In this work, a user-friendly MATLAB tool is introduced to solve nonlinear optimal control problems by applying collocation techniques using Coupled Radial Basis Functions (CRBFs). CRBFs are a new class of Radial Basis Functions combined with a conical spline r^5, which provides the advantage of insensitivity to the shape parameter while maintaining accuracy and robustness. To solve optimal control problems, software tools are often employed to implement numerical methods and apply advanced techniques to solving differential equations. Although several commercial software tools exist for solving optimal control problems, such as ICLOCS2, GPOPS, and DIDO, there are no options available that utilize adaptive collocation with CRBFs. A unified MATLAB tool named Radial Optimal Control Software (ROCS) is introduced and not only implements the CRBF method, but also enables any user, from professionals to students, to solve nonlinear optimal control problems through a user-friendly interface. The tool accepts user input for boundary conditions, necessary conditions, and the governing equations of motion. The two-point boundary value problem (TPBVP) is approximated through collocation using CRBFs, and the resulting nonlinear algebraic equations (NAEs) are solved with a MATLAB solver. The tool's usefulness and application are demonstrated by solving classical nonlinear optimal control problems and comparing the results with the solutions found in the literature. Compared to classical numerical method techniques, the present tool is shown to solve optimal control problems more efficiently for the same level of accuracy. By introducing this unified MATLAB tool to solving nonlinear optimal control problems, the intent is to enable professionals and students to solve nonlinear optimal control problems, e.g., in astrodynamics and space-flight mechanics, without the need for extensive manipulation of code in existing software tools and without extensive knowledge of applying numerical solvers.

<p>Multiple target tracking (MTT) is a major area that occurs in a variety of real world systems. The problem involves the detection and estimation of an unknown number of targets within a scenario space given a sequence of noisy, incomplete measurements. The classic approach to MTT performs data association between individual measurements, however, this step is a computationally complex problem. Recently, a series of algorithms based on Random Finite Set (RFS) theory, that do not require data association, have been introduced. This thesis addresses some of the main deficiencies involved with RFS methods and derives key extensions to improve them for use in real world systems.\\</p> <p>The first contribution is the Weight Partitioned PHD filter. It separates the Probability Hypothesis Density (PHD) surface into partitions that represent the individual state estimates both spatially and proportionally. The partitions are labeled and propagated over several time steps to form continuous track estimates. Multiple variants of the filter are presented. Next, the Multitarget Multi-Bernoulli (MeMBer) filter is extended to allow the tracking of manoeuvring targets. A model state variable is incorporated into the filter framework to estimate the probability of each motion model. The standard implementations are derived. Finally, a new linear variant of the Intensity filter (iFilter) is presented. A Gaussian Mixture approximation provides more computationally efficient implementation of the iFilter.</p> <p>Each of the new algorithms are validated on simulated data using standard multitarget tracking metrics. In each case, the methods improve on several aspects of multitarget tracking in the real world.</p> / Doctor of Engineering (DEng)

With the achievement of autonomous flight for small unmanned aircraft, currently ongoing research is expanding the capabilities of systems utilizing such vehicles for various tasks. This allows shifting the research focus from the individual systems to task execution benefits resulting from interaction and collaboration of several aircraft. Given that some available high-fidelity simulations do not yet support multi-vehicle scenarios, the presented work introduces a framework which allows several individual single-vehicle simulations to be combined into a larger multi-vehicle scenario with little to no special requirements towards the single-vehicle systems. The created multi-vehicle system offers real-time software-in-the-loop simulations of swarms of vehicles across multiple hosts and enables a single operator to command and control a swarm of unmanned aircraft beyond line-of-sight in geometrically correct two-dimensional cluttered environments through a multi-hop network of data-relaying intermediaries. This dissertation presents the main aspects of the developed system: the underlying software framework and application programming interface, the utilized inter- and intra-system communication architecture, the graphical user interface, and implemented algorithms and operator aid heuristics to support the management and placement of the vehicles. The effectiveness of the aid heuristics is validated through a human subject study which showed that the provided operator support systems significantly improve the operators' performance in a simulated first responder scenario. The presented software is released under the Apache License 2.0 and, where non-open-source parts are used, software packages with free academic licenses have been chosen--resulting in a framework that is completely free for academic research.

