars formed on image plane. After identification at the initial epoch, consequent instants can drive information from the previous matches so as to decrease the computational complexity and storage requirement for the subsequent instants. The memory constraints and computational overhead on the processor and the dynamic range of the image detector used in the star tracker are the limiting factors. The stars thus identified with the stars in the catalog are used for the estimation of attitude. A point solution to the attitude estimation problem is computed using a least square based algorithm called ESOQ-2. The algorithm for centroiding of star images and ESOQ-2 for finding the point solution satellite attitude is coded and tested on Da Vinci based emulator. This exercise shows that it is possible to implement above algorithm for real time operations. Estimation of attitude at a given epoch using algorithms like ESOQ-2 does not minimize the noise and error covariance as the attitude estimated at each instant of time depends only on the measurement taken at that particular instant. So a Kalman Filter (KF) based estimation using Integrated Rate Parameter (IRP) formulation called SIAVE algorithm, is adapted, with some modifications, for the estimation of incremental angle and attitude rates from vector observations of stars. From the point solution of attitude estimation problem of the satellite, the incremental angle and angular rate at successive time steps are predicted using a linear KF and refined with the measurements from the stand alone star tracker, taken at discrete time steps, using the SIAVE algorithm. The sensor noise is modeled from the characteristics of STAR1000 sensor array used in the algorithm in order to make the simulations more realistic in nature. The optimality of Kalman filter is based on the assumption that the state and measurement noises are white gaussian random processes and the state dynamics of the plant is completely known. However, for most real systems, modeling uncertainties are present. So a robust state estimator based on H∞ norm minimization is devised. The H∞ filter, based on game theory approach is used to minimize the worst case variance of noise signals with the only assumption on the noise signals that they are energy bounded. The aim is to find the feasibility of using H∞ filter for the estimation of incremental angle and attitude rate of the satellite. The studies shows that H∞ filter with proper tuning can serve as potential estimation scheme for the attitude and angular rate estimation of the satellite. It is found that both Kalman filter and H∞ are able to meet the specified accuracy desired from low cost accurate star sensor.

This dissertation addresses the problem of rigid-body attitude tracking control under three scenarios of high relevance to many aerospace guidance and control applications: adaptive attitude-tracking control law development for a spacecraft with time-varying inertia parameters, velocity-free attitude stabilization using only vector measurements for feedback, and smooth angular velocity observer design for attitude tracking in the absence of angular velocity measurements. Inertia matrix changes in spacecraft applications often occur due to fuel depletion or mass displacement in a flexible or deployable spacecraft. As such, an adaptive attitude control algorithm that delivers consistent performance when faced with uncertain time-varying inertia parameters is of significant interest. This dissertation presents a novel adaptive control algorithm that directly compensates for inertia variations that occur as either pure functions of the control input, or as functions of time and/or the state. Another important problem considered in this dissertation pertains to rigid-body attitude stabilization of a spacecraft when only a set of inertial sensor measurements are available for feedback. A novel gyro-free attitude stabilization solution is presented that directly utilizes unit vector measurements obtained from inertial sensors without relying on observers to reconstruct the spacecraft's attitude or angular velocity. As the third major contribution of this dissertation, the problem of attitude tracking control in the absence of angular velocity measurements is investigated through angular velocity observer (estimator) design. A new angular velocity observer is presented which is smoothed and ensures asymptotic convergence of the estimation errors irrespective of the initial true states of the spacecraft. The combined implementation of a separately designed proportional-derivative type controller using estimates generated by the observer results in global asymptotic stability of the overall closed-loop tracking error dynamics. Accordingly, a separation-type property is established for the rigid-body attitude dynamics, the first such result to the author's best knowledge, using a smooth (switching-free) observer formulation. / text

International Telemetering Conference Proceedings / October 30-November 02, 1995 / Riviera Hotel, Las Vegas, Nevada / The Stanford University Satellite Systems Development Laboratory will flight test a telemetry reengineering experiment on its student-built SAPPHIRE spacecraft. This experiment utilizes solar panel current information and knowledge of panel geometry in order to create a virtual sun sensor that can roughly determine the satellite's sun angle. The Omni-Directional Differential Sun Sensor (ODDSS) algorithm normalizes solar panel currents and differences them to create a quasi-linear signal over a particular sensing region. The specific configuration of the SAPPHIRE spacecraft permits the construction of 24 such regions. The algorithm will account for variations in panel outputs due to battery charging, seasonal fluctuations, solar cell degradation, and albedo affects. Operationally, ODDSS telemetry data will be verified through ground processing and comparison with data derived from SAPPHIRE's infrared sensors and digital camera. The expected sensing accuracy is seven degrees. This paper reviews current progress in the design and integration of the ODDSS algorithm through a discussion of the algorithm's strategy and a presentation of results from hardware testing and software simulation.

