Bearing Rigidity and Almost Global Bearing-Only Formation Stabilization

A fundamental problem that the bearing rigidity theory studies is to determine when a framework can be uniquely determined up to a translation and a scaling factor by its inter-neighbor bearings. While many previous works focused on the bearing rigidity of two-dimensional frameworks, a first contribution of this paper is to extend these results to arbitrary dimensions. It is shown that a framework in an arbitrary dimension can be uniquely determined up to a translation and a scaling factor by the bearings if and only if the framework is infinitesimally bearing rigid. In this paper, the proposed bearing rigidity theory is further applied to the bearing-only formation stabilization problem where the target formation is defined by inter-neighbor bearings and the feedback control uses only bearing measurements. Nonlinear distributed bearing-only formation control laws are proposed for the cases with and without a global orientation. It is proved that the control laws can almost globally stabilize infinitesimally bearing rigid formations. Numerical simulations are provided to support the analysis

Angle rigidity and its usage to stabilize multi-agent formations in 2D

Motivated by the challenging formation stabilization problem for mobile robotic teams wherein no distance or relative position measurements are available but each robot can only measure some of relative angles with respect to its neighbors in its local coordinate frame, we develop the notion of "angle rigidity" for a multi-point framework, named "angularity", consisting of a set of nodes embedded in a Euclidean space and a set of angle constraints among them. Different from bearings or angles defined in a global frame, the angles we use do not rely on the knowledge of a global frame and are signed according to the counter-clockwise direction. Here angle rigidity refers to the property specifying that under proper angle constraints, the angularity can only translate, rotate or scale as a whole when one or more of its nodes are perturbed locally. We first demonstrate that this angle rigidity property, in sharp comparison to bearing rigidity or other reported rigidity related to angles of frameworks in the literature, is not a global property since an angle rigid angularity may allow flex ambiguity. We then construct necessary and sufficient condit

The black hole in IC 1459 from HST observations of the ionized gas disk

The peculiar elliptical galaxy IC 1459 (M_V = -21.19, D = 16.5 Mpc) has a fast counterrotating stellar core, stellar shells and ripples, a blue nuclear point source and strong radio core emission. We present results of a detailed HST study of IC 1459, and in particular its central gas disk, aimed a constraining the central mass distribution. We obtained WFPC2 narrow-band imaging centered on the Halpha+[NII] emission lines to determine the flux distribution of the gas emission at small radii, and we obtained FOS spectra at six aperture positions along the major axis to sample the gas kinematics. We construct different dynamical models for the Halpha+[NII] and Hbeta kinematics that include a supermassive black hole, and in which the stellar mass distribution is constrained by the observed surface brightness distribution and ground-based stellar kinematics. All models are consistent with a black hole mass in the range Mbh=1-4 x 10^8 Msun, and models without a black hole are always ruled out at high confidence.Comment: 40 pages including 14 figures, Latex; submitted to A

Controlling a triangular flexible formation of autonomous agents

In formation control, triangular formations consisting of three autonomous agents serve as a class of benchmarks that can be used to test and compare the performances of different controllers. We present an algorithm that combines the advantages of both position- and distance-based gradient descent control laws. For example, only two pairs of neighboring agents need to be controlled, agents can work in their own local frame of coordinates and the orientation of the formation with respect to a global frame of coordinates is not prescribed. We first present a novel technique based on adding artificial biases to neighboring agents' range sensors such that their eventual positions correspond to a collinear configuration. Right after, a small modification in the bias terms by introducing a prescribed rotation matrix will allow the control of the bearing of the neighboring agents.Comment: 7 pages, accepted in the 20th World Congress of the International Federation of Automatic Control (IFAC

Line Emission from an Accretion Disk around a Black hole: Effects of Disk Structure

The observed iron K-alpha fluorescence lines in Seyfert-1 galaxies provide strong evidence for an accretion disk near a supermassive black hole as a source of the line emission. These lines serve as powerful probes for examining the structure of inner regions of accretion disks. Previous studies of line emission have considered geometrically thin disks only, where the gas moves along geodesics in the equatorial plane of a black hole. Here we extend this work to consider effects on line profiles from finite disk thickness, radial accretion flow and turbulence. We adopt the Novikov and Thorne (1973) solution, and find that within this framework, turbulent broadening is the dominant new effect. The most prominent change in the skewed, double-horned line profiles is a substantial reduction in the maximum flux at both red and blue peaks. The effect is most pronounced when the inclination angle is large, and when the accretion rate is high. Thus, the effects discussed here may be important for future detailed modeling of high quality observational data.Comment: 21 pages including 8 figures; LaTeX; ApJ format; accepted by ApJ; short results of this paper appeared before as a conference proceedings (astro-ph/9711214

Bearing rigidity theory and its applications for control and estimation of network systems: Life beyond distance rigidity

Distributed control and location estimation of multiagent systems have received tremendous research attention in recent years because of their potential across many application domains [1], [2]. The term agent can represent a sensor, autonomous vehicle, or any general dynamical system. Multiagent systems are attractive because of their robustness against system failure, ability to adapt to dynamic and uncertain environments, and economic advantages compared to the implementation of more expensive monolithic systems