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[AMR] Fix error

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Janis Hutz
2026-04-07 15:14:27 +02:00
parent 841f71814b
commit d1b69d3c3b
2 changed files with 6 additions and 6 deletions
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electives/others/amr/autonomous-mobile-robots-cheatsheet.pdf
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electives/others/amr/parts/01_kinematics/00_intro.tex
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@@ -6,21 +6,21 @@ $_{\color{blue}\fbox{W}}\,\vec{t}\,_{\color{red}\fbox{B}} = \, _{\color{blue}\fb
\shortdefinition[State vector] $x_R$: $x$, $v$ of rob in $W$, pos of sensors \shortdefinition[State vector] $x_R$: $x$, $v$ of rob in $W$, pos of sensors
\shortdefinition[Rot. Mat.] $\mat{R}_{z} = \begin{bmatrix} \shortdefinition[Rot. Mat.] $\mat{R}_{z}(\psi) = \begin{bmatrix}
c(\psi) & -s(\psi) & 0 \\ c(\psi) & -s(\psi) & 0 \\
s(\psi) & c(\psi) & 0 \\ s(\psi) & c(\psi) & 0 \\
0 & 0 & 1 0 & 0 & 1
\end{bmatrix}$\\ \end{bmatrix}$\\
$\mat{R}_y(\theta) = \begin{bmatrix} $\mat{R}_y(\theta) = \begin{bmatrix}
c(\psi) & 0 & s(\psi) \\ c(\theta) & 0 & s(\theta) \\
0 & 1 & 0 \\ 0 & 1 & 0 \\
-s(\psi) & 0 & c(\psi) \\ -s(\theta) & 0 & c(\theta) \\
\end{bmatrix} \end{bmatrix};
\mat{R}_x(\varphi) \mat{R}_x(\varphi)
\begin{bmatrix} \begin{bmatrix}
1 & 0 & 0 \\ 1 & 0 & 0 \\
0 & c(\psi) & -s(\psi) \\ 0 & c(\varphi) & -s(\varphi) \\
0 & s(\psi) & c(\psi) 0 & s(\varphi) & c(\varphi)
\end{bmatrix}$ \end{bmatrix}$
\shortremark Application: ${_W} \vec{a} = \mat{R}_{WB} {_B} \vec{a}$ \shortremark Application: ${_W} \vec{a} = \mat{R}_{WB} {_B} \vec{a}$