The control of multiple unmanned aerial vehicles (UAVs) in a swarm or cooperative team scenario has been a topic of great interest for well over a decade, growing steadily with the advancements in UAV technologies. In the academic community, a majority of the studies conducted rely on simulation to test developed control strategies, with only a few institutions known to have nurtured the infrastructure required to propel multiple UAV control studies beyond simulation and into experimental testing. With the Cal Poly UAV FLOC Project, such an infrastructure was created, paving the way for future experimentation with multiple UAV control systems. The control system architecture presented was built on concepts developed in previous work by Cal Poly faculty and graduate students. An outer-loop formation flight controller based on a virtual waypoint implementation of potential function guidance was developed for use on an embedded microcontroller. A commercially-available autopilot system, designed for fully autonomous waypoint navigation utilizing low cost hardware and open source software, was modified to include the formation flight controller and an inter-UAV communication network. A hardware-in-the-loop (HIL) simulation was set up for multiple UAV testing and was utilized to verify the functionality of the modified autopilot system. HIL simulation results demonstrated leader-follower formation convergence to 15 meters as well as formation flight with three UAVs. Several sets of flight tests were conducted, demonstrating a successful leader-follower formation, but with relative distance convergence only reaching a steady state value of approximately 35 +/- 5 meters away from the leader.

A platoon of autonomous underwater vehicles provides a compelling platform for studying many challenging issues in multi-agent cooperative control. These challenges include developing cooperative algorithms suitable to practical multi-vehicle applications. They also include addressing intervehicle communication issues, such as sharing information via limited bandwidth channels and selecting network architecture to facilitate control design. This work addresses problems in each of these areas. Environmental tracking and formation control serves as the main application upon which this work focuses. In the tracking and formation control application, a team of vehicles obtains a spatial average of an environmental feature by collecting and sharing local measurements. To achieve this objective, vehicles track a desired environmental field contour with their average position while maintaining a desired spatial formation about the average. A decentralized consensus-based algorithm is developed for controlling the platoon. In a novel two-level consensus approach, each vehicle estimates a virtual leader trajectory using local and shared measurements at one level, then positions itself about the virtual leader at a second level. Due to very low bandwidth underwater communication, vehicles share information intermittently, and the platoon network is effectively disconnected at every instant of time. This issue is addressed by modeling the platoon as a periodic switched system whose frozen-time subsystems possess disconnected networks, but whose time-averaged system is connected. The stability and input-output properties of the switched system are related to those of the corresponding average system. Under sufficiently fast switching, asymptotic stability of the average system implies asymptotic stability of the switched system and the existence of an L2 gain. Estimates of the slowest stabilizing switching rate and the L2 gain are derived. Controller and estimator design are complicated by the lack of a separation principle for decentralized systems and by the effects of intervehicle coupling. The potential for choosing the communication topology in a manner that leads to design simplifications is investigated. In particular, a transformation is presented that converts the platoon state coefficient matrix to block diagonal form when the communication network has a circulant structure. / Ph. D.

