A route calculation for unmanned vessel

Рассматривается проблема определения маршрута движения безэкипажного судна с учетом жестких требований контроля положения и курса судна. Современные электронно-картографические навигационно-информационные системы в режиме управления траекторией определяют точку поворота для выхода на новый участок маршрута, что недостаточно для управления безэкипажным судном в автономном режиме. Для повышения точности предложено проводить расчет траектории движения безэкипажного судна в географических координатах c учетом движения судна по радиусу поворота между участками траектории без перевода в прямоугольную систему координат. Показано, что при движении в свободной акватории проблема может быть сведена к решению обратной геодезической задачи. Предложен универсальный алгоритм расчета траектории в виде сегментов дуг большого круга, позволяющий получить путевые точки маршрута с любой заданной точностью. В случае возникновения ограничений на движение между двумя участками по внутреннему радиусу необходимо рассчитать альтернативный маршрут обхода препятствия. Для данного случая предложен расчетный маневр, полученный на основе решения задачи Дубинса. Альтернативный маршрут формируется в виде последовательности криволинейных сегментов, соответствующих заданному радиусу поворота. Алгоритм расчета путевых точек позволяет получить траекторию обхода препятствия с любой степенью детализации. A route calculation problem for unmanned vessels is investigated according to the control position and course high requirements. Present day electronic chart display and information systems (ECDIS) operating on the track control regime provide wheel-of-point calculation to course changing. It is not enough to control unmanned ship on the route in the autonomous mode. To increase control precision a new route calculation routine is suggested. The routine provides route calculation in the geodesic coordinates without Cartesian reference system mapping. It is shown that in the empty water the routine can be reduced to an inverse survey computation. A universal route calculation algorithm providing great circle arc segmentation with any given accuracy is suggested. In the case of course changing restricted area, it is needed to calculate an alternate route for obstacle or collision avoidance. The algorithm of alternate route calculation based on Dubins problem solution is applied. The route is found as a sequence of great circle arcs according to the ship turn radius. The shown algorithm allows finding avoidance route waypoints with any given resolution.

The Clustering of Orbital Poles Induced by the LMC: Hints for the Origin of Planes of Satellites

A significant fraction of Milky Way (MW) satellites exhibit phase-space properties consistent with a coherent orbital plane. Using tailored N-body simulations of a spherical MW halo that recently captured a massive (1.8 × 1011 M ⊙) LMC-like satellite, we identify the physical mechanisms that may enhance the clustering of orbital poles of objects orbiting the MW. The LMC deviates the orbital poles of MW dark matter particles from the present-day random distribution. Instead, the orbital poles of particles beyond R ≈ 50 kpc cluster near the present-day orbital pole of the LMC along a sinusoidal pattern across the sky. The density of orbital poles is enhanced near the LMC by a factor δ ρ max = 30% (50%) with respect to underdense regions and δ ρ iso = 15% (30%) relative to the isolated MW simulation (no LMC) between 50 and 150 kpc (150–300 kpc). The clustering appears after the LMC’s pericenter (≈50 Myr ago, 49 kpc) and lasts for at least 1 Gyr. Clustering occurs because of three effects: (1) the LMC shifts the velocity and position of the central density of the MW’s halo and disk; (2) the dark matter dynamical friction wake and collective response induced by the LMC change the kinematics of particles; (3) observations of particles selected within spatial planes suffer from a bias, such that measuring orbital poles in a great circle in the sky enhances the probability of their orbital poles being clustered. This scenario should be ubiquitous in hosts that recently captured a massive satellite (at least ≈1:10 mass ratio), causing the clustering of orbital poles of halo tracers.

New Horizons Detection of the Local Galactic Lyman-α Background

Since 2007 the Alice spectrograph on the New Horizons (NH) spacecraft has been used to periodically observe the Lyman-α (Lyα) emissions of the interplanetary medium (IPM), which mostly result from resonant scattering of solar Lyα emissions by interstellar hydrogen atoms passing through the solar system. Three observations of IPM Lyα along a single great circle were made during the NH cruise to Pluto, and these have been supplemented by observations along six great circles (spread over the sky at 30° intervals), acquired one month before and one day after the NH flyby of Pluto, and on a further five occasions since then, out to just over 47 au from the Sun. These data indicate a distant Lyα background of 43 ± 3 Rayleigh brightness (equivalent to 56 ± 4 nW m−2 sr−1), which is present in all directions (i.e., not only in the upstream direction, as previously reported). This result is found independently by: (1) the falloff with distance from the Sun of the IPM Lyα brightness observed by NH–Alice in several directions on the sky, and (2) the residual between the observed brightness and a model brightness accounting for the resonantly scattered solar Lyα component alone. The repeated observations show that this distant Lyα background is constant and uniform over the sky, and represents the local Galactic Lyα background. The observations show no strong correlation with the cloud structure of the local IPM. The observed brightness constrains the absorption coefficient of interstellar dust at Lyα to 0.2 ± 0.01 kpc−1.

