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Sensor network localization (SNL) problems require determining the physical coordinates of all sensors in a network. This process relies on the global coordinates of anchors and the available measurements between non-anchor and anchor nodes. Attributed to the intrinsic non-convexity, obtaining a globally optimal solution to SNL is challenging, as well as implementing corresponding algorithms. In this paper, we formulate a non-convex multi-player potential game for a generic SNL problem to investigate the identification condition of the global Nash equilibrium (NE) therein, where the global NE represents the global solution of SNL. We employ canonical duality theory to transform the non-convex game into a complementary dual problem. Then we develop a conjugation-based algorithm to compute the stationary points of the complementary dual problem. On this basis, we show an identification condition of the global NE: the stationary point of the proposed algorithm satisfies a duality relation. Finally, simulation results are provided to validate the effectiveness of the theoretical results., Part of ISBN [9783907144107]QC 20240830

In this paper we develop a multiple model reference adaptive controller (MMRAC) with blending. The systems under consideration are non-square, i.e., the number of inputs is not equal to the number of states; multi-input, linear, time-invariant with uncertain parameters that lie inside of a known, compact, and convex set. Moreover, the full state of the plant is available for feedback. A multiple model online identification scheme for the plant's state and input matrices is developed that guarantees the estimated parameters converge to the underlying plant model under the assumption of persistence of excitation. Using an exact matching condition, the parameter estimates are used in a control law such that the plant's states asymptotically track the reference signal generated by a state-space model reference. The control architecture is proven to provide boundedness of all closed-loop signals and to asymptotically drive the state tracking error to zero. Numerical simulations illustrate the stability and efficacy of the proposed MMRAC scheme., Comment: 10 pages, 7 figures, IEEE Journal Submission

Consider a sensor network consisting of both anchor and non-anchor nodes. We address the following sensor network localization (SNL) problem: given the physical locations of anchor nodes and relative measurements among all nodes, determine the locations of all non-anchor nodes. The solution to the SNL problem is challenging due to its inherent non-convexity. In this paper, the problem takes on the form of a multi-player non-convex potential game in which canonical duality theory is used to define a complementary dual potential function. After showing the Nash equilibrium (NE) correspondent to the SNL solution, we provide a necessary and sufficient condition for a stationary point to coincide with the NE. An algorithm is proposed to reach the NE and shown to have convergence rate $\mathcal{O}(1/\sqrt{k})$. With the aim of reducing the information exchange within a network, a distributed algorithm for NE seeking is implemented and its global convergence analysis is provided. Extensive simulations show the validity and effectiveness of the proposed approach to solve the SNL problem., Comment: arXiv admin note: text overlap with arXiv:2311.03326

This paper studies formation control of multi-lane platoons of vehicles, endowed with local positioning capabilities, under the influence of noises and inconsistencies of intervehicle relative position measurements. We propose a distributed two-level control framework that consists of a high-level relative position based distributed formation control scheme and low-level individual dynamic controllers of the platoon vehicles. The proposed formation control scheme utilizes deadzone based switching for robustness against sensor noises and adaptive longitudinal controllers for enabling the platoon of heterogeneous vehicles to track the desired platoon velocity.

In this paper, we propose a method to replan coverage paths for a robot operating in an environment with initially unknown static obstacles. Existing coverage approaches reduce coverage time by covering along the minimum number of coverage lines (straight-line paths). However, recomputing such paths online can be computationally expensive resulting in robot stoppages that increase coverage time. A naive alternative is greedy detour replanning, i.e., replanning with minimum deviation from the initial path, which is efficient to compute but may result in unnecessary detours. In this work, we propose an anytime coverage replanning approach named OARP-Replan that performs near-optimal replans to an interrupted coverage path within a given time budget. We do this by solving linear relaxations of mixed-integer linear programs (MILPs) to identify sections of the interrupted path that can be optimally replanned within the time budget. We validate our approach in simulation using maps of real-world environments and compare our approach against a greedy detour replanner and other state-of-the-art approaches., Comment: 14 pages, 15 figures, Paper submitted to T-RO

Sensor network localization (SNL) problems require determining the physical coordinates of all sensors in a network. This process relies on the global coordinates of anchors and the available measurements between non-anchor and anchor nodes. Attributed to the intrinsic non-convexity, obtaining a globally optimal solution to SNL is challenging, as well as implementing corresponding algorithms. In this paper, we formulate a non-convex multi-player potential game for a generic SNL problem to investigate the identification condition of the global Nash equilibrium (NE) therein, where the global NE represents the global solution of SNL. We employ canonical duality theory to transform the non-convex game into a complementary dual problem. Then we develop a conjugation-based algorithm to compute the stationary points of the complementary dual problem. On this basis, we show an identification condition of the global NE: the stationary point of the proposed algorithm satisfies a duality relation. Finally, simulation results are provided to validate the effectiveness of the theoretical results.

