This thesis contains new results on the problem of coordinating a group of vehicles. The main motivation driving this work is the development of control laws that steer individual members of a formation, such that desired group behavior emerges. Special attention is paid to analysis of coordination issues, in particular formation control of marine craft where robustness to unknown environmental forces is important. Coordinated control applications for marine craft include: underway replenishment, maintaining a formation for increased safety during travel and instrument resolution, and cooperative transportation. A review of formation control structures is given, together with a discussion of special issues that arise in coordination of independent vehicles. The main contributions of this thesis may be grouped into two categories: • Path-following designs for controlling a group of vehicles • Multi-body motivated formation modeling and control A previously developed path following design is used to control a group of vehicles by synchronizing the individual path parameters. The path following design is advantageous since the path parameter, i.e., that parameter which determines position along a path, is scalar; hence coordination is achieved with a little amount of real-time communication. The path following design is also extended to the output-feedback case for systems where only parts of the state vector are known. The path following scheme is exploited further in a passivity-based design for coordination where the structural properties render an extended selection of functions for synchronization available. Performance and robustness properties in different operational conditions can be enhanced with a careful selection of these functions. Two designs are presented; a cascaded interconnection where a consensus system provides synchronized path parameters as input to the individual path following systems renders time-varying formations possible and increases robustness to communication problems; a feedback interconnection which is more robust to vehicle failures. Both designs are extended to sampled-data designs where plant and controller dynamics are updated in continuous-time and path parameters are exchanged over a communication network where transmission occurs at discrete intervals. Bias estimation is included to provide integral action against slowlyvarying environmental forces and model uncertainties. A scheme for formation modeling and control, inspired by analytical mechanics of multi-body systems and Lagrangian multipliers, is proposed. In this approach to formation control, various formation behaviors are determined by imposing constraint functions on group members. Several examples illustrate these formation behaviors. The stabilization scheme presented is made more robust with respect to unknown time-varying disturbances. In addition, the scheme is extended towards adaptive estimation of unknown plant and parameters. Furthermore, it can be applied with no major modifications to the case of position control for a single vehicle. The formation control scheme is such that it may be used in combination with a set of position control laws for a single vessel, thus enabling the designer to choose from a large class of control laws available in the literature. The input-to-state stability (ISS) framework is utilised to investigate robustness to environmental and communication disturbances. A loop-transform, together with the ISS framework, yields an upper bound on the inter-vessel time delay below which formation stability is maintained.

All-electric ship power systems have limited generation capacity and finite rotating inertia compared with large power systems. Moreover, all-electric ship power systems include large portions of nonlinear loads and dynamic loads relative to the total power capacity, which may significantly reduce the stability margin. Pulse loads and other high-energy weapon loads in the system draw a large amount of power intermittently, which may cause significant frequency and voltage oscillations in the system. Thus, an effective real-time load management technique is needed to dynamically balance the load and generation to operate the system normally. Multi-agent systems, inspired by biological phenomena, aim to cooperatively achieve system objectives that are difficult to reach by a single agent or centralized controller. Since power systems include various electrical components with different dynamical systems, conventional homogeneous multi-agent system cooperative controllers have difficulties solving the real-time load management problem with heterogeneous agents. In this dissertation, a novel heterogeneous multi-agent system cooperative control methodology is presented based on artificial potential functions and reduced-order agent models to cooperatively achieve real-time load management for all-electric ship power systems. The technique integrates high-order system dynamics and various kinds of operational constraints into the multi-agent system, which improves the accuracy of the cooperative controller. The multi-agent system includes a MVAC multiagent system and a DC zone multi-agent, which are coordinated by an AC-DC communication agent. The developed multi-agent system framework and the notional all-electric ship power system model were simulated in PSCAD software. Case studies and performance analysis of the MVAC multi-agent system and the DC zone multi-agent system were performed. The simulation results indicated that propulsion loads and pulse loads can be successfully coordinated to reduce the impact of pulse loads on the power quality of all-electric ship power systems. Further, the switch status or power set-point of loads in DC zones can be optimally determined to dynamically balance the generation and load while satisfying the operational constraints of the system and considering load priorities. The method has great potential to be extended to other isolated power systems, such as microgrids.