On the Hofer girth of the sphere of great circles

An oriented equator of [Formula: see text] is the image of an oriented embedding [Formula: see text] such that it divides [Formula: see text] into two equal area halves. Following Chekanov, we define the Hofer distance between two oriented equators as the infimal Hofer norm of a Hamiltonian diffeomorphism taking one to another. Consider [Formula: see text] the space of oriented equators. We define the Hofer girth of an embedding [Formula: see text] as the infimum of the Hofer diameter of [Formula: see text], where [Formula: see text] is homotopic to [Formula: see text]. There is a natural embedding [Formula: see text], sending a point on the sphere to the positively oriented great circle perpendicular to it. In this paper, we provide an upper bound on the Hofer girth of [Formula: see text].

Regression and Evaluation on a Forward Interpolated Version of the Great Circle Arcs–Based Distortion Metric of Map Projections

We studied the numerical approximation problem of distortion in map projections. Most widely used differential methods calculate area distortion and maximum angular distortion using partial derivatives of forward equations of map projections. However, in certain map projections, partial derivatives are difficult to calculate because of the complicated forms of forward equations, e.g., equations with iterations, integrations, or multi-way branches. As an alternative, the spherical great circle arcs–based metric employs the inverse equations of map projections to transform sample points from the projection plane to the spherical surface, and then calculates a differential-independent distortion metric for the map projections. We introduce a novel forward interpolated version of the previous spherical great circle arcs–based metric, solely dependent on the forward equations of map projections. In our proposed numerical solution, a rational function–based regression is also devised and applied to our metric to obtain an approximate metric of angular distortion. The statistical and graphical results indicate that the errors of the proposed metric are fairly low, and a good numerical estimation with high correlation to the differential-based metric can be achieved.

Calibration Method for Central Catadioptric Camera Using Multiple Groups of Parallel Lines and Their Properties

This paper presents an approach for calibrating omnidirectional single-viewpoint sensors using the central catadioptric projection properties of parallel lines. Single-viewpoint sensors are widely used in robot navigation and driverless cars; thus, a high degree of calibration accuracy is needed. In the unit viewing sphere model of central catadioptric cameras, a line in a three-dimensional space is projected to a great circle, resulting in the projections of a group of parallel lines intersecting only at the endpoints of the diameter of the great circle. Based on this property, when there are multiple groups of parallel lines, a group of orthogonal directions can be determined by a rectangle constructed by two groups of parallel lines in different directions. When there is a single group of parallel lines in space, the diameter and tangents at their endpoints determine a group of orthogonal directions for the plane containing the great circle. The intrinsic parameters of the camera can be obtained from the orthogonal vanishing points in the central catadioptric image plane. An optimization algorithm for line image fitting based on the properties of antipodal points is proposed. The performance of the algorithm is verified using simulated setups. Our calibration method was validated though simulations and real experiments with a catadioptric camera.

Empirical Estimation of Shortest Route Length along U.S. Interstate Highways Based on Great Circle Distance

In this study, 98 regression models were specified for easily estimating shortest distances based on great circle distances along the U.S. interstate highways nationwide and for each of the continental 48 states. This allows transportation professionals to quickly generate distance, or even distance matrix, without expending significant efforts on complicated shortest path calculations. For simple usage by all professionals, all models are present in the simple linear regression form. Only one explanatory variable, the great circle distance, is considered to calculate the route distance. For each geographic scope (i.e., the national or one of the states), two different models were considered, with and without the intercept. Based on the adjusted R-squared, it was observed that models without intercepts generally have better fitness. All these models generally have good fitness with the linear regression relationship between the great circle distance and route distance. At the state level, significant variations in the slope coefficients between the state-level models were also observed. Furthermore, a preliminary analysis of the effect of highway density on this variation was conducted.

An Axiom of True Courses Calculation in Great Circle Navigation

Based on traditional expressions and spherical trigonometry, at present, great circle navigation is undertaken using various navigational software packages. Recent research has mainly focused on vector algebra. These problems are calculated numerically and are thus suited to computer-aided great circle navigation. However, essential knowledge requires the navigator to be able to calculate navigation parameters without the use of aids. This requirement is met using spherical trigonometry functions and the Napier wheel. In addition, to facilitate calculation, certain axioms have been developed to determine a vessel’s true course. These axioms can lead to misleading results due to the limitations of the trigonometric functions, mathematical errors, and the type of great circle navigation. The aim of this paper is to determine a reliable trigonometric function for calculating a vessel’s course in regular and composite great circle navigation, which can be used with the proposed axioms. This was achieved using analysis of the trigonometric functions, and assessment of their impact on the vessel’s calculated course and established axioms.