In this paper, we tackle the problem of planning an optimal coverage path for a robot operating indoors. Many existing approaches attempt to discourage turns in the path by covering the environment along the least number of coverage lines, i.e., straight-line paths. This is because turning not only slows down the robot but also negatively affects the quality of coverage, e.g., tools like cameras and cleaning attachments commonly have poor performance around turns. The problem of minimizing coverage lines however is typically solved using heuristics that do not guarantee optimality. In this work, we propose a turn-minimizing coverage planning method that computes the optimal number of axis-parallel (horizontal/vertical) coverage lines for the environment in polynomial time. We do this by formulating a linear program (LP) that optimally partitions the environment into axis-parallel ranks (non-intersecting rectangles of width equal to the tool width). We then generate coverage paths for a set of real-world indoor environments and compare the results with state-of-the-art coverage approaches., Comment: 8 pages, 9 figures, submitted to RA-L with IROS 2022 option

Adaptive control strategies usually are designed based on gradient methods for the sake of simplicity in Lyapunov analysis. However, least squares (LS)-based parameter identifiers, with proper selection of design parameters, exhibit better transient performance than the gradient-based ones, from the aspects of convergence speed and robustness to measurement noise. On the other hand, most of the LS-based adaptive control procedures are designed via the indirect adaptive control approaches, due to the difficulty in integrating an LS-based adaptive law within the direct approaches starting with a certain Lyapunov-like cost function to be driven to (a neighborhood of) zero. In this paper, a formal constructive analysis framework is proposed to integrate the recursive LS-based parameter identification with direct adaptive control. To this end, a Lyapunov-like function is proposed for the analysis to achieve adaptive laws, which guarantee the exponential convergence of the parameters. Application of the proposed procedure in adaptive cruise control design is studied through Matlab/Simulink and CarSim simulations, validating the analytical results., Comment: This is the second version of the arXiv:2007.08578 in Arxiv and it is submitted to IEEE CDC 2022. 8 pages, 3 figures

Extremum seeking (ES) optimization approach has been very popular due to its non-model based analysis and implementation. This approach has been mostly used with gradient based search algorithms. Since least squares (LS) algorithms are typically observed to be superior, in terms of convergence speed and robustness to measurement noises, over gradient algorithms, it is expected that LS based ES schemes will also provide faster convergence and robustness to sensor noises. In this paper, with this motivation, a recursive least squares (RLS) estimation based ES scheme is designed and analysed for application to scalar parameter and vector parameter static map and dynamic systems. Asymptotic convergence to the extremum is established for all the cases. Simulation studies are provided to validate the performance of proposed scheme., Comment: 6 pages, 8 figures, will be submitted to L-CSS with CDC Option 2020

A novel cyber physical method is proposed and experimentally verified for reliable distributed estimation of vehicle longitudinal velocity, robustly to road friction condition variations. In this method, the vehicle speed estimated at each of the four corners of the vehicle, using a linear parameter-varying observer in the physical layer, and speed data measured by a conventional low-cost GPS are incorporated in a distributed structure (in the cyber layer) to enhance the reliability of the estimate. The method minimizes a cost function quantizing the effect of disturbances on each corner's estimation and adversaries due to occasional GPS signal drops. A fault-tolerant estimation policy is integrated to deal with large deviations in corner estimations, which have unexpectedly high levels of confidence. The main advantages of the proposed method are increased reliability on various road surface conditions and robustness to faults, as confirmed by road tests. Several experimental tests, including lane change and low-excitation maneuvers, with various powertrain configurations on dry and slippery roads demonstrate the efficiency of the algorithm., QC 20191031

We consider trajectories where the sign of the derivative of each entry is opposite to that of the corresponding entry in the gradient of an energy function. We show that this condition guarantees convergence when the energy function is quadratic and positive definite and partly extend that result to some classes of positive semi-definite quadratic functions including those defined using a graph Laplacian. We show how this condition allows establishing the convergence of a platoon application in which it naturally appears, due to deadzones in the control laws designed to avoid instabilities caused by inconsistent measurements of the same distance by different agents

