Autonomous mobile sensor networks consist of a number of autonomous mobile robots equipped with various sensors and tasked with a common mission. This thesis considers the topology control of such an ad hoc mobile sensor network. In particular, I studied the problem of controlling the size, with respect to a distance metric, of the network for general interactive forcing among agents. Developed is a stability result, allowing one to design force laws to control the spread of the network. Many of the current results assume a known and/or fixed topology of the graph representing the communication between the nodes, i.e. the graph laplacian is assumed constant. They also assume fixed and known force-laws. Hence, the results are limited to time-invariant dynamics. The research considers stability analysis of sensor networks, unconstrained by specific forcing functions or algorithms, and communication topologies. Since the graph topologies are allowed to change as the agents move about, the system dynamics become discontinuous in nature. Filippov’s calculus of differential equations with discontinuous right hand sides is used to formally characterize the multi-agent system with the above attributes. Lyapunov’s Stability Theory, applied to discontinuous systems, is then used to derive bounds on the norm of the system states given bounds on its initial states and input. The above derived stability results lend themselves to the derivation of methods for the design of algorithms or force-laws for mobile sensor networks. The efficacy of the derived results is illustrated through several examples where it is shown how they may be used for synthesizing a topology managing strategy. Examples are given of designing force-laws that limit the network in a desired area.

In this thesis we develop a rigorous mathematical framework for analyzing and approximating optimal sensor placement problems for distributed parameter systems and apply these results to PDE problems defined by the convection-diffusion equations. The mathematical problem is formulated as a distributed parameter optimal control problem with integral Riccati equations as constraints. In order to prove existence of the optimal sensor network and to construct a framework in which to develop rigorous numerical integration of the Riccati equations, we develop a theory based on Bochner integrable solutions of the Riccati equations. In particular, we focus on ℐ_p-valued continuous solutions of the Bochner integral Riccati equation. We give new results concerning the smoothing effect achieved by multiplying a general strongly continuous mapping by operators in ℐ_p. These smoothing results are essential to the proofs of the existence of Bochner integrable solutions of the Riccati integral equations. We also establish that multiplication of continuous ℐ_p-valued functions improves convergence properties of strongly continuous approximating mappings and specifically approximating C₀-semigroups. We develop a Galerkin type numerical scheme for approximating the solutions of the integral Riccati equation and prove convergence of the approximating solutions in the ℐ_p-norm. Numerical examples are given to illustrate the theory. / Ph. D.

A fundamental problem in mobile robotics is the exploration of unknown fields that might be inaccessible or hostile to humans. Exploration missions of great importance include geological survey, disaster prediction and recovery, and search and rescue. For missions in relatively large regions, mobile sensor networks (MSN) are ideal candidates. The basic idea of MSN is that mobile robots form a sensor network that collects information, meanwhile, the behaviors of the mobile robots adapt to changes in the environment. To design feasible motion patterns and control of MSN, we draw inspiration from biology, where animal groups demonstrate amazingly complex but adaptive collective behaviors to changing environments. The main contributions of this thesis include platform independent mathematical models for the coupled motion-sensing dynamics of MSN and biologically-inspired provably convergent cooperative control and filtering algorithms for MSN exploring unknown scalar fields in both 2D and 3D spaces. We introduce a novel model of behaviors of mobile agents that leads to fundamental theoretical results for evaluating the feasibility and difficulty of exploring a field using MSN. Under this framework, we propose and implement source seeking algorithms using MSN inspired by behaviors of fish schools. To balance the cost and performance in exploration tasks, a switching strategy, which allows the mobile sensing agents to switch between individual and cooperative exploration, is developed. Compared to fixed strategies, the switching strategy brings in more flexibility in engineering design. To reveal the geometry of 3D spaces, we propose a control and sensing co-design for MSN to detect and track a line of curvature on a desired level surface.

