Concurrent Mapping And Localization
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Concurrent Mapping And Localization
Simultaneous localization and mapping (SLAM) is the computational problem of constructing or updating a map of an unknown environment while simultaneously keeping track of an agent's location within it. While this initially appears to be a chicken-and-egg problem, there are several algorithms known for solving it in, at least approximately, tractable time for certain environments. Popular approximate solution methods include the particle filter, extended Kalman filter, covariance intersection, and GraphSLAM. SLAM algorithms are based on concepts in computational geometry and computer vision, and are used in robot navigation, robotic mapping and odometry for virtual reality or augmented reality. SLAM algorithms are tailored to the available resources and are not aimed at perfection but at operational compliance. Published approaches are employed in self-driving cars, unmanned aerial vehicles, autonomous underwater vehicles, planetary rovers, newer domestic robots and ...
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Stanley2
Stanley may refer to: Arts and entertainment Film and television * ''Stanley'' (1972 film), an American horror film * ''Stanley'' (1984 film), an Australian comedy * ''Stanley'' (1999 film), an animated short * ''Stanley'' (1956 TV series), an American situation comedy * ''Stanley'' (2001 TV series), an American animated series Other uses in arts and entertainment * ''Stanley'' (play), by Pam Gems, 1996 * Stanley Award, an Australian Cartoonists' Association award * '' Stanley: The Search for Dr. Livingston'', a video game * Stanley (Cars), a character in ''Cars Toons: Mater's Tall Tales'' * ''The Stanley Parable'', a 2011 video game developed by Galactic Cafe, and its titular character, Stanley Businesses and organisations * Stanley, Inc., American information technology company * Stanley Aviation, American aerospace company * Stanley Black & Decker, formerly The Stanley Works, American hardware manufacturer ** Stanley knife, a utility knife * Stanley bottle, a bran ...
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Rover (space Exploration)
A rover (or sometimes planetary rover) is a planetary surface exploration device designed to move across the solid surface on a planet or other planetary mass celestial bodies. Some rovers have been designed as land vehicles to transport members of a human spaceflight crew; others have been partially or fully autonomous robots. Rovers are typically created to land on another planet (other than Earth) via a lander (spacecraft), lander-style spacecraft, tasked to collect information about the terrain, and to take crust (geology), crust samples such as dust, soil, rocks, and even liquids. They are essential tools in space exploration. Features Rovers arrive on spacecraft and are used in conditions very distinct from those on the Earth, which makes some demands on their design. Reliability Rovers have to withstand high levels of acceleration, high and low temperatures, pressure, dust, corrosion, cosmic rays, remaining functional without repair for a needed period of time. ...
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Grid Map
Grid, The Grid, or GRID may refer to: Common usage * Cattle grid or stock grid, a type of obstacle is used to prevent livestock from crossing the road * Grid reference, used to define a location on a map Arts, entertainment, and media * News grid, used in communications/public relations Fictional entities * Grid (comics), a fictional character in the DC Comics Universe * Grid (Jotun), Gríðr, a giantess in Norse mythology * The grid, the virtual environment of the game ''Second Life'' * ''The Grid'', the computerized virtual world in which the Tron franchise exists Games and gaming * Nvidia GRID, a cloud gaming platform for Nvidia Tegra products * ''Power Grid'', the English-language edition of the multiplayer German-style board game ''Funkenschlag'' * Grid (series), a series of racing video games developed by Codemasters * Spooks 3 Games - ''The Grid'', a video game based on the television show ''Spooks'' * ''The Grid'' (video game), a 2001 third-person shooter Music * ' ...
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Topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Twist (mathematics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity (mathematics), continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopy, homotopies. A property that is invariant under such deformations is a topological property. Basic exampl ...
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Topological Map
In cartography and geology, a topological map is a type of diagram that has been simplified so that only vital information remains and unnecessary detail has been removed. These maps lack scale, also distance and direction are subject to change and/or variation, but the topological relationship between points is maintained. A good example are the tube maps for the London Underground and the New York City Subway. See also *Outline of cartography The following outline is provided as an overview of and topical guide to cartography: Cartography (also called mapmaking) – study and practice of making and using maps or globes. Maps have traditionally been made using pen and paper, but ... References Map types {{Cartography-stub ...
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Project Tango
Tango (formerly named Project Tango, while in testing) was an augmented reality computing platform, developed and authored by the Advanced Technology and Projects (ATAP), a skunkworks division of Google. It used computer vision to enable mobile devices, such as smartphones and tablets, to detect their position relative to the world around them without using GPS or other external signals. This allowed application developers to create user experiences that include indoor navigation, 3D mapping, physical space measurement, environmental recognition, augmented reality, and windows into a virtual world. The first product to emerge from ATAP, Tango was developed by a team led by computer scientist Johnny Lee, a core contributor to Microsoft's Kinect. In an interview in June 2015, Lee said, "We're developing the hardware and software technologies to help everything and everyone understand precisely where they are, anywhere." Google produced two devices to demonstrate the Tango tec ...