The objectives of this research are to extend cooperative control methods based on potential games to dynamic environments and to develop an experimental test bed to illustrate theoretical results. Cooperative control concerns coordinating a collective performance of multiple autonomous agents. Possible applications include mobile sensor networks, distributed computation, and unmanned vehicle teams. Prior work has explored game theory, specifically the framework of potential games, as an approach to cooperative control, but has been restricted to static environments. This research shows that potential game based cooperative control also can be applied to dynamic environment problems. The approach is illustrated on three example problems. The first one is a moving target tracking problem using a modified form of the learning algorithm, restrictive log-linear learning. The second example is mobile sensor coverage for an unknown dynamic environment. The last example is multi-agent path optimization using payoff based learning. The performances of the developed systems are studied by simulation. The last part of this thesis develops an experimental moving target tracking system using multiple mobile robots. Finally, the thesis concludes with suggestions for future research directions.

This dissertation solves variations of three mathematical problems for autonomous vehicle formations: (1) formation shape control in the plane, (2) robust information architecture design, and (3) formation attitude synchronization. An autonomous vehicle formation is a collection of vehicles, each with computation, communication, sensing, and control capabilities, that cooperate to achieve a common objective. Accelerating advancements are making possible a range of science and engineering applications, such as satellite formations for deep-space imaging, teams of unmanned aircraft for military reconnaissance and surveillance missions, and submarine swarms for oceanic exploration. The ubiquitous potential of these applications is driving theoretical work on autonomous vehicle formations across a range of disciplines. A major theoretical question in the field of control theory, and the main focus of this dissertation, is how the properties of the information architecture (i.e. a mapping of the information flow amongst the agents), relate to the stability properties of the desired shape and orientation under certain control laws. A secondary focus is how to design the information flow so that loss of an agent does not destroy the formation's ability to maintain a desired shape. As a motivating example, a solution to a coordinated standoff tracking problem is presented to demonstrate how an instance of a class of information architectures, which are called persistent and related to rigid graph theory, can be used to achieve a formation objective in a practical scenario involving a team of unmanned aircraft. A generalized formation shape control problem is then solved for a class of persistent architectures. This solution gives only local stability results; global stability is analyzed for a four-agent formation and several open problems are identified. The problem of agent loss is addressed by performing a self-repair operation in the event of agent loss and separately by designing robustness into the information architecture a priori. Finally, a rigid body attitude synchronization problem with communication time delays is solved for a class of information architectures based on spectral graph theory. / text

The proposed project is the simulation of a system to search for air vehicles which have splashed-down in the ocean. The system comprises a group of 10+ autonomous underwater vehicles, which cooperate in order to locate the aircraft. The search algorithm used in this system is based on a quadratic Newton method and was developed at Sandia National Laboratories. The method has already been successfully applied to several two dimensional problems at Sandia. The original 2D algorithm was converted to 3D and tested for robustness in the presence of sensor error, position error and navigational error. Treating the robots as point masses, the system was found to be robust for all such errors. Several real-life adaptations were necessary. A round-robin communication strategy was implemented on the system to properly simulate the dissemination of information throughout the group. Time to convergence is delayed but the system still functioned adequately. Once simulations for the point masses had been exhausted, the dynamics of the robots were included. The robot equations of motion were described using Kane's equations. Path-planning was investigated using optimal control methods. The Variational Calculus approach was attempted using a line search tool "fsolve" found in Matlab and a Genetic Algorithm. A dynamic programming technique was also investigated using a method recently developed by Sandia National Laboratories. The Dynamic Programming with Interior Points (DPIP) method was a very effcient method for path planning and performed well in the presence of system constraints. Finally all components of the system were integrated. The motion of the robot exactly matched the motion of the particles, even when subjected to the same robustness tests carried out on the point masses. This thesis provides exciting developments for all types of cooperative projects.

