Baris Fidan

Wireless sensor network localization techniques

Wireless sensor network localization is an important area that attracted significant research interest. This interest is expected to grow further with the proliferation of wireless sensor network applications. This paper provides an overview of the measurement techniques in sensor network localization and the one-hop localization algorithms based on these measurements. A detailed investigation on multi-hop connectivity-based and distance-based localization algorithms are presented. A list of open research problems in the area of distance-based sensor network localization is provided with discussion on possible approaches to them.

Rigid graph control architectures for autonomous formations

This article sets out the rudiments of a theory for analyzing and creating architectures appropriate to the control of formations of autonomous vehicles. The theory rests on ideas of rigid graph theory, some but not all of which are old. The theory, however, has some gaps in it, and their elimination would help in applications. Some of the gaps in the relevant graph theory are as follows. First, there is as yet no analogue for three-dimensional graphs of Lamans theorem, which provides a combinatorial criterion for rigidity in two-dimensional graphs. Second, for three-dimensional graphs there is no analogue of the two-dimensional Henneberg construction for growing or deconstructing minimally rigid graphs although there are conjectures. Third, global rigidity can easily be characterized for two-dimensional graphs, but not for three-dimensional graphs.

Optimality analysis of sensor-target localization geometries

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.

Path loss exponent estimation for wireless sensor network localization

The wireless received signal strength (RSS) based localization techniques have attracted significant research interest for their simplicity. The RSS based localization techniques can be divided into two categories: the distance estimation based and the RSS profiling based techniques. The path loss exponent (PLE) is a key parameter in the distance estimation based localization algorithms, where distance is estimated from the RSS. The PLE measures the rate at which the RSS decreases with distance, and its value depends on the specific propagation environment. Existing techniques on PLE estimation rely on both RSS measurements and distance measurements in the same environment to calibrate the PLE. However, distance measurements can be difficult and expensive to obtain in some environments. In this paper we propose several techniques for online calibration of the PLE in wireless sensor networks without relying on distance measurements. We demonstrate that it is possible to estimate the PLE using only power measurements and the geometric constraints associated with planarity in a wireless sensor network. This may have a significant impact on distance-based wireless sensor network localization.

Flight Dynamics and Control of Air-Breathing Hypersonic Vehicles: Review and New Directions

The current air-breathing hypersonic flight (AHF) technology programs focus on development of flight test vehicles and operational vehicle prototypes that utilize airframe-integrated scramjet engines. A key issue in making AHF feasible and efficient is the control design. The non-standard dynamic characteristics of air-breathing hypersonic flight vehicles (AHFVs) together with the aerodynamic effects of hypersonic flight make the system modeling and controller design highly challenging. Moreover the wide range of speed during operation and the lack of a broad flight dynamics database add significant plant parameter variations and uncertainties to the AHF modeling and control problem. In this paper, first, different approaches to this challenging problem presented in the literature are reviewed. Basic dynamic characteristics of AHFVs are described and various mathematical models developed for the flight dynamics of AHFVs are presented. Major nonlinearity and uncertainty sources in the AHF dynamics are explained. The theoretical and practical AHF control designs in the literature, including the control schemes in use at NASA research centers, are examined and compared. The review is supported by a brief history of the scramjet and AHF research in order to give a perspective of the AHF technology. Next, the existing gaps in AHF control and the emerging trends in the air-breathing hypersonic transportation are discussed. Potential control design directions to fill these gaps and meet the trends are addressed. The major problem in AHF control is the handling of the various coupling effects, nonlinearities, uncertainties, and plant parameter variations. As a potential solution, the use of integrated robust (adaptive) nonlinear controllers based on time varying decentralized/triangular models is proposed. This specific approach is motivated by the promise of novel techniques in control theory developed in recent years. ∗This work was supported in parts by Air Force Office of Scientific Research under Grant #F49620-01-1-0489 and by NASA under grant URC Grant #NCC4-158. †Student Member AIAA, graduate student, Electrical Engineering Department. ‡Member AIAA, professor, Mechanical Engineering Department. §Professor, Electrical Engineering Department Nomenclature The following notation is used throughout the paper, unless otherwise stated. a∞ : free stream velocity of sound ĀD : diffuser exit/inlet (area) ratio c : reference length CD : drag coefficient CL : lift coefficient Cm : pitching moment coefficient (pmc) Cm(q) : pmc due to pitch rate Cm(α) : pmc angle of attack Cmα : ∂Cm/∂α Cm(δe): pmc due to δe CT : thrust coefficient fs : stoichiometric ratio for hydrogen, 0.029 h : vehicle altitude I (In) : the (n× n) identity matrix Iyy : vehicle y-axis inertia per unit width m : vehicle mass m : vehicle mass per unit width ṁair : air mass flow rate ṁf : fuel mass flow rate M : pitching moment M∞ : vehicle flight Mach Number nx : acceleration along the vehicle x-axis nz : acceleration along the vehicle z-axis P : pressure q : pitch rate Q : generalized elastic force re : radial distance from Earth’s center Re : radius of the Earth, 20,903,500 ft S : reference area T0 : temperature across the combustor Th : thrust u : speed along the vehicle x-axis V : vehicle velocity X : force along the vehicle x-axis Z : force along the vehicle z-axis α : angle of attack γ : flight path angle (γ = θ − α) δe : pitch control surface deflection δt : throttle setting ∆τ1 : fore-body elastic mode shape ∆τ2 : after-body elastic mode shape ζ1 : damping ratio of the first vibration mode η : generalized elastic coordinate 1 American Institute of Aeronautics and Astronautics 12th AIAA International Space Planes and Hypersonic Systems and Technologies 15 19 December 2003, Norfolk, Virginia AIAA 2003-7081 Copyright