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Maximum A Posteriori Estimation
In Bayesian statistics, a maximum a posteriori probability (MAP) estimate is an estimate of an unknown quantity, that equals the mode of the posterior distribution. The MAP can be used to obtain a point estimate of an unobserved quantity on the basis of empirical data. It is closely related to the method of maximum likelihood (ML) estimation, but employs an augmented optimization objective which incorporates a prior distribution (that quantifies the additional information available through prior knowledge of a related event) over the quantity one wants to estimate. MAP estimation can therefore be seen as a regularization of maximum likelihood estimation. Description Assume that we want to estimate an unobserved population parameter \theta on the basis of observations x. Let f be the sampling distribution of x, so that f(x\mid\theta) is the probability of x when the underlying population parameter is \theta. Then the function: :\theta \mapsto f(x \mid \theta) \! is known as th ...
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Bundle Adjustment
In photogrammetry and computer stereo vision, bundle adjustment is simultaneous refining of the 3D coordinates describing the scene geometry, the parameters of the relative motion, and the optical characteristics of the camera(s) employed to acquire the images, given a set of images depicting a number of 3D points from different viewpoints. Its name refers to the '' geometrical bundles'' of light rays originating from each 3D feature and converging on each camera's optical center, which are adjusted optimally according to an optimality criterion involving the corresponding image projections of all points. Uses Bundle adjustment is almost always used as the last step of every feature-based 3D reconstruction algorithm. It amounts to an optimization problem on the 3D structure and viewing parameters (i.e., camera pose and possibly intrinsic calibration and radial distortion), to obtain a reconstruction which is optimal under certain assumptions regarding the noise pertaining t ...
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Interval Propagation
In numerical mathematics, interval propagation or interval constraint propagation is the problem of contracting interval domains associated to variables of R without removing any value that is consistent with a set of constraints (i.e., equations or inequalities). It can be used to propagate uncertainties in the situation where errors are represented by intervals. Interval propagation considers an estimation problem as a constraint satisfaction problem. Atomic contractors A contractor associated to an equation involving the variables ''x''1,...,''x''''n'' is an operator which contracts the intervals 'x''1..., 'x''''n''(that are supposed to enclose the ''x''''i'''s) without removing any value for the variables that is consistent with the equation. A contractor is said to be ''atomic'' if it is not built as a composition of other contractors. The main theory that is used to build atomic contractors are based on interval analysis Interval arithmetic (also known as interva ...
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Set Estimation
In statistics, a random vector ''x'' is classically represented by a probability density function. In a set-membership approach or set estimation, ''x'' is represented by a set ''X'' to which ''x'' is assumed to belong. This means that the support of the probability distribution function of ''x'' is included inside ''X''. On the one hand, representing random vectors by sets makes it possible to provide fewer assumptions on the random variables (such as independence) and dealing with nonlinearities is easier. On the other hand, a probability distribution function provides a more accurate information than a set enclosing its support. Set-membership estimation Set membership estimation (or ''set estimation'' for short) is an estimation approach which considers that measurements are represented by a set ''Y'' (most of the time a box of R''m'', where ''m'' is the number of measurements) of the measurement space. If ''p'' is the parameter vector and ''f'' is the model function, then t ...
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Covariance Intersection
Covariance intersection is an algorithm for combining two or more estimates of state variables in a Kalman filter when the correlation between them is unknown. Specification Items of information a and b are known and are to be fused into information item c. We know a and b have mean/covariance \hat a, A and \hat b, B, but the cross correlation is not known. The covariance intersection update gives mean and covariance for c as : C^ = \omega A^ + (1-\omega) B^ \, , : \hat c = C(\omega A^ \hat a + (1-\omega)B^ \hat b) \, . where ''ω'' is computed to minimize a selected norm, e.g., logdet or trace. While it is necessary to solve an optimization problem for higher dimensions, closed-form solutions exist for lower dimensions. CI can be used in place of the conventional Kalman update equations to ensure that the resulting estimate is conservative, regardless of the correlation between the two estimates, with covariance strictly non-increasing according to the chosen measure. The ...
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Posterior Probability Distribution
The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood via an application of Bayes' rule. From an epistemological perspective, the posterior probability contains everything there is to know about an uncertain proposition (such as a scientific hypothesis, or parameter values), given prior knowledge and a mathematical model describing the observations available at a particular time. After the arrival of new information, the current posterior probability may serve as the prior in another round of Bayesian updating. In the context of Bayesian statistics, the posterior probability distribution usually describes the epistemic uncertainty about statistical parameters conditional on a collection of observed data. From a given posterior distribution, various point and interval estimates can be derived, such as the maximum a posteriori (MAP) or the highest posterior density interval (HPDI ...
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