La localisation d’un véhicule via les techniques de SLAM (Simultaneous Localization And Mapping pour cartographie et localisation simultanées) a connu un essor important durant les 20 dernières années. Pourtant, peu d’approches ont tenté d’étendre ces algorithmes à une flotte de véhicules malgré les nombreuses applications potentielles. C’est ici l’objectif de cette thèse. Pour ce faire, une approche de SLAM monoculaire pour un seul véhicule a d’abord été développée. Celle-ci propose de coupler un filtre de Kalman étendu avec une représentation cartésienne des amers afin de produire des cartes de faible densité mais de qualité. En effet, l’extension à plusieurs véhicules nécessite des échanges permanents par l’intermédiaire de communications sans fil. Avec peu d’amers dans les cartes, notre approche s’accommode bien du nombre de véhicules de la flotte. Des capteurs peu onéreux ont aussi été privilégiés (une unique caméra et un odomètre) afin de réduire le coût d’une extension multivéhicule. Des correctifs ont été proposés afin d’éviter les problèmes de divergence induits par les choix précédents. Des expérimentations ont montré que la solution de SLAM produite était légère et rapide tout en fournissant une localisation de qualité. La dérive, inhérente à tout algorithme de SLAM, a également fait l’objet d’une analyse. Celle-ci a été intégrée au SLAM par l’intermédiaire d’une architecture dédiée et d’un modèle dynamique. Le but est de pouvoir rendre consistante la localisation fournie par le SLAM, même en l’absence d’estimation de la dérive. Cela permet d’effectuer des fermetures de boucle ou encore d’intégrer des informations géo-référencées de manière naturelle tout en conservant l’intégrité de la solution. En multivéhicule, cet aspect est un point clef puisque chaque véhicule dérive différemment des autres. Il est donc important de le prendre en compte. Enfin, le SLAM a été étendu à plusieurs véhicules. Une structure générique a été prévue afin que notre approche monoculaire puisse être remplacée par n’importe quel algorithme de SLAM. Notre architecture décentralisée évite la consanguinité des données (le fait de compter deux fois une même information) et gère les défaillances réseau, que cela soit des ruptures de communication ou encore des latences dans la réception des données. La partie statique du modèle de dérive permet également de prendre en compte le fait que les positions initiales des véhicules d’une flotte puissent être inconnues. L’intégrité est ainsi maintenue en permanence. Enfin, notre approche étant entièrement décentralisée, elle a pu être testée et validée en simulation et avec des expérimentations réelles dans diverses configurations (convoi en colonne ou en ligne, avec 2 ou 3 véhicules). / The localization of a vehicle with the use of SLAM techniques (Simultaneous Localization And Mapping) has been extensively studied during the last 20 years. However, only a few approaches have tried to extend these algorithms to a fleet of vehicles despite the many potential applications. It is the objective of this thesis. First of all, a monocular SLAM for a single vehicle has been developed. This one proposes to pair an Extended Kalman Filter with a Cartesian representation for landmarks so as to produce accurate low density maps. Indeed, the extension of SLAM to several vehicles requires permanent communications inside the fleet. With only a few landmarks mapped, our approach scales nicely with the number of vehicles. Cheap sensors have been favored (a single camera and an odometer) in order to spread more easily the use of multi-vehicle applications. Correctives have been proposed in order to avoid the divergence problems induced by such a scheme. The experiments showed that our SLAM is able to furnish good localization results while being light and fast.The drift affecting every SLAM algorithm has also been studied. Its integration inside the SLAM process, thanks to a dedicated architecture and a dynamic model, allows to ensure consistency even without an estimation of it. Loop closures or the integration of geo-referenced information becomes straightforward. They naturally correct all the past positions while still maintaining consistency. In a multi-vehicle scenario, it is a key aspect as each vehicle drifts differently from one another. It is consequently important to take it into account. Our SLAM algorithm has then been extended to several vehicles. A generic structure has been used so as to allow any SLAM algorithm to replace our monocular SLAM. The multi-vehicle architecture avoids data incest (double-counting information) and handles network failures, be they communication breakdowns or latencies when receiving data. The static part of the drift model allows to take into account the fact that the initial positions of the different vehicles composing the fleet might be unknown. Consistency is thus permanently preserved. Our approach has been successfully tested using simulations and real experiments with various settings (row or column convoy with 2 or 3 vehicles) in a fully decentralized way.

Using a new implementation of a NASA flight simulation of the Quiet Short-Haul Research Aircraft, autopilots were designed to be capable of flying both straight in (ILS) approaches, and circling (SNI) approaches. A standard glideslope coupler was sufficient for most conditions, but a standard Proportional-Integral-Derivative (PID) based localizer tracker was not sufficient for maintaining a lateral track on the SNI course. To track the SNI course, a feed-forward system, using GPS steering provided much better results. NASA and the FAA embrace the concept of a Simultaneous, Non-Interfering (SNI) approach as a way to increase airport throughput while reducing the noise footprints of aircraft on approach. The NASA concept for the SNI approach for Short Takeoff and Landing (STOL) aircraft involves a straight in segment flown above the flight path of a normal approach, followed by a spiraling descent to the runway. As this is a procedure that would be utilized by regional airliners, it is assumed that it would be conducted under Instrument Flight Rules (IFR). GPS or INS guidance would be required to fly this approach, and it is likely that it would be necessary to fly the approach with a coupled autopilot: a stabilized, curving, instrument approach to decision altitude would be exceedingly difficult to fly. The autopilots in many current commuter and general aviation aircraft, however, were designed before the event of GPS, and do not have provisions for tracking curved paths. This study identifies problem areas in implementing the SNI circling approach on aircraft and avionics as they stand today and also gives examples of what can be done for the SNI approach to be successful.

With unmanned aerial vehicles (UAVs), also known as drones, becoming readily available and affordable, applications for these devices have grown immensely. One type of application is the use of drones to fly over large areas and detect desired entities. For example, a swarm of drones could detect marine creatures near the surface of the ocean and provide users the location and type of animal found. However, even with the reduction in cost of drone technology, such applications result costly due to the use of custom hardware with built-in advanced capabilities. Therefore, the focus of this thesis is to compile an easily customizable, low-cost drone design with the necessary hardware for autonomous behavior, swarm coordination, and on-board object detection capabilities. Additionally, this thesis outlines the necessary network architecture to handle the interconnection and bandwidth requirements of the drone swarm. The drone on-board system uses a PixHawk 4 flight controller to handle flight mechanics, a Raspberry Pi 4 as a companion computer for general-purpose computing power, and a NVIDIA Jetson Nano Developer Kit to perform object detection in real-time. The implemented network follows the 802.11s standard for multi-hop communications with the HWMP routing protocol. This topology allows drones to forward packets through the network, significantly extending the flight range of the swarm. Our experiments show that the selected hardware and implemented network can provide direct point-to-point communications at a range of up to 1000 feet, with extended range possible through message forwarding. The network also provides sufficient bandwidth for bandwidth intensive data such as live video streams. With an expected flight time of about 17 minutes, the proposed design offers a low-cost drone swarm solution for mid-range aerial surveillance applications.