This thesis presents contributions to node localization in mobile sensor networks. Considering the importance of localization algorithms in identifying the location of an event in order to better determine the action to be taken by the user, a new localization algorithm to operate in mobile networks was designed, assuming an uncontrollable movement of the nodes. This algorithm, which we call CentroidM, has the Centroid method as a stand. Positive features of the Centroid algorithm were kept while their limitations due to the dynamic characteristcs of the network movement were mitigated. Besides the concern regarding the accuracy of the method, the power consumption of the algorithm was addressed too. The design of an dedicated integrated circuit to deal with the localization task in a mobile network is justified given the high activity of such a subsystem in the given scenario. This way, the focus of this Thesis relies on a low power localization algorithm for mobile networks, with characteristics to allow raising calculated coordinates accuracy in both static and mobile scenarios. The results show that the CentroidM is 30% more accurate than the Centroid on a static scenario, and 40% when we consider a node movement without actuators. These benefits have some computational overhead, increasing 2.76 times the time spent by the CentroidM to run a localization process. However, simulation results showed it is possible to remove such overhead and still keep the achieved estimation gains near 10%. The implementation of the localization method was accomplished through an integrated circuit, which reduced the energy expended during the computation of the coordinates by an order of magnitude when comparing with the execution of the algorithm in a low power commercial microcontroller. / Esta Tese apresenta contribuições ao processo de localização de nodos em redes de sensores móveis. Considerando a importância de algoritmos de localização em uma rede para identificar o local do evento sob estudo e determinar a ação a ser tomada pelo usuário, é desenvolvido um novo algoritmo de localização para operar em redes de sensores móveis, focando o aspecto da mobilidade não controlada dos nodos. Este algoritmo, ao qual denominamos CentroidM, teve como base de desenvolvimento o método Centroid. Foram mantidas as características positivas do Centroid e exploradas as limitações do método para a sua execução em uma rede que considera o movimento. Além do objetivo em reduzir o erro das estimativas de posicionamento calculadas pelo algoritmo, o consumo de potência do método apresentado neste trabalho é enfatizado. O projeto de um circuito integrado dedicado que desempenhe o processo de localização em uma rede móvel é justificado pela intensa utilização de tal subsistema neste tipo de rede, além dos benefícios que um hardware dedicado traz face à redução da energia gasta nesta operação. Desta forma, o foco deste trabalho recai sobre um algoritmo de localização para redes móveis e as características desta abordagem que permitiram aumentar a precisão das estimativas de posicionamento tanto em um cenário com ausência de movimento dos nodos, quanto em outro onde o aspecto da mobilidade sem atuadores foi considerada. Os resultados obtidos nesta Tese demostraram que o CentroidM é 30% mais preciso que o Centroid para um cenário estático e 40% considerando a mobilidade da rede. O ganho alcançado em precisão teve um custo computacional que elevou em 2, 76 vezes o tempo gasto pelo CentroidM para realizar um procedimento de localização. Contudo, os resultados de simulação mostraram que é possível eliminar a sobrecarga computacional e ainda assim atingir ganhos em precisão próximos a 10%. O desenvolvimento do método de localização é complementado pela sua implementação em um circuito integrado dedicado, reduzindo a energia gasta no processo de estimativa da posição em uma ordem da magnitude face à execução do algoritmo em um microcontrolador comercial de baixo consumo.

In this work, connectivity graphs have been studied as models of local interactions in multi-agent robotic systems. A systematic study of the space of connectivity graphs has been done from a geometric and topological point of view. Some results on the realization of connectivity graphs in their respective configuration spaces have been given. A complexity analysis of networks, from the point of view of intrinsic structural complexity, has been given. Various topological spaces in networks, as induced from their connectivity graphs, have been recognized and put into applications, such as those concerning coverage problems in sensor networks. A framework for studying dynamic connectivity graphs has been proposed. This framework has been used for several applications that include the generation of low-complexity formations as well as collaborative beamforming in sensor networks. The theory has been verified by generating extensive simulations, with the help of software tools of computational homology and semi-definite programming. Finally, several open problems and areas of further research have been identified.