This paper focuses on the problem of estimating bearing vectors between the agents in a two dimensional multi-agent network based on subtended angle measurements, called edge localization problem. We propose an edge localization graph to investigate the solvability of this problem and a distributed estimation method via orientation estimation of virtual agents to solve the problem. Under the proposed method, the estimated bearing vector exponentially converges to the real one with a common bias if and only if the edge localization graph has an oriented spanning tree. Furthermore, the estimated variables exponentially converge to the true values if the edge localization graph has an oriented spanning tree with a root knowing the bearing vector from it to one of its neighbors., Comment: 12 pages, 12 figures, Brief version of a paper named "Distributed Bearing Vector Estimation in Multi-agent Networks" published in Automatica

We consider trajectories where the sign of the derivative of each entry is opposite to that of the corresponding entry in the gradient of an energy function. We show that this condition guarantees convergence when the energy function is quadratic and positive definite and partly extend that result to some classes of positive semi-definite quadratic functions including those defined using a graph Laplacian. We show how this condition allows establishing the convergence of a platoon application in which it naturally appears, due to deadzones in the control laws designed to avoid instabilities caused by inconsistent measurements of the same distance by different agents., Comment: 6 pages, 2 figures, double columns

In this paper, a combined formation acquisition and cooperative extremum seeking control scheme is proposed for a team of three robots moving on a plane. The extremum seeking task is to find the maximizer of an unknown two-dimensional function on the plane. The function represents the signal strength field due to a source located at the maximizer, and is assumed to be locally concave around the maximizer and monotonically decreasing in distance to the source location. Taylor expansions of the field function at the location of a particular lead robot and the maximizer are used together with a gradient estimator based on signal strength measurements of the robots to design and analyze the proposed control scheme. The proposed scheme is proven to exponentially and simultaneously (i) acquire the specified geometric formation and (ii) drive the lead robot to a specified neighbourhood disk around the maximizer, whose radius depends on the specified desired formation size as well as the norm bounds of the Hessian of the field function. The performance of the proposed control scheme is evaluated using a set of simulation experiments.

In this paper, a combined formation acquisition and cooperative extremum seeking control scheme is proposed for a team of three robots moving on a plane. The extremum seeking task is to find the maximizer of an unknown two-dimensional function on the plane. The function represents the signal strength field due to a source located at maximizer, and is assumed to be locally concave around maximizer and monotonically decreasing in distance to the source location. Taylor expansions of the field function at the location of a particular lead robot and the maximizer are used together with a gradient estimator based on signal strength measurements of the robots to design and analyze the proposed control scheme. The proposed scheme is proven to exponentially and simultaneously (i) acquire the specified geometric formation and (ii) drive the lead robot to a specified neighborhood disk around maximizer, whose radius depends on the specified desired formation size as well as the norm bounds of the Hessian of the field function. The performance of the proposed control scheme is evaluated using a set of simulation experiments., Comment: Presented at the 2018 IEEE Conference on Decision and Control (CDC), Miami Beach, FL, USA

We develop a novel localization theory for networks of nodes that measure each other's bearing, i.e.; we assume that nodes do not have the ability to perform measurements expressed in a common reference frame. We begin with some basic definitions of frame localizability and orientation localizability. Based on some key kinematic relationships, we characterize orientation localizability for planar networks with angle-of-arrival sensing. We then address the orientation localization problem in the presence of noisy measurements. Our first algorithm computes a least-squares estimate of the unknown node orientations in a ring network given angle-of-arrival sensing. For arbitrary connected graphs, our second algorithm exploits kinematic relationships among the orientations of nodes in loops in order to reduce the effect of noise. We establish the convergence of the algorithm, and through some simulations we show that the algorithm reduces the mean-square error due to the noisy measurements in a way that is comparable to the amount of noise reduction obtained by the classic least-square estimator. We then consider networks in 3-dimensional space and we explore necessary and sufficient conditions for orientation localizability in the noiseless case., QC 20130205

