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).