This paper describes decentralized control laws for the coordination of multiple vehicles performing spatially distributed tasks. The control laws are based on a gradient descent scheme applied to a class of decentralized utility functions that encode optimal coverage and sensing policies. These utility functions are studied in geographical optimization problems and they arise naturally in vector quantization and in sensor allocation tasks. The approach exploits the computational geometry of spatial structures such as Voronoi diagrams.

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Coverage control for mobile sensing networks

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

We consider the problem of choosing a set of k sensor measurements, from a set of m possible or potential sensor measurements, that minimizes the error in estimating some parameters. Solving this problem by evaluating the performance for each of the (m k) possible choices of sensor measurements is not practical unless m and k are small. In this paper, we describe a heuristic, based on convex optimization, for approximately solving this problem. Our heuristic gives a subset selection as well as a bound on the best performance that can be achieved by any selection of k sensor measurements. There is no guarantee that the gap between the performance of the chosen subset and the performance bound is always small; but numerical experiments suggest that the gap is small in many cases. Our heuristic method requires on the order of m 3 operations; for m= 1000 possible sensors, we can carry out sensor selection in a few seconds on a 2-GHz personal computer.

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Sensor Selection via Convex Optimization

Fault detection, isolation, and reconfiguration (FDIR) is an important and challenging problem in many engineering applications and continues to be an active area of research in the control community. This paper presents a survey of the various model-based FDIR methods developed in the last decade. In the paper, the FDIR problem is divided into the fault detection and isolation (FDI) step, and the controller reconfiguration step. For FDI, we discuss various model-based techniques to generate residuals that are robust to noise, unknown disturbance, and model uncertainties, as well as various statistical techniques of testing the residuals for abrupt changes (or faults). We then discuss various techniques of implementing reconfigurable control strategy in response to faults.

A Survey of Fault Detection, Isolation, and Reconfiguration Methods

This paper provides a survey of modern nonlinear filtering methods for attitude estimation. Early applications relied mostly on the extended Kalman filter for attitude estimation. Since these applications, several new approaches have been developed that have proven to be superior to the extended Kalman filter. Several of these approaches maintain the basic structure of the extended Kalman filter, but employ various modifications in order to provide better convergence or improve other performance characteristics. Examples of such approaches include: filter QUEST, extended QUEST and the backwards-smoothing extended Kalman filter. Filters that propagate and update a discrete set of sigma points rather than using linearized equations for the mean and covariance are also reviewed. A twostep approach is discussed with a first-step state that linearizes the measurement model and an iterative second step to recover the desired attitude states. These approaches are all based on the Gaussian assumption that the probability density function is adequately specified by its mean and covariance. Other approaches that do not require this assumption are reviewed, Associate Professor, Department of Mechanical & Aerospace Engineering. Email: johnc@eng.buffalo.edu. Associate Fellow AIAA. Aerospace Engineer, Guidance, Navigation and Control Systems Engineering Branch. Email: Landis.Markley@nasa.gov. Fellow AIAA. Postdoctoral Research Fellow, Department of Mechanical & Aerospace Engineering. Email: cheng3@eng.buffalo.edu. Member AIAA.

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Survey of nonlinear attitude estimation methods

The problem of bearings-only target localization is to estimate the location of a fixed target from a sequence of noisy bearing measurements. Although, in theory, this process is observable even without an observer maneuver, estimation performance (i.e., accuracy, stability and convergence rate) can be greatly enhanced by properly exploiting observer motion to increase observability. This work addresses the optimization of observer trajectories for bearings-only fixed-target localization. The approach presented herein is based on maximizing the determinant of the Fisher information matrix (FIM), subject to state constraints imposed on the observer trajectory (e.g., by the target defense system). Direct optimal control numerical schemes, including the recently introduced differential inclusion (DI) method, are used to solve the resulting optimal control problem. Computer simulations, utilizing the familiar Stansfield and maximum likelihood (ML) estimators, demonstrate the enhancement to target position estimability using the optimal observer trajectories.