We develop a novel localization theory for networks of nodes that measure each other's bearing, i.e.; we assume that nodes do not have the ability to perform measurements expressed in a common reference frame. We begin with some basic definitions of frame localizability and orientation localizability. Based on some key kinematic relationships, we characterize orientation localizability for planar networks with angle-of-arrival sensing. We then address the orientation localization problem in the presence of noisy measurements. Our first algorithm computes a least-squares estimate of the unknown node orientations in a ring network given angle-of-arrival sensing. For arbitrary connected graphs, our second algorithm exploits kinematic relationships among the orientations of nodes in loops in order to reduce the effect of noise. We establish the convergence of the algorithm, and through some simulations we show that the algorithm reduces the mean-square error due to the noisy measurements in a way that is comparable to the amount of noise reduction obtained by the classic least-square estimator. We then consider networks in 3-dimensional space and we explore necessary and sufficient conditions for orientation localizability in the noiseless case., QC 20130205

We develop a novel localization theory for networks of nodes that measure each other's bearing, i.e.; we assume that nodes do not have the ability to perform measurements expressed in a common reference frame. We begin with some basic definitions of frame localizability and orientation localizability. Based on some key kinematic relationships, we characterize orientation localizability for planar networks with angle-of-arrival sensing. We then address the orientation localization problem in the presence of noisy measurements. Our first algorithm computes a least-squares estimate of the unknown node orientations in a ring network given angle-of-arrival sensing. For arbitrary connected graphs, our second algorithm exploits kinematic relationships among the orientations of nodes in loops in order to reduce the effect of noise. We establish the convergence of the algorithm, and through some simulations we show that the algorithm reduces the mean-square error due to the noisy measurements in a way that is comparable to the amount of noise reduction obtained by the classic least-square estimator. We then consider networks in 3-dimensional space and we explore necessary and sufficient conditions for orientation localizability in the noiseless case., QC 20130205

We develop a novel localization theory for networks of nodes that measure each other's bearing, i.e.; we assume that nodes do not have the ability to perform measurements expressed in a common reference frame. We begin with some basic definitions of frame localizability and orientation localizability. Based on some key kinematic relationships, we characterize orientation localizability for planar networks with angle-of-arrival sensing. We then address the orientation localization problem in the presence of noisy measurements. Our first algorithm computes a least-squares estimate of the unknown node orientations in a ring network given angle-of-arrival sensing. For arbitrary connected graphs, our second algorithm exploits kinematic relationships among the orientations of nodes in loops in order to reduce the effect of noise. We establish the convergence of the algorithm, and through some simulations we show that the algorithm reduces the mean-square error due to the noisy measurements in a way that is comparable to the amount of noise reduction obtained by the classic least-square estimator. We then consider networks in 3-dimensional space and we explore necessary and sufficient conditions for orientation localizability in the noiseless case.

This paper presents an adaptive scheme for localization of a target from distance measurements and motion control of a mobile agent to pursue this target. The localization and motion control task of interest is approached within a parameter-identifier-based adaptive control framework, where the localization is formulated as a parameter identification problem and the motion control is achieved using an adaptive controller based on the produced location estimates of the target. First, a robust adaptive law is designed to generate location estimate of the target using distance measurements. Then, following the standard certainty equivalence approach, a motion control law is developed considering substitution of the estimate generated by the localization algorithm for the unknown location of the target. Noting that there is some incompatibility between the persistence of excitation requirements of the localization algorithm and the target pursuit goal of the motion control law, the base motion control law is (re)designed to eliminate the effects of this incompatibility. The novelty of this paper is in this motion control design eliminating the persistence of excitation incompatibility. Stability and convergence analysis for the overall adaptive control scheme is presented. The results are valid in both two and three dimensions of motion space. The applications of the adaptive scheme include rescue localization, surveillance of signal sources, and formation acquisition of autonomous multi-robot/vehicle systems.

We develop a novel localization theory for networks of nodes that measure each other's bearing, i.e.; we assume that nodes do not have the ability to perform measurements expressed in a common reference frame. We begin with some basic definitions of frame localizability and orientation localizability. Based on some key kinematic relationships, we characterize orientation localizability for planar networks with angle-of-arrival sensing. We then address the orientation localization problem in the presence of noisy measurements. Our first algorithm computes a least-squares estimate of the unknown node orientations in a ring network given angle-of-arrival sensing. For arbitrary connected graphs, our second algorithm exploits kinematic relationships among the orientations of nodes in loops in order to reduce the effect of noise. We establish the convergence of the algorithm, and through some simulations we show that the algorithm reduces the mean-square error due to the noisy measurements in a way that is comparable to the amount of noise reduction obtained by the classic least-square estimator. We then consider networks in 3-dimensional space and we explore necessary and sufficient conditions for orientation localizability in the noiseless case., QC 20130205