Mobile sinks are vital in many wireless sensor applications for efficient data collection, data querying, and localized sensor reprogramming. Mobile sinks prolong the lifetime of a sensor network. However, when sensor networks with mobile sinks are deployed in a hostile environment, security became a critical issue. They become exposed to varieties of malicious attacks. Thus, anti threats schemes and security services, such as mobile sink?s authentication and pairwise key establishment, are essential components for the secure operation of such networks. Due to the sensors, limited resources designing efficient security schemes with low communication overhead to secure communication links between sensors and MS (Mobile Sink) is not a trivial task. In addition to the sensors limited resources, sink mobility required frequent exchange of cryptography information between the sensors and MS each time the MS updates its location which imposes extra communication overhead on the sensors. In this dissertation, we consider a number of security schemes for WSN (wireless sensor network) with MS. The schemes offer high network?s resiliency and low communication overhead against nodes capture, MS replication and wormhole attacks. We propose two schemes based on the polynomial pool scheme for tolerating nodes capture: the probabilistic generation key pre-distribution scheme combined with polynomial pool scheme, and the Q-composite generation key scheme combined with polynomial pool scheme. The schemes ensure low communication overhead and high resiliency. For anti MS replication attack scheme, we propose the multiple polynomial pools scheme that provide much higher resiliency to MS replication attack as compared to the single polynomial pool approach. Furthermore, to improve the network resiliency against wormhole attack, two defensive mechanisms were developed according to the MS mobility type. In the first technique, MS uses controlled mobility. We investigate the problem of using a single authentication code by sensors network to verify the source of MS beacons, and then we develop a defensive approach that divide the sensor network into different authentication code?s grids. In the second technique, random mobility is used by MS. We explore the use of different communication channels available in the sensor hardware combined with polynomial pool scheme.

This thesis proposes a framework for controlling mobile robot networks based on a fluid dynamics paradigm. The approach is inspired by natural behaviors of fluids demonstrating desirable characteristics for collective robots. The underlying mathematical formalism is developed through establishing analogies between fluid bodies and multi-robot systems such that robots are modeled as fluid elements that constitute a fluid body. The governing equations of fluid dynamics are adapted to multi-robot systems and applied on control of robots. The model governs flow of a robot based on its local interactions with neighboring robots and surrounding environment. Therefore, it provides a layer of decentralized reactive control on low level behaviors, such as obstacle avoidance, deployment, and flow. These behaviors are inherent to the nature of fluids and provide emergent coordination among robots. The framework also introduces a high-level control layer that can be designed according to requirements of the particular task. Emergence of cooperation and collective behavior can be controlled in this layer via a set of parameters obtained from the mathematical description of the system in the lower layer. Validity and potential of the approach have been experimented through simulations primarily on two common collective robotic tasks / deployment and navigation. It is shown that gas-like mobile sensor networks can provide effective coverage in unknown, unstructured, and dynamically changing environments through self-spreading. On the other hand, robots can also demonstrate directional flow in navigation or path following tasks, showing that a wide range of multi-robot applications can potentially be developed using the framework.

A new class of wireless sensor networks has recently appeared due to the pervasiness of cellular phones with embedded sensors, mobile Internet connectivity, and location technologies. This mobile wireless sensor network has the potential to address large-scale societal problems and improve the people's quality of life in a better, faster and less expensive fashion than current solutions based on static wireless sensor networks. Ubiquitous Sensing is the umbrella term used in this dissertation that encompasses location-based services, human-centric, and participatory sensing applications. At the same time, ubiquitous sensing applications are bringing a new series of challenging problems. This dissertation proposes and evaluates G-Sense, for Global-Sense, an architecture that integrates mobile and static wireless sensor networks, and addresses several new problems related to location-based services, participatory sensing, and human-centric sensing applications. G-Sense features the critical point algorithms, which are specific mechanisms to reduce the power consumption by continous sensing applications in cellular phones, and reduce the amount of data generated by these applications. As ubiquitous sensing applications have the potential to gather data from many users around the globe, G-Sense introduces a peer-to-peer system to interconnect sensing servers based on the locality of the data. Finally, this dissertation proposes and evaluates a multiobjective model and a hybrid evolutionary algorithm to address the efficient deployment of static wireless sensor nodes when monitoring critical areas of interest.

