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.

The NASA Scatterometer (NSCAT) was launched August 20, 1996 aboard the National Space Development Agency of Japan's Advanced Earth Observing Spacecraft (ADEOS). NSCAT's primary mission was to measure radar backscatter over the world's oceans. These measurements are used to generate estimates of ocean wind speed and direction. Scatterometers must be calibrated before their measurements are scientifically useful. However, the calibration of NSCAT must be done in orbit. A new methodology for selecting land regions for use in extended target spaceborne scatterometer calibration is first developed. Next, a summary of the calibration technique used in this thesis is presented. While the foundation of this technique was previously developed theoretically, the work in this thesis is its first application for calibration/validation of an on-line spaceborne radar system. The technique is extended to estimate simultaneously NSCAT's calibration and the host spacecraft's attitude error. The attitude references reported by the attitude control system on-board ADEOS are deemed erroneous. Results of this expanded technique, applied under varying assumptions, are presented for consideration. A summary and suggestions for future research conclude this work.

The transition from a mathematical algorithm to a physical hardware implementation is non-trivial. This thesis discusses the issues involved in the transition from the theory of real-time trajectory generation all the way through a hardware experiment. Documentation of the validation process as well as modifications to the existing theory as a result of hardware testing are treated at length. The results of hardware experimentation show that trajectory generation can be done in real-time in a manner facilitating coordination of multiple small UAVs.

The quadrotor helicopter is a unique flying vehicle which uses the thrust from four motors to provide hover flight capability. The uncoupled nature of the longitudinal and lateral axes and its ability to support large payloads with respect to its size make it an attractive vehicle for autonomous vehicle research. In this thesis, the quadrotor is modeled based on first principles and a proportional-derivative control method is applied for attitude stabilization and position control. A unique means of using an optic flow sensor for velocity and position estimation in an indoor setting is presented with flight results. Reliable hover flight and hallway following capabilities are exhibited in GPS-denied indoor flight using only onboard sensors. Attitude angles can be reliably estimated in the short run by integrating the angular rates from MEMS gyros, but noise on the signal leads to drift which renders the measurement unsuitable to attitude estimation. Typical methods of providing vector attitude corrections such as accelerometers and magnetometers have inherent weaknesses on hovering vehicles. Thus, an additional vector measurement is necessary to correct attitude readings for long-term flights. Two methods of using image processing to determine vanishing points in a hallway are demonstrated. The more promising of the two uses a Hough transform to detect lines in the image and forms a histogram of the intersections to detect likely vanishing point candidates. Once the vanishing point is detected, it acts as a vector measurement to correct attitude estimates on the quadrotor vehicle. Results using onboard vision to estimate heading are demonstrated on a test stand. Together, these capabilities improve the utility of the quadrotor platform for flight without the need of any external sensing capability.

Utilizing the Euler-Rodrigues symmetric parameters (attitude quaternion) to describe vehicle orientation, we develop a multiplicative, nonlinear (extended) variation of the Kalman filter (MEKF) to fuse data from low-cost sensors. The sensor suite is comprised of gyroscopes, accelerometers, and a GPS receiver. In contrast to the common approach of using the complete vehicle attitude as the quantities to be estimated, our filter states consist of the three components of an attitude error vector. In parallel with the time update of the attitude error estimate, we utilize the gyroscope measurements for the time propagation of the attitude quaternion. The accelerometer and the GPS sensors are used independently for the measurement update portion of the Kalman filter. For both sensors, a vector arithmetic approach is used to determine the attitude error vector. Following each measurement update, a multiplicative reset operation moves the attitude error information from the filter state into the attitude estimate. This reset operation utilizes quaternion algebra to implicitly maintain the unity-norm constraint. We demonstrate the effectiveness of our attitude estimation algorithm through flight simulations and flight tests of aggressive maneuvers such as loops and small-radius circles. We implement an approach to aerobatic maneuvering for miniature air vehicles (MAVs) using time-parameterized attitude trajectory generation and an associated attitude tracking control law. We designed two methodologies, polynomial and trigonometric, for creating functions that specify pitch and roll angles as a function of time. For both approaches, the functions are constrained by the maneuver boundary conditions of aircraft position and velocity. We construct a trajectory tracking feedback control law to regulate aircraft orientation throughout the maneuvers. The trajectory generation algorithm was used to construct several maneuvers and trajectory tracking control law successfully executed the maneuvers in the flight simulator. In addition to the simulation results, MAV flight tests verified the performance of the maneuver generation and control. To achieve obstacle avoidance maneuvering, the time parameterized trajectories were converted to spatially parameterized paths, which allowed for inertial reference frame position error to be included in the control law feedback loop. We develop a novel method to achieve the spatial parameterization using a prediction and correction approach. Additionally, the first derivative of position of the desired path is modified using a corrective parameter scheme prior to being used in the control. Using the path position error and the corrected derivative, we utilize a unit-norm quaternion framework to implement a proportional-derivative (PD) control law. This control law was demonstrated in simulation and hardware on maneuvers designed specifically to avoid obstacles, namely the Immelmann and the Close-Q, as well as a basic loop.