We develop a novel localization theory for networks of nodes that measure each other's bearing, i.e.; we assume that nodes do not have the ability to perform measurements expressed in a common reference frame. We begin with some basic definitions of frame localizability and orientation localizability. Based on some key kinematic relationships, we characterize orientation localizability for planar networks with angle-of-arrival sensing. We then address the orientation localization problem in the presence of noisy measurements. Our first algorithm computes a least-squares estimate of the unknown node orientations in a ring network given angle-of-arrival sensing. For arbitrary connected graphs, our second algorithm exploits kinematic relationships among the orientations of nodes in loops in order to reduce the effect of noise. We establish the convergence of the algorithm, and through some simulations we show that the algorithm reduces the mean-square error due to the noisy measurements in a way that is comparable to the amount of noise reduction obtained by the classic least-square estimator. We then consider networks in 3-dimensional space and we explore necessary and sufficient conditions for orientation localizability in the noiseless case., QC 20130205

Consider an agent A at an unknown location, undergoing sufficiently slow drift, and a mobile agent B that must move to the vicinity of and then circumnavigate A at a prescribed distance from A. In doing so, B can only measure its distance from A, and knows its own position in some reference frame. This paper considers this problem, which has applications to surveillance and orbit maintenance. In many of these applications it is difficult for B to directly sense the location of A, e.g. when all that B can sense is the intensity of a signal emitted by A. This intensity does, however provide a measure of the distance. We propose a nonlinear periodic continuous time control law that achieves the objective using this distance measurement. Fundamentally, a) B must exploit its motion to estimate the location of A, and b) use its best instantaneous estimate of where A resides, to move itself to achieve the circumnavigation objective. For a) we use an open loop algorithm formulated by us in an earlier paper. The key challenge tackled in this paper is to design a control law that closes the loop by marrrying the two goals. As long as the initial estimate of the source location is not coincident with the intial position of B, the algorithm is guaranteed to be exponentially convergent when A is stationary. Under the same condition, we establish that when A drifts with a sufficiently small, unknown velocity, B globally achieves its circumnavigation objective, to within a margin proportional to the drift velocity., QC 20120508

This paper presents an adaptive scheme for localization of a target from distance measurements and motion control of a mobile agent to pursue this target. First, a robust adaptive law is designed to generate location estimate of the target using distance

Consider an agent A at an unknown location, undergoing sufficiently slow drift, and a mobile agent B that must move to the vicinity of and then circumnavigate A at a prescribed distance from A. In doing so, B can only measure its distance from A, and knows its own position in some reference frame. This paper considers this problem, which has applications to surveillance and orbit maintenance. In many of these applications it is difficult for B to directly sense the location of A, e.g. when all that B can sense is the intensity of a signal emitted by A. This intensity does, however provide a measure of the distance. We propose a nonlinear periodic continuous time control law that achieves the objective using this distance measurement. Fundamentally, a) B must exploit its motion to estimate the location of A, and b) use its best instantaneous estimate of where A resides, to move itself to achieve the circumnavigation objective. For a) we use an open loop algorithm formulated by us in an earlier paper. The key challenge tackled in this paper is to design a control law that closes the loop by marrrying the two goals. As long as the initial estimate of the source location is not coincident with the intial position of B, the algorithm is guaranteed to be exponentially convergent when A is stationary. Under the same condition, we establish that when A drifts with a sufficiently small, unknown velocity, B globally achieves its circumnavigation objective, to within a margin proportional to the drift velocity.