This thesis considers the cooperation and coordination of multi vehicle systems cohesively in order to keep the formation geometry and provide the string stability. We first present the modeling of aerial and road vehicles representing different motion characteristics suitable for cooperative operations. Then, a set of three dimensional cohesive motion coordination and formation control schemes for teams of autonomous vehicles is proposed. The two main components of these schemes are i) platform free high level online trajectory generation algorithms and ii) individual trajectory tracking controllers. High level algorithms generate the desired trajectories for three dimensional leader-follower structured tight formations, and then distributed controllers provide the individual control of each agent for tracking the desired trajectories. The generic goal of the control scheme is to move the agents while maintaining the formation geometry. We propose a distributed control scheme to solve this problem utilizing the notions of graph rigidity and persistence as well as techniques of virtual target tracking and smooth switching. The distributed control scheme is developed by modeling the agent kinematics as a single-velocity integrator; nevertheless, extension to the cases with simplified kinematic and dynamic models of fixed-wing autonomous aerial vehicles and quadrotors is discussed. The cohesive cooperation in three dimensions is so beneficial for surveillance and reconnaissance activities with optimal geometries, operation security in military activities, more viable with autonomous flying, and future aeronautics aspects, such as fractionated spacecraft and tethered formation flying. We then focus on motion control task modeling for three dimensional agent kinematics and considering parametric uncertainties originated from inertial measurement noise. We design an adaptive controller to perform the three dimensional motion control task, paying attention to the parametric uncertainties, and employing a recently developed immersion and invariance based scheme. Next, the cooperative driving of road vehicles in a platoon and string stability concepts in one-dimensional traffic are discussed. Collaborative driving of commercial vehicles has significant advantages while platooning on highways, including increased road-capacity and reduced traffic congestion in daily traffic. Several companies in the automotive sector have started implementing driver assistance systems and adaptive cruise control (ACC) support, which enables implementation of high level cooperative algorithms with additional softwares and simple electronic modifications. In this context, the cooperative adaptive cruise control approach are discussed for specific urban and highway platooning missions. In addition, we provide details of vehicle parameters, mathematical models of control structures, and experimental tests for the validation of our models. Moreover, the impact of vehicle to vehicle communication in the existence of static road-side units are given. Finally, we propose a set of stability guaranteed controllers for highway platooning missions. Formal problem definition of highway platooning considering constant and velocity dependent spacing strategies, and formal string stability analysis are included. Additionally, we provide the design of novel intervehicle distance based priority coefficient of feed-forward filter for robust platooning. In conclusion, the importance of increasing level of autonomy of single agents and platoon topology is discussed in performing cohesive coordination and collaborative driving missions and in mitigating sensory errors. Simulation and experimental results demonstrate the performance of our cohesive motion and string stable controllers, in addition we discuss application in formation control of autonomous multi-agent systems.

Cette dissertation fait face au problème de la localisation de sources, un sujet qui a été largement étudié dans la littérature récente au vu de son grand nombre d'applications. En particulier, ce travail se concentre sur le pilotage de multiples capteurs, capables de prendre des mesures ponctuelles de la quantité émise, vers la source sans faire usage d'aucune information de position, qui se trouve être indisponible dans de nombreux cas pratiques (par exemple, sous l'eau ou dans l'exploration souterraine). En faisant quelques hypothèses sur le processus de diffusion, nous développons un modèle qui permet d'utiliser des outils mathématiques (l'intégrale de Poisson et ses dérivées) pour obtenir une simple approximation du gradient de la fonction décrivant le processus de diffusion, dont la source représente le maximum, ce qui permet d'utiliser l'algorithme du gradient et trouver l'emplacement de la source. Les contributions sont de trois ordres : d'abord, nous utilisons ces outils pour résoudre le problème de la recherche d'une source en deux dimensions à travers d'un contrôle centralisé, où un seul véhicule, équipé de multiples capteurs et sans information de position, se déplace dans un environnement planaire où se trouve une source. Ensuite, nous étendons cette recherche à un cadre en trois dimensions, en considérant un engin volant équipé de capteurs qui se déplace dans l'espace ; pour ce cas plus général, outre la validation par simulations, nous fournissons également une étude théorique des propriétes de convergence de la loi de commande proposée. Enfin, nous abordons le problème de la localisation de source de façon distribuée, compte tenu de plusieurs capteurs autonomes mobiles (en deux dimensions) ; outre le problème de mettre en oeuvre l'algorithme de localisation de source de manière distribuée, nous devons garantir un contrôle de la formation approprié pour assurer l'exactitude de l'estimation du gradient, et donc atteindre la source.} / The dissertation faces the problem of source localisation, a topic which has been extensively studied in recent literature due to its large number of applications. In particular, it focuses on steering multiple sensors, able to take point-wise measurements of the emitted quantity, towards the source without making use of any position information, which happens to be unavailable in many practical cases (for example, underwater or underground exploration). By making some assumptions on the diffusion process, we develop a model which allows us to use some mathematical tools (the Poisson integral and its derivatives) for a simple approximation of the gradient of the function describing the diffusion process, whose source represents its maximum, making it possible to perform a gradient ascent to find the source location. The contributions are threefold: first, we use such tools to solve a 2-dimensional centralised source-seeking problem, where a single vehicle, equipped with multiple sensors and without position information, is moving in a planar environment where a source is supposed to emit. Then, we extend it to a 3-dimensional framework, considering a flying vehicle equipped with sensors moving in the space; for this more general case, in addition to simulation validation, we provide a theoretical study of the convergence properties of the proposed control law. Finally, we tackle the distributed source-localisation problem, considering several autonomous moving sensors (in two dimensions); in addition to the problem of implementing the source-localisation algorithm in a distributed manner, in this latter case we have also to guarantee a suitable formation control, to ensure the correctness of the gradient estimation and hence reach the source.