Control of Minimally Persistent Formations in the Plane

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.

Three and higher dimensional autonomous formations: Rigidity, persistence and structural persistence

In this paper, we generalize the notion of persistence, which has been originally introduced for two-dimensional formations, to R^d for d>=3, seeking to provide a theoretical framework for real world applications, which often are in three-dimensional space as opposed to the plane. Persistence captures the desirable property that a formation moves as a cohesive whole when certain agents maintain their distances from certain other agents. We verify that many of the properties of rigid and/or persistent formations established in R^2 are also valid for higher dimensions. Analysing the closed subgraphs and directed paths in persistent graphs, we derive some further properties of persistent formations. We also provide an easily checkable necessary condition for persistence. We then turn our attention to consider some practical issues raised in multi-agent formation control in three-dimensional space. We display a new phenomenon, not present in R^2, whereby subsets of agents can behave in a problematic way. When this behaviour is precluded, we say that the graph depicting the multi-agent formation has structural persistence. In real deployment of controlled multi-agent systems, formations with underlying structurally persistent graphs are of interest. We analyse the characteristics of structurally persistent graphs and provide a streamlined test for structural persistence. We study the connections between the allocation of degrees of freedom (DOFs) across agents and the characteristics of persistence and/or structural persistence of a directed graph. We also show how to transfer DOFs among agents, when the formation changes with new agent(s) added, to preserve persistence and/or structural persistence.

Coordination and control of multi-agent dynamic systems: models and approaches

The field of multi-agent dynamic systems is an inter-disciplinary research field that has become very popular in the recent years in parallel with the significant interest in the practical applications of such systems in various areas including robotics. In this article we give a relatively short review of this field from the system dynamics and control perspective. We first focus on mathematical modelling of multi-agent systems paying particular attention on the agent dynamics models available in the literature. Then we present a number of problems on coordination and control of multi-agent systems which have gained significant attention recently and various approaches to these problems. Relevant to these problems and approaches, we summarize some of the recent results on stability, robustness, and performance of multi-agent dynamic systems which appeared in the literature. The article is concluded with some remarks on the implementation and application side of the control designs developed for multi-agent systems.

Backstepping control of linear time-varying systems with known and unknown parameters

The backstepping control design procedure has been used to develop stabilizing controllers for time invariant plants that are linear or belong to some class of nonlinear systems. The use of such a procedure to design stabilizing controllers for plants with time varying parameters has been an open problem. In this paper we consider the backstepping design procedure for linear time varying (LTV) plants with known and unknown parameters. We first show that a backstepping controller can be designed for an LTV plant by following the same steps as in the linear time-invariant (LTI) case and treating the plant parameters as constants at each time t. Its stability properties however cannot be established by using the same Lyapunov function and techniques as in the LTI case. We then introduce a new parametrization and filter structure that takes into account the plant parameter variations leading to a new backstepping controller. The new control design guarantees exponential convergence of the tracking error to zero if the plant parameters are exactly known. If the parameters are not precisely known but the time variations of the parameters associated with the system zeros are known, the appropriate choice of certain design parameters, without using any adaptive law, leads to closed-loop stability and perfect regulation. This new control design is modified and supplemented with an update law to be applicable to LTV plants with unknown parameters. In the adaptive control design, the notion of structured parameter variations is used in order to include possible a priori information about the plant parameter variations. With this formulation, only the unstructured plant parameters are estimated and are required to be slowly time varying, and the structured plant parameters are allowed to have any finite speed of variation. The adaptive controller is shown to be robust with respect to the unknown but slow parameter variations in the global sense. We derive performance bounds which can be used to select certain design parameters for performance improvement. The properties of the proposed control scheme are demonstrated using simulation results.

Circumnavigation Using Distance Measurements Under Slow Drift

Consider an agent A at an unknown location, under going 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 circum navigation 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.