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pd1C!S2$9|7^#9-8p{tvTi<_s5xdj>rn41U8hek*DMM)CvKLDCN%6tF- diff --git a/electives/others/amr/autonomous-mobile-robots-cheatsheet.tex b/electives/others/amr/autonomous-mobile-robots-cheatsheet.tex index be2e645..8e31315 100644 --- a/electives/others/amr/autonomous-mobile-robots-cheatsheet.tex +++ b/electives/others/amr/autonomous-mobile-robots-cheatsheet.tex @@ -9,6 +9,7 @@ \fboxsep 1pt \fboxrule 0.1pt \renewcommand{\vec}[1]{\textbf{#1}} +\newcommand{\mat}[1]{\textbf{#1}} \noverticalspacing \setupCheatSheet{Autonomous Mobile Robots} diff --git a/electives/others/amr/parts/01_kinematics/00_intro.tex b/electives/others/amr/parts/01_kinematics/00_intro.tex index 6c73910..19c431c 100644 --- a/electives/others/amr/parts/01_kinematics/00_intro.tex +++ b/electives/others/amr/parts/01_kinematics/00_intro.tex @@ -1,6 +1,33 @@ \subsection{Positioning} \shortdefinition[Position Vector] $_{\color{blue}\fbox{W}}\,\vec{t}\,_{\color{red}\fbox{B}} = \, _{\color{blue}\fbox{W}}\,\vec{t}\,_{\color{ForestGreen}\fbox{W}}\,_{\color{red}\fbox{B}}$, -{\color{blue} Original Frame}, {\color{red} End point}, {\color{ForestGreen} Target Frame} +{\color{blue} Original Frame}, {\color{red} End point}, {\color{ForestGreen} Target Frame}, +\hl{$\sin = s$, $\cos = c$} \shortdefinition[State vector] $x_R$: $x$, $v$ of rob in $W$, pos of sensors + +\shortdefinition[Rot. Mat.] $\mat{R}_{z} = \begin{bmatrix} + c(\psi) & -s(\psi) & 0 \\ + s(\psi) & c(\psi) & 0 \\ + 0 & 0 & 1 + \end{bmatrix}$\\ +$\mat{R}_y(\theta) = \begin{bmatrix} + c(\psi) & 0 & s(\psi) \\ + 0 & 1 & 0 \\ + -s(\psi) & 0 & c(\psi) \\ + \end{bmatrix} + \mat{R}_x(\varphi) + \begin{bmatrix} + 1 & 0 & 0 \\ + 0 & c(\psi) & -s(\psi) \\ + 0 & s(\psi) & c(\psi) + \end{bmatrix}$ + +\shortremark Application: ${_W} \vec{a} = \mat{R}_{WB} {_B} \vec{a}$ + +\shortlemma $\mat{R}_{BW} = \mat{R}_{WB}^{-1} = \mat{R}_{WB}^\top$, $\det(\mat{R}_{WB}) = 1$ (orth.) + +\shortremark Cols of $\mat{R}_{WB}$ are basis vec. of Frame $\underset{\rightarrow}{\cF}{_B}$ in $\underset{\rightarrow}{\cF}{_W}$ + +\shortdefinition[Euler Angles] Yaw ($z$), Pitch ($y$), Roll ($x$), mult. rotation matrices, e.g. +$\mat{R}_{EB} = \mat{R}_z(\psi) \cdot \mat{R}_y(\theta) \cdot \mat{R}_x(\varphi)$, \hl{bound.}