This thesis develops a new nonlinear robust control design procedure which addresses some of the challenges associated with the control of uncertain nonlinear system and applies the proposed method to tracking control of an Air-breathing Hypersonic Flight Vehicle (AHFV). The AHFV is a highly nonlinear system and the combination of nonlinear dynamics, parameter uncertainty and complex constraints make the flight control design a challenging task for this type of vehicle. The main contribution of this thesis lies in the fact that it presents a robust feedback linerization based strategy which solves the control issue of a class of nonlinear systems subject to parametric uncertainty. The method is effectively applied to the tracking control of an AHFV. It is also demonstrated that the proposed approach can be used to design a single robust controller for a large flight envelope rather than using several gain scheduled controllers. This research, firstly presents three different approaches to develop linearized uncertainty models for a class of nonlinear systems using a robust feedback lnearization method. The feedback linearization approach to linearize the nonlinear dynamics has some advantages over the point linearization (Jacobian linearization) method. However, the feedback linearization method only linearizes the nominal model of a system and in the presence of uncertainty in the model the exact linearization is not possible. In this thesis, we present a robust approach to deal with the nonlinearities arising from the uncertainties in the system and use a nonlinear AHFV model to demonstrate the effectiveness of the method. Besides parametric uncertainty, due to the presence of body-integrated propulsion system, and the flexible modes, the nonlinear model of AHFV does not possess full relative degree. Any attempt to feedback linearize this nonlinear model will result into having input term in low order derivatives of the system output. In this research, we strategi

This paper considers the problem of localizing multiple agents, e.g. unmanned aerial vehicles (UAVs), robots, etc., moving in two-dimensional space when the known data comprise 1) the inter-agent distances, and 2) the angle subtended at each agent by lines drawn from two landmarks at known positions. Later it is shown that this result has direct application in a different general robotic problem, viz. robot-to-robot relative pose determination (relative reference frame determination), using measured distances. The methods proposed are validated through simulations and experiments.

This chapter reviews a series of results obtained in the field of localization that are based on polynomial optimization. First, it provides a review of a set of polynomial function optimization tools, including sum of squares (SOS). Then the chapter presents several applications of these tools in various sensor network localization tasks. As the first application, it proposes a method based on SOS relaxation for node localization using noisy measurements and describes the solution through semidefinite programming (SDP). Later, the chapter applies this method to address the problems of target localization in the presence of noise and relative reference frame determination based on range and bearing measurements. Finally, it provides some simulation and experiment results to show the applicability of the methods.

In this paper, a dynamic antiwindup compensator design is proposed which augments the main controller and guarantees robust performance in the event of input saturation. This is a two stage process in which first a robust optimal controller is designed for an uncertain linear system which guarantees the internal stability of the closed loop system and provides robust performance in the absence of input saturation. Then a minimax linear quadratic Gaussian (LQG) compensator is designed to guarantee the performance in certain domain of attraction, in the presence of input saturation. This antiwindup augmentation only comes into action when plant is subject to input saturation. In order to illustrate the effectiveness of this approach, the proposed method is applied to a tracking control problem for an air-breathing hypersonic flight vehicle (AHFV)., Comment: Australian control conference paper, 7 pages

The problem of target localization involves estimating the position of a target from multiple noisy sensor measurements. It is well known that the relative sensor-target geometry can significantly affect the performance of any particular localization algorithm. The localization performance can be explicitly characterized by certain measures, for example, by the Cramer-Rao lower bound (which is equal to the inverse Fisher information matrix) on the estimator variance. In addition, the Cramer-Rao lower bound is commonly used to generate a so-called uncertainty ellipse which characterizes the spatial variance distribution of an efficient estimate, i.e. an estimate which achieves the lower bound. The aim of this work is to identify those relative sensor-target geometries which result in a measure of the uncertainty ellipse being minimized. Deeming such sensor-target geometries to be optimal with respect to the chosen measure, the optimal sensor-target geometries for range-only, time-of-arrival-based and bearing-only localization are identified and studied in this work. The optimal geometries for an arbitrary number of sensors are identified and it is shown that an optimal sensor-target configuration is not, in general, unique. The importance of understanding the influence of the sensor-target geometry on the potential localization performance is highlighted via formal analytical results and a number of illustrative examples., QC 20110112

Graph theory has been used to characterize t he solvability of the sensor network localization problem. If sensors correspond to vertices and edges correspond to sensor pairs between which the distance is known, a significant result in the theory of range-based sensor network localization is that if the graph underlying the sensor network is generically globally rigid and there is a suitable set of anchors at known positions, then the network can be localized, i.e., a unique set of sensor positions can be determined that is consistent with the data. In particular, for planar problems, provided the sensor network has three or more noncollinear anchors at known points, all sensors are located at generic points, and the intersensor distances corresponding to the graph edges are precisely known rather than being subject to measurement noise, generic global rigidity of the graph is necessary and sufficient for the network to be localizable (in the absence of any further information). In practice, however, distance measurements will never be exact, and the equations whose solutions deliver sensor positions in the noiseless case in general no longer have a solution. This paper then argues that if the distance measurement errors are not too great and otherwise the associated graph is generically globally rigid and there are three or more noncollinear anchors, the network will be approximately localizable, in the sense that estimates can be found for the sensor positions which are near the correct values; in particular, a bound on the position errors can be found in terms of a bound on the distance errors. The sensor positions in this case can be found by minimizing a cost function which, although nonconvex, does have a global minimum.

