A Modified Dubins Method for Optimal Path Planning of a Miniature Air Vehicle Converging to a Straight Line Path

This paper presents a Dubins model based strategy to determine the optimal path of a Miniature Air Vehicle (MAV), constrained by a bounded turning rate, that would enable it to fly along a given straight line, starting from an arbitrary initial position and orientation. The method is then extended to meet the same objective in the presence of wind which has a magnitude comparable to the speed of the MAV. We use a modification of the Dubins' path method to obtain the complete optimal solution to this problem in all its generality.

Average corotation of line segments near a point and vortex identification

An easy-to-interpret kinematic quantity measuring the average corotation of material line segments near a point is introduced and applied to vortex identification. At a given point, the vector of average corotation of line segments is defined as the average of the instantaneous local rigid-body rotation over "all planar cross sections" passing through the examined point. The vortex-identification method based on average corotation is a one-parameter, region-type local method sensitive to the axial stretching rate as well as to the inner configuration of the velocity gradient tensor. The method is derived from a well-defined interpretation of the local flow kinematics to determine the "plane of swirling" and is also applicable to compressible and variable-density flows. Practical application to direct numerical simulation datasets includes a hairpin vortex of boundary-layer transition, the reconnection process of two Burgers vortices, a flow around an inclined flat plate, and a flow around a revolving insect wing. The results agree well with some popular local methods and perform better in regions of strong shearing. Copyright © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

History does not move in a straight line. CEPS Commentary, 5 July 2012

Eight years have passed since the EU launched its European Neighbourhood Policy, aimed at inducing its neighbours to the east to converge on modern European values and economic norms. In this Commentary, Michael Emerson reflects on the curious and circuitous turn of events in the region during this period. Michael Emerson is Senior Associate Research Fellow at CEPS.

On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

An algorithm for fitting related sets of straight-line data /

Includes bibliographies (p. 12).

Computation of drawdowns at equilibrium caused by wells drawing water from an aquifer fed by a finite straight line source /

Mode of access: Internet.

Method of determining the coefficient of storage from straight-line plots without extrapolation /

Mode of access: Internet.

Drawdown patterns for two-well systems as applied to straight-line-boundary conditions /

Mode of access: Internet.

Geometry without axioms; or the first book of Euclid's elements. With alterations and familiar notes; and an intercalary book in which the straight line and plane are derived from properties of the sphere ... To which is added an appendix ...

Mode of access: Internet.

Elements of analytical geometry: embracing the equations of the point, the straight line, the conic sections, and surfaces of the first and second order.

Mode of access: Internet.

Elements of analytical geometry; embracing the equations of the point, the straight line, the conic sections, and surfaces of the first and second order,

Mode of access: Internet.

A treatise on plane co-ordinate geometry : as applied to the straight line and the conic sections : with numerous examples /

Mode of access: Internet.

The principles of projective geometry applied to the straight line and conic,

Mode of access: Internet.

Robust Stereo Visual Odometry through a Probabilistic Combination of Points and Line Segments

Most approaches to stereo visual odometry reconstruct the motion based on the tracking of point features along a sequence of images. However, in low-textured scenes it is often difficult to encounter a large set of point features, or it may happen that they are not well distributed over the image, so that the behavior of these algorithms deteriorates. This paper proposes a probabilistic approach to stereo visual odometry based on the combination of both point and line segment that works robustly in a wide variety of scenarios. The camera motion is recovered through non-linear minimization of the projection errors of both point and line segment features. In order to effectively combine both types of features, their associated errors are weighted according to their covariance matrices, computed from the propagation of Gaussian distribution errors in the sensor measurements. The method, of course, is computationally more expensive that using only one type of feature, but still can run in real-time on a standard computer and provides interesting advantages, including a straightforward integration into any probabilistic framework commonly employed in mobile robotics.