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Hand–eye Calibration Problem
In robotics and mathematics, the hand–eye calibration problem (also called the robot–sensor or robot–world calibration problem) is the problem of determining the transformation between a robot end-effector and a sensor or sensors (camera or laser scanner) or between a robot base and the world coordinate system. It is conceptually analogous to biological hand–eye coordination (hence the name). It takes the form of , where ''A'' and ''B'' are two systems, usually a robot base and a camera, and and are unknown transformation matrices. A highly studied special case of the problem occurs where , taking the form of the problem . Solutions to the problem take the forms of several types of methods, including separable closed-form solutions, simultaneous closed-form solutions, and iterative solutions. The covariance of in the equation can be calculated for any randomly perturbed matrices and . The problem is an important part of robot calibration, with efficiency and accuracy of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robotics
Robotics is the interdisciplinary study and practice of the design, construction, operation, and use of robots. Within mechanical engineering, robotics is the design and construction of the physical structures of robots, while in computer science, robotics focuses on robotic automation algorithms. Other disciplines contributing to robotics include electrical engineering, electrical, control engineering, control, software engineering, software, Information engineering (field), information, electronics, electronic, telecommunications engineering, telecommunication, computer engineering, computer, mechatronic, and materials engineering, materials engineering. The goal of most robotics is to design machines that can help and assist humans. Many robots are built to do jobs that are hazardous to people, such as finding survivors in unstable ruins, and exploring space, mines and shipwrecks. Others replace people in jobs that are boring, repetitive, or unpleasant, such as cleaning, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
End-effector
An end effector is the device at the end of a robotic arm, designed to interact with the environment. The exact nature of this device depends on the application of the robot. In the strict definition, which originates from serial robotic manipulators, the end effector means the last link (or end) of the robot. At this endpoint, the tools are attached. In a wider sense, an end effector can be seen as the part of a robot that interacts with the work environment. This does not refer to the wheels of a mobile robot or the feet of a humanoid robot, which are not end effectors but rather part of a robot's mobility. End effectors may consist of a gripper or a tool. Grippers Categories When referring to robotic prehension there are four general categories of robot grippers: # Impactive: jaws or claws which physically grasp by direct impact upon the object. # Ingressive: pins, needles or hackles which physically penetrate the surface of the object (used in textile, carbon, and glas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eye–hand Coordination
Hand–eye coordination (also known as eye–hand coordination) is the coordinated motor control of eye movement with hand movement and the processing of visual input to guide reaching and grasping along with the use of proprioception of the hands to guide the eyes, a modality of multisensory integration. Eye–hand coordination has been studied in activities as diverse as the movement of solid objects such as wooden blocks, archery, sporting performance, music reading, computer gaming, copy-typing, and even tea-making. It is part of the mechanisms of performing everyday tasks; in its absence, most people would not be able to carry out even the simplest of actions such as picking up a book from a table. Behaviour and kinematics Neuroscientists have extensively researched human gaze behaviour, noting that the use of the gaze is very task-specific, but that humans typically exhibit proactive control to guide their movement. Usually the eyes fixate on a target before the hands a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robot Calibration
Robot calibration is a process used to improve the accuracy of robots, particularly industrial robots which are highly repeatable but not accurate. Robot calibration is the process of identifying certain parameters in the kinematic structure of an industrial robot, such as the relative position of robot links. Depending on the type of errors modeled, the calibration can be classified in three different ways. Level-1 calibration only models differences between actual and reported joint displacement values, (also known as mastering). Level-2 calibration, also known as kinematic calibration, concerns the entire geometric robot calibration which includes angle offsets and joint lengths. Level-3 calibration, also called a non-kinematic calibration, models errors other than geometric defaults such as stiffness, joint compliance, and friction. Often Level-1 and Level-2 calibration are sufficient for most practical needs. Parametric robot calibration is the process of determining the actual ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quaternion