This manuscript considers the problem of close target reconnaissance by a group of autonomous agents. The overall close target reconnaissance (CTR) involves subtasks of avoiding inter-agent collisions, reaching a close vicinity of a specific target position, and forming an equilateral polygon formation around the target. The agents performing the task fly at a constant speed to mimic the velocity behavior of small fixed-wing unmanned aerial vehicles (UAV). A decentralized control scheme is developed for this overall task and the finite-time convergence of the system under the proposed control law is established. Furthermore, it is guaranteed that no collision occurs among the agent. The relevant analysis and simulation test results are provided.

This paper proposes a systematic approach to solve the closing rank problem for a rigid multi-agent formation, viz. restoring rigidity after loss of an agent. The approach is based on a particular graph operation, the edge contraction operation. It is proven that when an agent is lost in an arbitrary two-dimensional rigid formation, rigidity can always be restored by transferring all links to which this agent was incident on to one of its neighbors, though not in general any arbitrary one of them. From a graph theoretical point of view, this corresponds to contraction of a certain edge incident to the vertex representing the agent being lost. It is established, for any two-dimensional rigid formation (graph), that there exists at least two such edges that can be contracted to solve the closing ranks problem. Later, it is demonstrated that any potential decentralized algorithm to check if an arbitrary edge is contractible would need to use information on vertices and edges that can be at arbitrarily large distance from the edge considered; and a set of rigid graph theoretical results are established for several general settings, which can be used in selection of the edge to contract in these settings in order to solve the corresponding closing ranks problems. Partial results are also obtained for three-dimensional formations, and it is shown that the two-dimensional results do not generalize as such to higher dimension.

The problem of target localization involves estimating the position of a target from multiple noisy sensor measurements. It is well known that the relative sensor-target geometry can significantly affect the performance of any particular localization algorithm. The localization performance can be explicitly characterized by certain measures, for example, by the Cramer-Rao lower bound (which is equal to the inverse Fisher information matrix) on the estimator variance. In addition, the Cramer-Rao lower bound is commonly used to generate a so-called uncertainty ellipse which characterizes the spatial variance distribution of an efficient estimate, i.e. an estimate which achieves the lower bound. The aim of this work is to identify those relative sensor-target geometries which result in a measure of the uncertainty ellipse being minimized. Deeming such sensor-target geometries to be optimal with respect to the chosen measure, the optimal sensor-target geometries for range-only, time-of-arrival-based and bearing-only localization are identified and studied in this work. The optimal geometries for an arbitrary number of sensors are identified and it is shown that an optimal sensor-target configuration is not, in general, unique. The importance of understanding the influence of the sensor-target geometry on the potential localization performance is highlighted via formal analytical results and a number of illustrative examples.

Erroneous local geometric realizations in some parts of the network due to their sensitivity to certain distance measurement errors is a major problem in wireless sensor network localization. This may in turn affect the localization of either the entire network or a large portion of it. This phenomenon is well-described using the notion of "flip ambiguity" in rigid graph theory. In this paper we analytically derive an expression for the flip ambiguity probabilities of arbitrary neighborhoods in two dimensional sensor networks. This probability can be used to mitigate flip ambiguities in two ways: 1) If an unknown sensor finds the probability of flip ambiguity on its location estimate larger than a predefined threshold, it may choose not to localize itself 2) Every known neighbor can be assigned with a confidence factor to its estimated location, reflecting the probability of flip ambiguity; a sensor with an initially unknown location can then choose only those known neighbors with a confidence factor greater than a predefined threshold. A recent study by co-authors have shown that the performance of sequential and cluster based localization schemes in the literature can be significantly improved by correctly identifying and removing neighborhoods with possible flip ambiguities from the localization process. One motivation of this paper is to enhance the performance of the robustness criterion presented in that study by accurately identifying the flip ambiguity probabilities of arbitrary neighborhoods. The various simulations done in this study show that our analytical calculations of the probability of flip ambiguity matches with the simulated detection of the probability very accurately.