<p>The quality of cameras is currently increasing very fast meanwhile the price of them is decreasing. The possibilities of using a camera as a measurement and navigation instrument are thus getting bigger all the time. This thesis studies the transformation relations between a camera image and the scene in space that is projected to it. A theoretical derivation of the transform will be presented, and methods and algorithms for applications based on the transform will be developed.</p><p>The above mentioned transform is called the camera matrix, which contains information about the camera attitude, the camera position, and the internal structure of the camera. Useful information for several different applications can be extracted from the camera image with the help of the camera matrix.</p><p>In one of the applications, treated in this Master´s thesis, the camera attitude is estimated when the camera is calibrated and its position is known. Another application is that of absolute target positioning, where a point in a digital map is searched from its position in a camera image. Better accuracy in the measurements can though be obtained with relative target positioning i.e., estimation of distance and angle between two points in the digital map by picking them out in the image. This is because that the errors of the</p><p>absolute target positioning for each of the two points are dependent and thus partly will cancel each other out when their relative position and angle is measured.</p>

The quality of cameras is currently increasing very fast meanwhile the price of them is decreasing. The possibilities of using a camera as a measurement and navigation instrument are thus getting bigger all the time. This thesis studies the transformation relations between a camera image and the scene in space that is projected to it. A theoretical derivation of the transform will be presented, and methods and algorithms for applications based on the transform will be developed. The above mentioned transform is called the camera matrix, which contains information about the camera attitude, the camera position, and the internal structure of the camera. Useful information for several different applications can be extracted from the camera image with the help of the camera matrix. In one of the applications, treated in this Master´s thesis, the camera attitude is estimated when the camera is calibrated and its position is known. Another application is that of absolute target positioning, where a point in a digital map is searched from its position in a camera image. Better accuracy in the measurements can though be obtained with relative target positioning i.e., estimation of distance and angle between two points in the digital map by picking them out in the image. This is because that the errors of the absolute target positioning for each of the two points are dependent and thus partly will cancel each other out when their relative position and angle is measured.

A major motivation for Lie group observers is their application as sensor fusion algorithms for an inertial measurement unit which can be used to estimate the orientation of a rigid-body. In the first part of this thesis we propose several types of nonlinear, deterministic, locally exponentially convergent, state observers for systems with all, or part, of their states evolving on the general linear Lie group of invertible matrices. Our proposed Lie group observer with full-state measurement is applicable to left-invariant systems on linear Lie groups and yields linear estimation error dynamics. We also propose a way to extend our full-state observer, to build observers with partial-state measurement, i.e., only a proper subset of the states are available for measurement. Our proposed Lie group observer with partial-state measurement is applicable when the measured states are evolving on a Lie group and the rest of the states are evolving on the Lie algebra of this Lie group. We illustrate our observer designs on various examples, including rigid-body orientation estimation and dynamic homography estimation. In the second part of this thesis we propose a nonlinear, deterministic state observer, for systems that evolve on real, finite-dimensional vector spaces. This observer uses the property of high-gain observers, that they are approximate differentiators of the output signal of a plant. Our new observer is called a composite high-gain observer because it consists of a chain of two or more sub-observers. The first sub-observer in the chain differentiates the output of the plant. The second sub-observer in the chain differentiates a certain function of the states of the first sub-observer. Effectiveness of the composite observer is demonstrated via simulation.

A major motivation for Lie group observers is their application as sensor fusion algorithms for an inertial measurement unit which can be used to estimate the orientation of a rigid-body. In the first part of this thesis we propose several types of nonlinear, deterministic, locally exponentially convergent, state observers for systems with all, or part, of their states evolving on the general linear Lie group of invertible matrices. Our proposed Lie group observer with full-state measurement is applicable to left-invariant systems on linear Lie groups and yields linear estimation error dynamics. We also propose a way to extend our full-state observer, to build observers with partial-state measurement, i.e., only a proper subset of the states are available for measurement. Our proposed Lie group observer with partial-state measurement is applicable when the measured states are evolving on a Lie group and the rest of the states are evolving on the Lie algebra of this Lie group. We illustrate our observer designs on various examples, including rigid-body orientation estimation and dynamic homography estimation. In the second part of this thesis we propose a nonlinear, deterministic state observer, for systems that evolve on real, finite-dimensional vector spaces. This observer uses the property of high-gain observers, that they are approximate differentiators of the output signal of a plant. Our new observer is called a composite high-gain observer because it consists of a chain of two or more sub-observers. The first sub-observer in the chain differentiates the output of the plant. The second sub-observer in the chain differentiates a certain function of the states of the first sub-observer. Effectiveness of the composite observer is demonstrated via simulation.

