*************************** Matrices, Vectors & Algebra *************************** The rw::math namespace includes many math types for representing different types of vectors. Math types in RobWork are based on :ref:`license_eigen`. .. Matrix types: CameraMatrix InertiaMatrix Jacobian PerspectiveTransform2D Pose ProjectionMatrix Rotations Transforms Others: Line2D Line2DPolar Math::skew Vector types: Q Quaternion Rotation3DVector RPY VectorXX VelocityScrew6D Wrench6D Notation ======== In general a diagonal notation form will be used to describe the relation of vectors, rotation matrices, homogeneous transform, velocity screw, and so on. +------------------------------------------+-----------------------------------------------------------------+ | Expression | Description | +==========================================+=================================================================+ | :math:`{}^{a}{\mathbf{P}}` | Vector P seen in frame *a* | +------------------------------------------+-----------------------------------------------------------------+ | :math:`{}^{a}{b}_{\mathbf{P}}` | Translation of frame *b* seen in frame *a* | +------------------------------------------+-----------------------------------------------------------------+ | :math:`{}^{a}{b}_{\mathbf{R}}` | Rotation of frame **b** seen in frame *a* | +------------------------------------------+-----------------------------------------------------------------+ | :math:`{}^{a}{b}_{\mathbf{T}}` | Homogeneous transform of frame *b* seen in frame *a* | +------------------------------------------+-----------------------------------------------------------------+ | :math:`{}^{a}_{b}{\mathbf{T}_v}^{c}_{d}` | | Velocity transform that transforms the reference frame from | | | | *b* to *a* and the velocity reference point from *c* to *d* | +------------------------------------------+-----------------------------------------------------------------+ | :math:`{}^{a}_{b}{\mathbf{T}_f}^{c}_{d}` | | Force transform that transforms the reference frame from | | | | *b* to *a* and the force reference point from **c** to **d** | +------------------------------------------+-----------------------------------------------------------------+ | :math:`{}^{a}{b}_{\mathbf{J}}` | A Jacobian matrix defined from reference frame *a* to frame *b* | +------------------------------------------+-----------------------------------------------------------------+ When coordinate frames are visualized the axes are illustrated with the colors RGB, such that Red(x-axis), Green(y-axis) and Blue(z-axis). Jacobians =================== .. note:: Documentation is being written... Polynomials =================== .. note:: Documentation is being written... Singular Value Decomposition (SVD) ================================== .. note:: Documentation is being written... Linear Algebra ================================== .. note:: Documentation is being written... .. pseudoInverse, determinant, inverse EigenDecomposition Polynomials ================================== .. note:: Documentation is being written...