Cette thèse concerne le contrôle coopératif de systèmes multi-agents. Ce sujet a été largement étudié dans la littérature récente en raison de son grand nombre d'applications. Cette thèse propose de nouvelles conceptions de stratégies de contrôle collaboratif afin de réaliser une mission d'exploration sous-marine. En particulier, l'objectif final est de diriger une flotte de véhicules autonomes sous-marins, équipés de capteurs appropriés, jusqu'à l'emplacement d'une source de température, de polluants ou d'eau douce. Dans cette situation, il est pertinent de considérer les contraintes de communication entre véhicules qui sont décrites au moyen de graphe de communication. Les premières contributions traitent du développement de commandes de formation qui stabilisent la flotte vers des formations variant dans le temps, et qui, de plus, distribuent uniformément les véhicules le long de la formation. Enfin, le problème de recherche est abordée par l'interprétation de la flotte de véhicules comme un réseau mobile de capteurs. En particulier, il est démontré que les mesures recueillies par la flotte de véhicules permet d'estimer le gradient de concentration de la quantité d'intérêt. Suivant cette idée, un algorithme distribué basé sur des algorithmes de consensus est proposé d'estimer la direction du gradient d'une distribution du signal. / This dissertation focuses on cooperative control of multi-agent systems. This topic has been extensively studied in recent literature due to its large number of applications. This thesis is concerned by the design of collaborative control strategies in order to achieve an underwater exploration mission. In particular, the final aim is to steer a fleet of autonomous underwater vehicles, which are equipped by appropriate sensors, to the location of a source of temperature, pollutant or fresh water. In this situation it is relevant to consider constraints in the communication between vehicles which are described by means of a communication graph. The first contributions deal with the development of cooperative formation control laws which stabilize the fleet to time-varying formations and, in addition, which also distribute the vehicles uniformly along the formation. Finally, the source-seeking problem is tackled by interpreting the fleet of vehicles as a mobile sensors network. In particular, it is shown that the measurements collected by the fleet of vehicles allows us to approximate the gradient of a scalar field. Following this idea, a distributed algorithm based on consensus algorithms is proposed to estimate the gradient direction of a signal distribution.

Cette thèse porte sur des stratégies distribuées pour systèmes multi-robot. Tout d'abord, nous nous focalisons sur des algorithmes de consensus pour des systèmes hétérogènes qui représente, par exemple, différents modèles ou générations de robots. Dans la suite, nous proposons deux solutions pour améliorer les propriétés de connectivité du système. Tout d'abord, nous montrons comment améliorer la vitesse de convergence des algorithmes de consensus en modifiant les protocoles classiques. Plus précisément, nous appliquons le principe de retard stabilisant et nous montrons comment de l'information échantillonné convenablement peut être utilisée dans la design du contrôleur. Enfin, nous concevons et analysons un algorithme pour le déploiement d'agents compact. Dans cette approche, qui augmente le nombre de connexions du graphe, la configuration souhaitée de l'ensemble des robots est entièrement spécifiée par les angles inter-agents. La stratégie proposée est un algorithme complètement distribué, uniquement basée sur l'information locale qui permet l'auto-organisation du système. / This dissertation focuses on distributed agreement strategies for multi-robot systems. First of all, we deal with consensus algorithms for heterogeneous systems, representing, for example, different models or generations of robots. In the sequel, we propose two solutions to improve the connectivity properties of the system. Firstly, we show how to improve the consensus algorithm's convergence rate by modifying the classical control algorithms. More precisely, we apply the stabilizing delay principle and we show how appropriately sampled information can be used in the controller's design. Finally, we design and analyse an algorithm for the compact deployment of agents. In this approach, that increases the number of connections of the graph, the desired configuration of the swarm is entirely specified by the inter-agent angles. The proposed strategy is a completely distributed algorithm, only based on local information that allows swarm's self-organization.