<p>This dissertation presents a novel distributed optimal control (DOC) problem formulation that is applicable to multiscale dynamical systems comprised of numerous interacting systems, or agents, that together give rise to coherent macroscopic behaviors, or coarse dynamics, that can be modeled by partial differential equations (PDEs) on larger spatial and time scales. The DOC methodology seeks to obtain optimal agent state and control trajectories by representing the system's performance as an integral cost function of the macroscopic state, which is optimized subject to the agents' dynamics. The macroscopic state is identified as a time-varying probability density function to which the states of the individual agents can be mapped via a restriction operator. Optimality conditions for the DOC problem are derived analytically, and the optimal trajectories of the macroscopic state and control are computed using direct and indirect optimization algorithms. Feedback microscopic control laws are then derived from the optimal macroscopic description using a potential function approach.</p><p>The DOC approach is demonstrated numerically through benchmark multi-agent trajectory optimization problems, where large systems of agents were given the objectives of traveling to goal state distributions, avoiding obstacles, maintaining formations, and minimizing energy consumption through control. Comparisons are provided between the direct and indirect optimization techniques, as well as existing methods from the literature, and a computational complexity analysis is presented. The methodology is also applied to a track coverage optimization problem for the control of distributed networks of mobile omnidirectional sensors, where the sensors move to maximize the probability of track detection of a known distribution of mobile targets traversing a region of interest (ROI). Through extensive simulations, DOC is shown to outperform several existing sensor deployment and control strategies. Furthermore, the computation required by the DOC algorithm is proven to be far reduced compared to that of classical, direct optimal control algorithms.</p> / Dissertation

Ce manuscrit contient d'abord l'étude d'une extension du modèle des protocoles de populations, qui représentent des réseaux de capteurs asynchrones, passivement mobiles, limités en ressources et anonymes. Pour la première fois (à notre connaissance), un modèle formel de consommation d'énergie est proposé pour les protocoles de populations. A titre d'application, nous étudions à la complexité en énergie (dans le pire des cas et en moyenne) pour le problème de collecte de données. Deux protocoles prenant en compte la consommation d'énergie sont proposés. Le premier est déterministe et le second randomisé. Pour déterminer les valeurs optimales des paramètres, nous faisons appel aux techniques d'optimisation. Nous appliquons aussi ces techniques dans un cadre différent, celui des réseaux de capteurs corporels (WBAN). Une formulation de flux est proposée pour acheminer de manière optimale les paquets de données en minimisant la pire consommation d'énergie. Une procédure de recherche à voisinage variable est développée et les résultats numériques montrent son efficacité. Enfin, nous considérons le problème d'optimisation avec des paramètres aléatoires. Précisément, nous étudions un modèle semi-défini positif sous contrainte en probabilité. Un nouvel algorithme basé sur la simulation est proposé et testé sur un problème réel de théorie du contrôle. Nous montrons que notre méthode permet de trouver une solution moins conservatrice que d'autres approches en un temps de calcul raisonnable. / In this thesis, we propose a formal energy model which allows an analytical study of energy consumption, for the first time in the context of population protocols. Population protocols model one special kind of sensor networks where anonymous and uniformly bounded memory sensors move unpredictably and communicate in pairs. To illustrate the power and the usefulness of the proposed energy model, we present formal analyses on time and energy, for the worst and the average cases, for accomplishing the fundamental task of data collection. Two power-aware population protocols, (deterministic) EB-TTFM and (randomized) lazy-TTF, are proposed and studied for two different fairness conditions, respectively. Moreover, to obtain the best parameters in lazy-TTF, we adopt optimization techniques and evaluate the resulting performance by experiments. Then, we continue the study on optimization for the power-aware data collection problem in wireless body area networks. A minmax multi-commodity netflow formulation is proposed to optimally route data packets by minimizing the worst power consumption. Then, a variable neighborhood search approach is developed and the numerical results show its efficiency. At last, a stochastic optimization model, namely the chance constrained semidefinite programs, is considered for the realistic decision making problems with random parameters. A novel simulation-based algorithm is proposed with experiments on a real control theory problem. We show that our method allows a less conservative solution, than other approaches, within reasonable time.