In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quaternions is often denoted by (for ''Hamilton''), or in blackboard bold by \mathbb H. Quaternions are not a field, because multiplication of quaternions is not, in general, commutative. Quaternions provide a definition of the quotient of two vectors in a three-dimensional space. Quaternions are generally represented in the form a + b\,\mathbf i + c\,\mathbf j +d\,\mathbf k, where the coefficients , , , are real numbers, and , are the ''basis vectors'' or ''basis elements''. Quaternions are used in pure mathematics, but also have practical uses in applied mathematics, particularly for calculations involving three-dimensional rotations, such as in three-dimensional computer graphics, computer vision, robotics, magnetic resonance i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotation Matrix
In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation (mathematics), rotation in Euclidean space. For example, using the convention below, the matrix :R = \begin \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end rotates points in the plane counterclockwise through an angle about the origin of a two-dimensional Cartesian coordinate system. To perform the rotation on a plane point with standard coordinates , it should be written as a column vector, and matrix multiplication, multiplied by the matrix : : R\mathbf = \begin \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end \begin x \\ y \end = \begin x\cos\theta-y\sin\theta \\ x\sin\theta+y\cos\theta \end. If and are the coordinates of the endpoint of a vector with the length ''r'' and the angle \phi with respect to the -axis, so that x = r \cos \phi and y = r \sin \phi, then the above equations become the List of trigonometric identities#Angle sum and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Quaternion
In mathematics, the dual quaternions are an 8-dimensional real algebra isomorphic to the tensor product of the quaternions and the dual numbers. Thus, they may be constructed in the same way as the quaternions, except using dual numbers instead of real numbers as coefficients. A dual quaternion can be represented in the form , where ''A'' and ''B'' are ordinary quaternions and ''ε'' is the dual unit, which satisfies and commutes with every element of the algebra. Unlike quaternions, the dual quaternions do not form a division algebra. In mechanics, the dual quaternions are applied as a number system to represent rigid transformations in three dimensions. Since the space of dual quaternions is 8-dimensional and a rigid transformation has six real degrees of freedom, three for translations and three for rotations, dual quaternions obeying two algebraic constraints are used in this application. Since unit quaternions are subject to two algebraic constraints, unit quaternion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Equation
In mathematics, a linear equation is an equation that may be put in the form a_1x_1+\ldots+a_nx_n+b=0, where x_1,\ldots,x_n are the variables (or unknowns), and b,a_1,\ldots,a_n are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation and may be arbitrary expressions, provided they do not contain any of the variables. To yield a meaningful equation, the coefficients a_1, \ldots, a_n are required to not all be zero. Alternatively, a linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken. The solutions of such an equation are the values that, when substituted for the unknowns, make the equality true. In the case of just one variable, there is exactly one solution (provided that a_1\ne 0). Often, the term ''linear equation'' refers implicitly to this particular case, in which the variable is sensibly called the ''unknown''. In the case of two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Least Squares
The method of least squares is a mathematical optimization technique that aims to determine the best fit function by minimizing the sum of the squares of the differences between the observed values and the predicted values of the model. The method is widely used in areas such as regression analysis, curve fitting and data modeling. The least squares method can be categorized into linear and nonlinear forms, depending on the relationship between the model parameters and the observed data. The method was first proposed by Adrien-Marie Legendre in 1805 and further developed by Carl Friedrich Gauss. History Founding The method of least squares grew out of the fields of astronomy and geodesy, as scientists and mathematicians sought to provide solutions to the challenges of navigating the Earth's oceans during the Age of Discovery. The accurate description of the behavior of celestial bodies was the key to enabling ships to sail in open seas, where sailors could no longer rely on la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kronecker Product
In mathematics, the Kronecker product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix. It is a specialization of the tensor product (which is denoted by the same symbol) from vectors to matrices and gives the matrix of the tensor product linear map with respect to a standard choice of basis. The Kronecker product is to be distinguished from the usual matrix multiplication, which is an entirely different operation. The Kronecker product is also sometimes called matrix direct product. The Kronecker product is named after the German mathematician Leopold Kronecker (1823–1891), even though there is little evidence that he was the first to define and use it. The Kronecker product has also been called the ''Zehfuss matrix'', and the ''Zehfuss product'', after , who in 1858 described this matrix operation, but Kronecker product is currently the most widely used term. The misattribution to Kronecker rather than Zehfuss wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
