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Manipulability Ellipsoid
In robotics, the manipulability ellipsoid is the geometric interpretation of the scaled eigenvectors resulting from the singular value decomposition In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any \ m \times n\ matrix. It is related ... of the jacobian that describes a robot's motion. Robot control Geometry {{robotics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robotics
Robotics is an interdisciplinary branch of computer science and engineering. Robotics involves design, construction, operation, and use of robots. The goal of robotics is to design machines that can help and assist humans. Robotics integrates fields of mechanical engineering, electrical engineering, information engineering, mechatronics, electronics, bioengineering, computer engineering, control engineering, software engineering, mathematics, etc. Robotics develops machines that can substitute for humans and replicate human actions. Robots can be used in many situations for many purposes, but today many are used in dangerous environments (including inspection of radioactive materials, bomb detection and deactivation), manufacturing processes, or where humans cannot survive (e.g. in space, underwater, in high heat, and clean up and containment of hazardous materials and radiation). Robots can take any form, but some are made to resemble humans in appearance. This is claim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenvector
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by \lambda, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated. Formal definition If is a linear transformation from a vector space over a field into itself and is a nonzero vector in , then is an eigenvector of if is a scalar multiple of . This can be written as T(\mathbf) = \lambda \mathbf, where is a scalar in , known as the eigenvalue, characteristic value, or characteristic root ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singular Value Decomposition
In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any \ m \times n\ matrix. It is related to the polar decomposition. Specifically, the singular value decomposition of an \ m \times n\ complex matrix is a factorization of the form \ \mathbf = \mathbf\ , where is an \ m \times m\ complex unitary matrix, \ \mathbf\ is an \ m \times n\ rectangular diagonal matrix with non-negative real numbers on the diagonal, is an n \times n complex unitary matrix, and \ \mathbf\ is the conjugate transpose of . Such decomposition always exists for any complex matrix. If is real, then and can be guaranteed to be real orthogonal matrices; in such contexts, the SVD is often denoted \ \mathbf^\mathsf\ . The diagonal entries \ \sigma_i = \Sigma_\ of \ \mathbf\ are uniquely determined by and are known as the singular values of . The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacobian Matrix And Determinant
In vector calculus, the Jacobian matrix (, ) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. When this matrix is square, that is, when the function takes the same number of variables as input as the number of vector components of its output, its determinant is referred to as the Jacobian determinant. Both the matrix and (if applicable) the determinant are often referred to simply as the Jacobian in literature. Suppose is a function such that each of its first-order partial derivatives exist on . This function takes a point as input and produces the vector as output. Then the Jacobian matrix of is defined to be an matrix, denoted by , whose th entry is \mathbf J_ = \frac, or explicitly :\mathbf J = \begin \dfrac & \cdots & \dfrac \end = \begin \nabla^ f_1 \\ \vdots \\ \nabla^ f_m \end = \begin \dfrac & \cdots & \dfrac\\ \vdots & \ddots & \vdots\\ \dfrac & \cdots ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robot Control
Robotic control is the system that contributes to the movement of robots. This involves the mechanical aspects and programmable systems that makes it possible to control robots. Robotics could be controlled in various ways, which includes using manual control, wireless control, semi-autonomous (which is a mix of fully automatic and wireless control), and fully autonomous (which is when it uses artificial intelligence to move on its own, but there could be options to make it manually controlled). In the present day, as technological advancements progress, robots and their methods of control continue to develop and advance. Modern robots (2000-present) Medical and surgical In the medical field, robots are used to make precise movements that are humanly difficult. Robotic surgery involves the use of less-invasive surgical methods, which are “procedures performed through tiny incisions”. Currently, robots use the da Vinci surgical method, which involves the robotic arm (whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
