https://github.com/petercorke/rvc-notation
RVC notation
https://github.com/petercorke/rvc-notation
Last synced: 16 days ago
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RVC notation
- Host: GitHub
- URL: https://github.com/petercorke/rvc-notation
- Owner: petercorke
- License: mit
- Created: 2019-08-21T22:23:17.000Z (over 5 years ago)
- Default Branch: master
- Last Pushed: 2021-09-02T23:21:08.000Z (over 3 years ago)
- Last Synced: 2025-03-27T03:22:39.272Z (about 1 month ago)
- Language: TeX
- Size: 288 KB
- Stars: 20
- Watchers: 3
- Forks: 3
- Open Issues: 2
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# LaTeX macros for Robotics, Vision and Control
This file includes macros to create equations in the style of those used in the textbook ["Robotics, Vision & Control"](http://petercorke.com/wordpress/rvc), all editions.
```latex
\include{rvc-notation}
```
Make sure that `rvc-notation.tex` is in your LaTeX path.
A [PDF version of the cheatsheet is available here](https://github.com/petercorke/rvc-notation/blob/master/cheatsheet.pdf).
## Poses
* `\pose` abstract pose, greek letter ξ
* `\pose[f]` pose with respect to a frame
* `\pose_A` is the pose of frame A
* `\pose[B]_A` is the pose of frame A with respect to frame B
* `\estpose` estimated pose, greek letter ξ with hat
* `\posedot` derivative of abstract pose, greek letter ν
A leading superscript, the reference frame, is specified in square brackets. A trailing subscript, the target frame, is specified in the standard LaTeX way using `_`.
The operators ⊕ and ⊖ which are given by the LaTeX commands `\oplus` and `\ominus` respectively.
```\latex
$\ominus \pose[C]_A = \pose[A]_B \oplus \pose[B]_C$
```
We can apply a pose to a vector, which linearly transforms it by
```\latex
$\pose_b \sbullet \vec{b}_P$
```
You can tweak the size of the bullet by giving it a relative scale argument, ie. `\sbullet[2]` is very large.
There are also estimated pose and derivative of pose or spatial velocity
```\latex
$\estpose, \posedot$
```
## Coordinate frames
* `\cframe{A}` is coordinate frame A which renders as {A}
```latex
\cframe{A}
```
## Points
* `\point{A}` is point A which renders in Roman bold font
```latex
\point{P}
```
## Vectors
Vectors are displayed in bold italic font
* `\vec{t}` is a vector t
* `\vec[A]{t}` is a vector t with respect to frame A
* `\dvec{t}` is vector of `\dot{t}`
* `\dvec[A]{t}` is vector of `\dot{t}` with respect to frame A
* `\ddvec[f]{x`} a double dotted vector
* `\hvech[f]{x}` a homogeneous vector (tilde above)
* `\bvec[f]{x}` a vector with an over bar, eg. for mean value
* `\evec[f]{x}` an estimated vector with a hat
```latex
$\vec{v}, \dvec{v}, \ddvec{v}, \vec[a]{v}$
```
```latex
$ \hvec{v}, \evec{v}, \bvec{v}$
```
## Matrices
Matrices are displayed in bold Roman font
* `\mat{x}` a matrix
* `\mat[f]{x}` a matrix with a coordinate frame
* `\dmat[f]{x}` a matrix derivative
* `\zero` a zero matrix
* `\matfn{f}{x}` matrix function f of x
```latex
$\mat{A}, \mat[a]{R}_b, \dmat{A}, \emat{A}, \zero_{2\times 3}$
```
```latex
$\matfn{J}{\vec{q}}, \matfn[0]{J}{\vec{q}}$
```
## Skew symmetric matrices
* `\skx{v}` -> [v]x skew symmetric matrix
* `\sk{v}` -> [v] augmented skew symmetric matrix
* `\iskx{v}` -> inverse skew symmetric matrix, vex operator
* `\isk{v}` -> inverse augmented skew symmetric matrix
```latex
$\sk{v}, \skx{v}, \isk{A}, \iskx{A}$
```
## Unit Quaternion
* `\q` displays as q with a bubble on top
```latex
$\q, \q[a]_b$
```
## Mathematial Groups
Displayed in Roman font
* `\R` is the group of real numbers, an R in blackboard font
* `\SO{n}` special orthogonal group: SO(n)
* `\SE{n}` special Euclidean group: SE(n)
* `\so{n}` Lie algebra of SO(n): so(n)
* `\se{n}` Lie algebra of SE(n): se(n)
```latex
$\R^2, \SO{3}, \so{3}$
```
## MATLAB code
Display a block of code in blue fixed-width font
```latex
\begin{Code}
[x,e] = eig(A);
\end{Code}
```
For multi-line code blocks with line numbering
```latex
\begin{CodeNum}
[x,e] = eig(A);
z = x(:,2);
\end{CodeNum}
```
## Miscellaneous
### Smallest angular difference
The symbol ⊝ is used to represent the difference of two angles wrapped into the interval [-π π), which is produced by the LaTeX command `\circleddash`.
```latex
$\theta_1 \circleddash \theta_2$
```
### Units
* `\unit{U}` sets the contents in math mode with a preceding half space, eg. `\unit{m s^{-2})`
* `\mm`, `\um`, `\nm`
* `\Hz`, `\kHz`, `\MHz`
* `\ms`
* `\deg`
```latex
The object was 12\mm\ across,
accelerated at 2.3\unit{m s^{-2}},
the servo interval was 12\ms,
and the angle spanned 30\deg.
```
### Scientific notation
* `\sci{m}{e}` scientific notation with mantissa and exponent
```latex
\sci{5}{-2}
```
### Coordinates and vectors
```latex
$\coord{1}{2}, \vector{1}{2}{3}$
```
### Other symbols
* `\cspace` configuration space, caligraphic C