Matrices, Vectors & Algebra

The rw::math namespace includes many math types for representing different types of vectors. Math types in RobWork are based on Eigen 3.

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

\({}^{a}{\mathbf{P}}\)

Vector P seen in frame a

\({}^{a}{b}_{\mathbf{P}}\)

Translation of frame b seen in frame a

\({}^{a}{b}_{\mathbf{R}}\)

Rotation of frame b seen in frame a

\({}^{a}{b}_{\mathbf{T}}\)

Homogeneous transform of frame b seen in frame a

\({}^{a}_{b}{\mathbf{T}_v}^{c}_{d}\)

Velocity transform that transforms the reference frame from
b to a and the velocity reference point from c to d

\({}^{a}_{b}{\mathbf{T}_f}^{c}_{d}\)

Force transform that transforms the reference frame from
b to a and the force reference point from c to d

\({}^{a}{b}_{\mathbf{J}}\)

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…

Polynomials

Note

Documentation is being written…