A spacecraft formation possesses several benefits over a single-satellite mission. However, launching a fleet of satellites is a high-cost, high-risk venture. One way to mitigate much of this risk is to demonstrate hardware and algorithm performance in groundbased testbeds. It is typically difficult to experimentally replicate satellite dynamics in an Earth-bound laboratory because of the influences of gravity and friction. An air bearing provides a very low-torque environment for experimentation, thereby recapturing the freedom of the space environment as effectively as possible. Depending upon con- figuration, air-bearing systems provide some combination of translational and rotational freedom; the three degrees of rotational freedom provided by a spherical air bearing are ideal for investigation of spacecraft attitude dynamics and control problems. An interest in experimental demonstration of formation flying led directly to the development of the Distributed Spacecraft Attitude Control System Simulator (DSACSS). The DSACSS is a unique facility, as it uses two air-bearing platforms working in concert. Thus DSACSS provides a pair of "spacecraft" three degrees of attitude freedom each. Through use of the DSACSS we are able to replicate the relative attitude dynamics between nodes of a formation such as might be required for co-observation of a terrestrial target. Many dissertations present a new mathematical technique or prove a new theory. This dissertation presents the design and development of a new experimental system. Although the DSACSS is not yet fully operational, a great deal of work has gone into its development thus far. This work has ranged from configuration design to nonlinear analysis to structural and electrical manufacturing. In this dissertation we focus on the development of the attitude determination subsystem. This work includes development of the equations of motion and analysis of the sensor suite dynamics. We develop nonlinear filtering techniques for data fusion and attitude estimation, and extend this problem to include estimation of the mass properties of the system. We include recommendations for system modifications and improvements. / Ph. D.

An urban operation of unmanned aerial vehicles (UAVs) demands a high level of autonomy for tasks presented in a cluttered environment. While fixed-wing UAVs are well suited for long-endurance missions at a high altitude, enabling them to navigate inside an urban area brings another level of challenges. Their inability to hover and low agility in motion cause more difficulties on finding a feasible path to move safely in a compact region, and the limited payload allows only low-grade sensors for state estimation and control. We address the problem of achieving vision-based autonomous navigation for a small fixed-wing in an urban area with contributions to the following several key topics. Firstly, for robust attitude estimation during dynamic maneuvering, we take advantage of the line regularity in an urban scene, which features vertical and horizontal edges of man-made structures. The sensor fusion with gravity-related line segments and gyroscopes in a Kalman filter can provide driftless and realtime attitude for ight stabilization. Secondly, as a prerequisite to sensor fusion, we present a convenient self-calibration scheme based on the factorization method. Natural references such as gravity, vertical edges, and distant scene points, available in urban fields, are sufficient to find intrinsic and extrinsic parameters of inertial and vision sensors. Lastly, to generate a dynamically feasible motion plan, we propose a discrete planning method that encodes a path into interconnections of finite trim states, which allow a significant dimension reduction of a search space and result in naturally implementable paths integrated with ight controllers. The most probable path to reach a target is computed by the Markov Decision Process with motion uncertainty due to wind, and a minimum target observation time is imposed on the final motion plan to consider a camera's limited field-of-view. In this thesis, the effectiveness of our vision-based navigation system is demonstrated by what we call an "air slalom" task in which the UAV must autonomously search and localize multiple gates, and pass through them sequentially. Experiment results with a 1m wing-span airplane show essential navigation capabilities demanded in urban operations such as maneuvering passageways between buildings.