In passive target localization using direction finding (DF), there are particular sensor-target placements that cause large biases in the estimates or the failure of estimates to converge to a unique solution. Identification of such problematic configurations is crucial for implementing estimation and tracking algorithms effectively. In this paper we propose four methods for characterizing near-collinearity problems in a sensor-target configuration which enable one to quickly and easily identify cases in which DF-based localization will fail to obtain a solution or give unreliable results.

In this paper we report some new results obtained in the field of multi-agent systems that are based on convex optimization. First, we provide review of a set of polynomial function optimization tools including sum of squares (SOS) and semidefinite programming (SDP). Then we present several applications of these tools in various multiagent system localization and synchronization tasks. As the first application, we propose a method based on SOS relaxation for agent localization using noisy measurements and describe the solution through SDP. Later, we apply this method to address the problems of cooperative target localization in the presence of noise and robot pose determination based on range measurements. Then we introduce the problem of anchor selection for minimizing the effect of noise in sensor networks via SDP. We use the same machinery to propose a method based on SDP to enhance synchronizability in networks. We do so by proposing a distributed algorithm for adding new edges to the network to enhance synchronizability. Finally, we present a method to identify the node in a network loss of which inflicts the most damage on the synchronizability of the network. Conclusions are presented in the last section.

This paper considers the problem of reduction of self-localization errors in multi-agent autonomous formations when only distance measurements are available to the agents in a globally rigid formation. It is shown that there is a relationship between different selections of anchors, agents with exactly known positions, and the error induced by measurement error on localization solution. This fact is exploited to develop a mechanism to select anchors in order to minimize the effects of inter-agent distance measurement errors on localization solution. Finally, some simulation results are presented to demonstrate the optimal anchor selection for a particular general class of formations, the globally rigid formations.

This paper studies the problem of controlling the shape of a formation of point agents in the plane. A model is considered where the distance between certain agent pairs is maintained by one of the agents making up the pair; if enough appropriately chosen distances are maintained, with the number growing linearly with the number of agents, then the shape of the formation will be maintained. The detailed question examined in the paper is how one may construct decentralized nonlinear control laws to be operated at each agent that will restore the shape of the formation in the presence of small distortions from the nominal shape. Using the theory of rigid and persistent graphs, the question is answered. As it turns out, a certain submatrix of a matrix known as the rigidity matrix can be proved to have nonzero leading principal minors, which allows the determination of a stabilizing control law.

We examine the problem of optimal bearing-only localization of a single target using synchronous measurements from multiple sensors. We approach the problem by forming geometric relationships between the measured parameters and their corresponding errors

The problem of source localization has assumed increased importance in recent years. In this paper, we formulate a continuous time adaptive localization algorithm, that permits a mobile agent to estimate the location of a stationary source, using only the measured distance from the source. The algorithm is shown to be exponentially asymptotically stable, under a persistent excitation condition that has an appealing interpretation. We quantify the fact that exponential asymptotic stability endows the algorithm with the ability to track slow, bounded but potentially persistent and nontrivial drift in the source.

In this paper we propose a method for enhancing synchronizability using convex optimization. This method is based on adding new edges to the network, later the performance of the proposed method is tested through providing some numerical examples. Furthermore, a comparison with another method for adding edges, namely edge addition using an eigenvector criterion is presented. Moreover, the extension of the proposed method to the networks with different edge weights is described.

This paper is concerned with obstacle avoidance of robots moving on a plane, based on a fluid mechanical principle known as the Circle Theorem. Considering the motion region as a fictitious fluid environment surrounding the obstacles, fluid streamlines are calculated which correspond to unique smooth paths that a mobile robot can follow without colliding with the obstacles. The design and analysis are initially performed assuming simple integrator dynamics for the agent, and later extended for more realistic non-holonomic unicycle dynamic agent models, with the help of proportional integral (PI) control and backstepping principles. Both point and non-point (ellipse) geometric models are considered for the agents in design and analysis. The fluid dynamics based designs developed for obstacle avoiding motion control of agents with non-holonomic unicycle dynamics are novel, and successfully tested via an extensive set of simulations. Application of the developed designs for motion control of unmanned aerial vehicles (UAVs) under the constraint of constant speed is also presented.