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This dissertation proposes three control algorithms for active sensing with one or several autonomous robots.The algorithms all rely on models of the information content of the sensor measurement with respect to the relative poses between sensors and subjects.The approaches each predict how new information may impact the uncertainty in the subjects, controlling sensors to new locations or trajectories from where these uncertainties will me minimized.The first algorithm deals with the Next-Best-View (NBV) problem for a single robot, where the goal is to control a mobile camera so that the next image of a set of possibly mobile targets will be as informative as possible.The NBV controller is designed for a rig that hosts two cameras in a fronto-parallel arrangement, commonly known as stereo vision.Assuming that the objects, landmarks, or targets being estimated are visible by both cameras in the rig and that these observations are corrupted by zero-mean Gaussian errors, the control algorithm moves the rig through pose space in order to reduce the expected Kalman-filtered uncertainty in the next location point-estimate.This is done by differentiating the KF output error covariance matrix with respect to the sensor pose, which results in a nonlinear control problem.The controller is decomposed so that first the robot computes the NBV in coordinates relative to the body-frame of the stereo rig, and then it moves in pose space to realize this view.When an image is acquired, a switching signal changes the goal of pose control, giving rise to a stable hybrid system.Experiments of on a real robot localizing targets in a laboratory setting are presented.The second algorithm addresses the problem of estimating a finite set of hidden state vectors using a mobile robotic sensor network.For every hidden state that needs to be estimated, a local Dynamic Program (DP) in the joint state-space of robot positions and state uncertainties determines robot paths and associated sequences of state observations that collectively minimize the estimation uncertainty.It divides the collection of hidden states into clusters based on a prior belief of their geographic locations and, for each cluster, defines a second DP that determines how far along the local optimal trajectories the robot should travel before transitioning to estimating the next hidden state within the cluster.Finally, a distributed assignment algorithm dynamically allocates controllers to the robot team from the set of optimal control policies at every cluster.Assuming Gaussian priors on the hidden state vectors, the distributed state estimation method scales gracefully to large teams of mobile robots and hidden vectors and provide extensive simulations and real-world experiments using stereoscopic vision sensors to illustrate the approach.The third chapter addresses the problem of controlling a network of mobile sensors so that a set of hidden states are estimated up to a user-specified accuracy. The sensors take measurements and fuse them online using an Information Consensus Filter (ICF). At the same time, the local estimates guide the sensors to their next best configuration. This leads to an LMI-constrained optimization problem that we solve by means of a new distributed random approximate projections method. The new method is robust to the state disagreement errors that exist among the robots as the ICF fuses the collected measurements. Assuming that the noise corrupting the measurements is zero-mean and Gaussian and that the robots are self localized in the environment, the integrated system converges to the next best positions from where new observations will be taken. This process is repeated with the robots taking a sequence of observations until the hidden states are estimated up to the desired user-specified accuracy. It presents simulations of sparse landmark localization, where the robotic team is achieves the desired estimation tolerances while exhibiting interesting emergent behavior.Experiments of the first two algorithms are also presented.

Distributed optimization methods allow us to decompose an optimization probleminto smaller, more manageable subproblems that are solved in parallel. For thisreason, they are widely used to solve large-scale problems arising in areas as diverseas wireless communications, optimal control, machine learning, artificial intelligence,computational biology, finance and statistics, to name a few. Moreover, distributedalgorithms avoid the cost and fragility associated with centralized coordination, andprovide better privacy for the autonomous decision makers. These are desirableproperties, especially in applications involving networked robotics, communicationor sensor networks, and power distribution systems.In this thesis we propose the Accelerated Distributed Augmented Lagrangians(ADAL) algorithm, a novel decomposition method for convex optimization prob-lems with certain separability structure. The method is based on the augmentedLagrangian framework and addresses problems that involve multiple agents optimiz-ing a separable convex objective function subject to convex local constraints andlinear coupling constraints. We establish the convergence of ADAL and also showthat it has a worst-case O(1/k) convergence rate, where k denotes the number ofiterations.Moreover, we show that ADAL converges to a local minimum of the problemfor cases with non-convex objective functions. This is the first published work thatformally establishes the convergence of a distributed augmented Lagrangian methodivfor non-convex optimization problems. An alternative way to select the stepsizesused in the algorithm is also discussed. These two contributions are independentfrom each other, meaning that convergence of the non-convex ADAL method canstill be shown using the stepsizes from the convex case, and, similarly, convergenceof the convex ADAL method can be shown using the stepsizes proposed in the non-convex proof.Furthermore, we consider cases where the distributed algorithm needs to operatein the presence of uncertainty and noise and show that the generated sequences ofprimal and dual variables converge to their respective optimal sets almost surely. Inparticular, we are concerned with scenarios where: i) the local computation stepsare inexact or are performed in the presence of uncertainty, and ii) the messageexchanges between agents are corrupted by noise. In this case, the proposed schemecan be classified as a distributed stochastic approximation method. Compared toexisting literature in this area, our work is the first that utilizes the augmentedLagrangian framework. Moreover, the method allows us to solve a richer class ofproblems as compared to existing methods on distributed stochastic approximationthat consider only consensus constraints.Extensive numerical experiments have been carried out in an effort to validatethe novelty and effectiveness of the proposed method in all the areas of the afore-mentioned theoretical contributions. We examine problems in convex, non-convex,and stochastic settings where uncertainties and noise affect the execution of the al-gorithm. For the convex cases, we present applications of ADAL to certain popularnetwork optimization problems, as well as to a two-stage stochastic optimizationproblem. The simulation results suggest that the proposed method outperformsthe state-of-the-art distributed augmented Lagrangian methods that are known inthe literature. For the non-convex cases, we perform simulations on certain simplenon-convex problems to establish that ADAL indeed converges to non-trivial localvsolutions of the problems; in comparison, the straightforward implementation of theother distributed augmented Lagrangian methods on the same problems does notlead to convergence. For the stochastic setting, we present simulation results ofADAL applied on network optimization problems and examine the effect that noiseand uncertainties have in the convergence behavior of the method.As an extended and more involved application, we also consider the problemof relay cooperative beamforming in wireless communications systems. Specifically,we study the scenario of a multi-cluster network, in which each cluster containsmultiple single-antenna source destination pairs that communicate simultaneouslyover the same channel. The communications are supported by cooperating amplify-and-forward relays, which perform beamforming. Since the emerging problem is non-convex, we propose an approximate convex reformulation. Based on ADAL, we alsodiscuss two different ways to obtain a distributed solution that allows for autonomouscomputation of the optimal beamforming decisions by each cluster, while taking intoaccount intra- and inter-cluster interference effects.Our goal in this thesis is to advance the state-of-the-art in distributed optimization by proposing methods that combine fast convergence, wide applicability, easeof implementation, low computational complexity, and are robust with respect todelays, uncertainty in the problem parameters, noise corruption in the message ex-changes, and inexact computations.