Les drones ou systèmes de drones aériens jouent un rôle de plus en plus important danstous les domaines, spécialement les drones à décollage et atterrissage verticaux. L’un desplus connus est le Quadrotor et, sans doute, il est la plateforme de recherche la plus utilisée.Cette thèse traite le problème de l’estimation et de la commande d’attitude appliqué àun corps rigide se déplaçant dans l’espace 3D tel que le Quadrotor. La première contributionde cette thèse est la conception et l’implémentation d’une solution d’estimation d’attitude.Celle-ci est basée sur un ensemble de filtres complémentaires combinés avec un algorithmealgébrique tel que TRIAD, QUEST, etc. avec la possibilité de choisir deux formes différentesdes filtres: la première dénommée forme Directe, et la seconde dénommée forme Passive.Les filtres proposés ont une flexibilité dans le choix de l’ordre qui peut être pris grand afinde bien réduire l’effet du bruit de mesure et permettent d’aboutir à un estimateur qui peutprendre en compte le biais éventuel des gyromètres. L’analyse par la théorie de Lyapunovprouve que les erreurs d’estimation tendent globalement et asymptotiquement vers zéro. Unesuite logique de cette première contribution est la proposition d’une solution pour la commanded’attitude qui constitue la deuxième contribution de cette thèse. Elle se traduit par ledéveloppement d’une nouvelle loi de commande d’attitude d’un corps rigide dans l’espace3D, dans laquelle seulement les vecteurs de mesures inertiels avec les mesures des gyromètressont utilisés. Elle utilise le principe de fusion des données à travers un filtre complémentairepermettant l’élimination des bruits des mesures tout en assurant une stabilité presque globalede l’équilibre désiré. La troisième contribution est une loi de commande pour la stabilisationd’attitude sans mesure de vitesse angulaire, ni mesure d’attitude. Pour cela, un systèmelinéaire auxiliaire basé sur les mesures des vecteurs inertiels a été introduit. Ce dernier sesubstitue au manque de l’information de la vitesse angulaire. L’analyse de stabilité du contrôleurproposé est basée sur la théorie de Lyapunov couplée avec le théorème de LaSalle. Ellepermet de conclure sur la stabilité presque globale de l’équilibre désiré. Les performances dessolutions proposées ont été validées par un ensemble de tests expérimentaux / Nowadays, we see a growing popularity of the use of Unmanned Aerial Vehicles (UAV) ofespecially Vertical Take-Off and Landing (VTOL) type. One of the most known VTOL is thequadrotor or Quadcopter which is probably the most used one as a research platform. Thisthesis deal with attitude control and estimation techniques applied to a rigid body movingin 3D space such as Quadcopter VTOL. The first contribution of this thesis is the design ofa new class of complementary linear-like filters allowing the fusion of inertial vector measurementswith angular velocity measurements and combined with algebraic algorithms asTRIAD, QUEST etc. to give an efficient attitude estimation solution. This class of filtersallows several possibilities of implementation such as the order of the filters which can bechosen high in order to reduce more the measurement noise and the form of the filters thatcan be direct or passive and the ability to take into account the possible gyro bias. Lyapunovanalysis shows the global asymptotic convergence of the estimation errors to zero. The sameprinciple of data fusion is used for the proposed new attitude control law in which the complementaryfilters were included to reduce the effect of measurement noise. The obtainedcontroller ensures almost global stability of the desired equilibrium point; it represents thesecond contribution of this thesis. The third contribution takes into consideration an interestingspecial case, where instantaneous measurements of attitude and angular velocity areunavailable. A first order linear auxiliary system based directly on vector measurements isused in an observer-like system to handle the luck of angular velocity. The proposed controllerensures almost global asymptotic stability of the trajectories to the desired equilibriumpoint. Detailed sets of experiments were done to validate the obtained results

This thesis describes work in a variety of topics related to aerial robotics, including system identification, state estimation, control, and path planning. The path planners described in this thesis are used to guide a fixed-wing UAV along paths that optimize the aircraft's ability to track a ground target. Existing path planners in the literature either ignore occlusions entirely, or they have limited capability to handle different types of paths. The planners described in this thesis are novel in that they specifically account for the effect of occlusions in urban environments, and they can produce a much richer set of paths than existing planners that account for occlusions. A 3D camera positioning system from Motion Analysis is also described in the context of state estimation, system identification, and control of small unmanned rotorcraft. Specifically, the camera positioning system is integrated inside a control architecture that allows a quadrotor helicopter to fly autonomously using truth data from the positioning system. This thesis describes the system architecture in addition to experiments in state estimation, control, and system identification. There are subtleties involved in using accelerometers for state estimation onboard flying rotorcraft that are often ignored even by researchers well-acquainted with the UAV field. In this thesis, accelerometer-rotorcraft behavior is described in detail. The consequences of ignoring accelerometer-rotorcraft behavior are evaluated, and an observer is presented that achieves better performance by specifically modeling actual accelerometer behavior. The observer is implemented in hardware and results are presented.