Este trabalho apresenta o desenvolvimento de uma técnica de controle cooperativo aplicado para embarcações dotadas de sistema de posicionamento dinâmico (sistema DP). Um caso ilustrativo é estudado: o lançamento de um equipamento submarino utilizando duas embarcações DP. Neste exemplo, o sistema cooperativo controla a distância relativa das duas embarcações DP. As vantagens deste método se da no aumento da janela operacional, na tensão no cabo de lançamento que pode ser reduzida pela metade, entre outras. Um mapeamento dinâmico foi obtido utilizando um simulador 2D simplificado previamente validado por comparação com testes experimentais e o simulador no domínio do tempo TPN Tanque de Provas Numérico. Nestes mapas, duas regiões foram definidas, de ocorrência e não ocorrência de afrouxamento nos cabos em função da distancia entre as embarcações, profundidade do equipamento submarino e período da onda. Este mapa definiu as posições desejadas das embarcações para cada profundidade do equipamento. Foi proposto um controle da posição relativa das embarcações tentando manter os movimentos do ponto de conexão em oposição de fase. Isto evita a ocorrência de afrouxamentos no cabo de lançamento. Para isso, um algoritmo baseado em estimação de fase (Transformada de Hilbert) associado a um controlador PD foi implementado. Os resultados mostraram que o controle para ondas regulares é efetivo. Adicionalmente, o controle de pagamento de linha recebe as medidas do movimento vertical do ponto de conexão, e compensa esse movimento, mantendo constante seu comprimento. O controle foi implementado considerando erros de 10% e atrasos de até 1,5s nas medidas. Os resultados confirmaram que o controle pode eliminar os picos de tensão e a ocorrência de afrouxamento no cabo de lançamento. A conclusão deste trabalho sugere que a estratégia apropriada do controle, considerando ondas regulares, é combinar o controle de posição e o controle de pagamento de linha. O controle de posição, acoplado ao mapeamento dinâmico, define um caminho ótimo a ser seguido durante o içamento do equipamento, tentando manter as embarcações próximas da região de não ocorrência de afrouxamentos. / This work presents the development of cooperative control technique applied to vessels equipped with dynamic positioning (DP) system. An illustrative case study is suggested: the launching of subsea equipment using two DP vessels. In this example, the cooperative system controls the relative distance between the DP vessels. One of the advantages of this method is the increase of operations safety and operational window, since, among other factors, the tension in the launching cable is reduced by half. Initially, it was proposed the control of vessels relative positions, trying to keep the connection point movements in counter-phase. This avoids the slackening of the launching cable. For this, an algorithm based on phase estimator (Hilbert transform) associated with a PD control was implemented. The results showed that for regular waves this strategy was effective. A dynamic mapping was then obtained using simplified 2D simulator, previously validated by comparison with experimental tests. In these maps, two regions are defined - occurrence or non-occurrence of cable slackening - as a function of the distance of the vessels and the depth of the subsea equipment. This map defines the proper set-point for the DP systems for each depth of the subsea equipment. This map is used to define the best relative position for the vessels. In addition, the hoisting control receives the measurements of the vertical motion of the connection point, and compensates its motion, trying to maintain a constant lowering velocity. This control was implemented considering errors of 10% and delay of 0.5s in the measurements. The results confirmed that the control is able to eliminate the tension peaks and the occurrence of slackening in the launching cable. The conclusion is that the appropriate control strategy, considering regular waves, is to combine the control of both position of the vessels and hoisting of the cable. Therefore the position control, coupled with dynamic mapping, defines the \"optimal path\" to be followed during the line hoisting, trying to keep the vessels as close as possible to the \"no slackening\" region.