In this thesis, multiple on-road vehicle tracking problem is explored, with greater consideration of road constraints and interactions between vehicles. A comprehensive method for tracking multiple on-road vehicles is proposed by making use of domain knowledge of on-road vehicle motion. Starting with raw measurements provided by sensors, bias correction methods for sensors commonly used in vehicle tracking are briefly introduced and a fast but effective bias correction method for airborne video sensor is proposed. In the proposed method, by assuming errors in sensor parameter measurements are close to zero, the bias is separately addressed in converted measurements of target position by a linear term of errors in sensor parameter measurements. Based on this model, the bias is efficiently estimated by addressing it while tracking or using measurements of targets that are observed by multiple airborne video sensors simultaneously. The proposed method is compared with other airborne video bias correction methods through simulations. The numerical results demonstrate the effectiveness of the proposed method for correcting bias as well as its high computational efficiency. Then, a novel tracking algorithm that utilizes domain knowledge of on-road vehicle motion, i.e., road-map information and interactions among vehicles, by integrating a car-following model into a road coordinate system, is proposed for tracking multiple vehicles on single-lane roads. This algorithm is extended for tracking multiple vehicles on multi-lane roads: The road coordinate system is extended to two-dimension to express lanes on roads and a lane-changing model is integrated for modeling lane-changing behavior of vehicles. Since the longitudinal and lateral motions are mutually dependent, the longitudinal and lateral states of vehicles are estimated sequentially in a recursive manner. Two estimation strategies are proposed: a) The unscented Kalman filter combined with the multiple hypothesis tracking framework to estimate longitudinal and lateral states of vehicles, respectively. b) A unified particle filter framework with a specifically designed computationally-efficient joint sampling method to estimate longitudinal and lateral states of vehicles jointly. Both of two estimation methods can handle unknown parameters in motion models. A posterior Cramer-Rao lower bound is derived for quantifying achievable estimation accuracy in both single-lane and multi-lane cases, respectively. Numerical results show that the proposed algorithms achieve better track accuracy and consistency than conventional multi-vehicle tracking algorithms, which assumes that vehicles move independently of one another. / Thesis / Doctor of Philosophy (PhD)

Markov processes have been widely studied and used for modeling problems. A Markov process has two main components (i.e., an evolution law and an initial distribution). Markov processes are not suitable for modeling some problems, for example, the problem of predicting a trajectory with a known destination. Such a problem has three main components: an origin, an evolution law, and a destination. The conditionally Markov (CM) process is a powerful mathematical tool for generalizing the Markov process. One class of CM processes, called $CM_L$, fits the above components of trajectories with a destination. The CM process combines the Markov property and conditioning. The CM process has various classes that are more general and powerful than the Markov process, are useful for modeling various problems, and possess many Markov-like attractive properties. Reciprocal processes were introduced in connection to a problem in quantum mechanics and have been studied for years. But the existing viewpoint for studying reciprocal processes is not revealing and may lead to complicated results which are not necessarily easy to apply. We define and study various classes of Gaussian CM sequences, obtain their models and characterizations, study their relationships, demonstrate their applications, and provide general guidelines for applying Gaussian CM sequences. We develop various results about Gaussian CM sequences to provide a foundation and tools for general application of Gaussian CM sequences including trajectory modeling and prediction. We initiate the CM viewpoint to study reciprocal processes, demonstrate its significance, obtain simple and easy to apply results for Gaussian reciprocal sequences, and recommend studying reciprocal processes from the CM viewpoint. For example, we present a relationship between CM and reciprocal processes that provides a foundation for studying reciprocal processes from the CM viewpoint. Then, we obtain a model for nonsingular Gaussian reciprocal sequences with white dynamic noise, which is easy to apply. Also, this model is extended to the case of singular sequences and its application is demonstrated. A model for singular sequences has not been possible for years based on the existing viewpoint for studying reciprocal processes. This demonstrates the significance of studying reciprocal processes from the CM viewpoint.