Optimization of observer trajectories for bearings-only target localization

This paper presents a novel Kalman filter (KF) for estimating the attitude-quaternion as well as gyro random drifts from vector measurements. Employing a special manipulation on the measurement equation results in a linear pseudo-measurement equation whose error is state-dependent. Because the quaternion kinematics equation is linear, the combination of the two yields a linear KF that eliminates the usual linearization procedure and is less sensitive to initial estimation errors. General accurate expressions for the covariance matrices of the system state-dependent noises are developed. In addition, an analysis shows how to compute these covariance matrices efficiently. An adaptive version of the filter is also developed to handle modeling errors of the dynamic system noise statistics. Monte-Carlo simulations are carried out that demonstrate the efficiency of both versions of the filter. In the particular case of high initial estimation errors, a typical extended Kalman filter (EKF) fails to converge whereas the proposed filter succeeds.

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Novel quaternion Kalman filter

Two recursive estimation algorithms, which use pairs of measured vectors to yield minimum variance estimates of the quaternion of rotation, are presented. The nonlinear relations between the direction cosine matrix and the quaternion are linearized, and a variant of the extended Kalman filter is used to estimate the difference between the quaternion and its estimate. With each measurement this estimate is updated and added to the whole quaternion estimate. This operation constitutes a full state reset in the estimation process. Filter tuning is needed to obtain a converging filter. The second algorithm presented uses the normality property of the quaternion of rotation to obtain, in a straightforward design, a filter which converges, with a smaller error, to a normal quaternion. This algorithm changes the state but not the covariance computation of the original algorithm and implies only a partial reset. Results of Monte-Carlo simulation runs are presented which demonstrate the superiority of the normalized quaternion.

Attitude Determination from Vector Observations: Quaternion Estimation

A novel sensor selection strategy is introduced, which can be implemented on-line in time-varying discrete-time system. We consider a case in which several measurement subsystem are available, each of which may be used to drive a state estimation algorithm. However, due to practical implementation constraints (such as the ability of the on-board computer to process the acquired data), only one of these subsystems can actually by utilized at a measurement update. An algorithm is needed, by which the optimal measurement subsystem to be used is selected at each sensor selection epoch. The approach described is based on using the square root V-Lambda information filter as the underlying state estimation algorithm. This algorithm continuously provides its user with the spectral factors of the estimation error covariance matrix, which are used in this work as the basis for an on-line decision procedure by which the optimal measurement strategy is derived. At each sensor selection epoch, a measurement subsystem is selected, which contributes the largest amount of information along the principal state space direction associated with the largest current estimation error. A numerical example is presented, which demonstrates the performance of the new algorithm. The state estimation problem is solved for a third-order time-varying system equipped with three measurement subsystem, only one of which can be used at a measurement update. It is shown that the optimal measurement strategy algorithm enhances the estimator by substantially reducing the maximal estimation error. >

Optimal sensor selection strategy for discrete-time state estimators

REQUEST is a recursive algorithm for least-squares estimation of the attitude quaternion of a rigid body using vector measurements. It uses a constant, empirically chosen gain and is, therefore, suboptimal when filtering propagation noises. The algorithm presented here is an optimized REQUEST procedure, which optimally filters measurement as well as propagation noises. The special case of zero-mean white noises is considered. The solution approach is based on state-space modeling of the K-matrix system and uses Kalman-filtering techniques to estimate the optimal K matrix. Then, the attitude quaternion is extracted from the estimated K matrix. A simulation study is used to demonstrate the performance of the algorithm.

Yaakov Oshman

Papers

Optimization of observer trajectories for bearings-only target localization

Novel quaternion Kalman filter

Attitude Determination from Vector Observations: Quaternion Estimation

Optimal sensor selection strategy for discrete-time state estimators

Optimal-REQUEST Algorithm for Attitude Determination