[AMR] Reduce font size, some additions

electives/amr/autonomous-mobile-robots-cheatsheet.tex

@@ -1,4 +1,4 @@
-\documentclass{article}
+\documentclass[9pt]{extarticle}
 
 \PassOptionsToPackage{skip=0pt}{parskip}
 \input{~/projects/latex/janishutz-helpers.tex}
@@ -16,6 +16,7 @@
 \renewcommand{\theoremShortNamingEN}{Thm}
 
 \renewcommand{\descriptorNameDisplay}[1]{\textbf{#1}}
+\renewcommand{\backgroundPadding}{1pt}
 
 \fboxsep 1pt
 \fboxrule 0.1pt
@@ -47,8 +48,7 @@
 \section{Introduction}
 \input{parts/00_basics/00_probability.tex}
 \input{parts/00_basics/01_measurement-models.tex}
-% TODO: Add this (especially law of cosines)
+\input{parts/00_basics/02_trigonometry.tex}
-% \input{parts/00_basics/02_trigonometry.tex}
 
 \section{Locomotion \& Kinematics}
 \input{parts/01_kinematics/00_intro.tex}
@@ -86,6 +86,7 @@
 \input{parts/04_vision/04_dense-tracking_loop-closure.tex}
 % \input{parts/04_vision/}
 
+% TODO: Probably remove pseudocode
 \section{Planning \& Control}
 \input{parts/05_planning-control/00_feedback-control/00_siso-mimo.tex}
 \input{parts/05_planning-control/00_feedback-control/01_pid.tex}

electives/amr/parts/00_basics/02_trigonometry.tex

@@ -1,3 +1,7 @@
-\subsection{Trigonometry}
+\subsection{Trigonometry \& Linear Algebra}
-% TODO: Cosine rule (at least), probably also sine rule.
+\shortdefinition[Rule of cosines] $c^2 = a^2 + b^2 - 2ab \cos(\gamma)$
+
 % TODO: Add convenient results (such as cos2 + sin2 = 1)
+\shortdefinition[Orthogonal vec] $v^\top w = 0$
+
+\shortdefinition[Determinant] $ad - bc$ for mat $[a, b; c, d]$

electives/amr/parts/01_kinematics/01_forward.tex

@@ -1,15 +1,16 @@
 \subsection{Forward Kinematics (FK)}
-$\mat{T}_{WB_n}(\vec{\theta}) = \mat{T}_{WB_0} \mat{T}_{B_0B_1}(\theta_1) \cdots \mat{T}_{B_{n - 1}B_n}(\theta_n)$.\\
+$\mat{T}_{WB_n}(\vec{\theta}) = \mat{T}_{WB_0} \mat{T}_{B_0B_1}(\theta_1) \cdots \mat{T}_{B_{n - 1}B_n}(\theta_n)$.
-For 2R system:
+
-${_W}\vec{t}_{WE} =$
+For 2R system: ${_W}\vec{t}_{WE} =$
 {\scriptsize
 $ \begin{bmatrix}
         L_1 \cos(\theta_1) + L_2 \cos(\theta_1 + \theta_2) \\
         L_1 \sin(\theta_1) + L_2 \sin(\theta_1 + \theta_2)
     \end{bmatrix}$\\
 }
-Similar for $n$R sys (more angles). Wspc $W$ $\theta_1, \theta_2 \in [-\pi, \pi]$.
+Workspace $W$: $\theta_1, \theta_2 \in [-\pi, \pi]$.
-Last dim may be sum of angles. Jacobian: see \ref{sec:ms-lin}
+Similar for $n$R sys (more angles, more lengths).
+For 2D move in 3D space, last dim is sum of angles (or equiv). \bi{Jacobian}: see \ref{sec:ms-lin}
 
 \shortdefinition[Singularity] Loss of deg of Freed. $\det(\mat{J}(\vec{\theta})) = 0$
 % TODO: Determinant computation

electives/amr/parts/01_kinematics/06_wheeled-robot.tex

@@ -4,13 +4,18 @@
 \end{wrapfigure}
 \bi{Non-holonomic} systems \textbf{not integrable}, no inst. move in every direct.
 
-\bi{Wheel constraints} $v_i = \omega_i r_i$
+\bi{Wheel constraints} $v_i = \omega_i r_i$ ($r_i$ constraints)
-
 \begin{itemize}
     \item \textit{Driving straight} all $\vec{v}$ equal
-    \item \textit{Turning} Wheel axis must intersect the \bi{Instant Centre of Rotation} (ICR),
+    \item \textit{Turning} Wheel axis must intersect the \bi{Instant Centre of Rotation} (ICR) of vehicle,
-          speeds: $v_i \div R_i = \Omega$ ($R_i$ = dist. wheel-ICR; $\Omega$: vehicle body rotation rate)
+          speeds: $v_i \div R_i = \Omega$ ($R_i$ = dist. wheel-ICR; $\Omega$: vehicle rotation rate (around ICR))
 \end{itemize}
+Below: $\alpha$, $l$ pos in frame, $\beta$ rot at that pos ($z$-ax).
+To compute $\vec{c}$ in $\vec{c} \cdot {_B}\vec{v}_{WB} = \omega$
+(For multiple wheels, construct mat. from this)
+
+$c_i = [\sin(\alpha + \beta) \div r, -\cos(\alpha + \beta) \div r, -\cos(\beta) \cdot l \div r]$
+
 
 \bi{Maneuverability}
 \begin{itemize}

electives/amr/parts/03_multi-sensor-estimation/00_linearization.tex

@@ -2,7 +2,7 @@
 \label{sec:ms-lin}
 $\vec{f}(\vec{x}) \approx \vec{f}(\vec{\overline{x}}) + \mat{J}_{\vec{f}} \big|_{x = \overline{x}}(\vec{x} - \vec{\overline{x}})$, $f'$, no vec in 1D; $\vec{\overline{x}}$ lin. p.
 
-\shortdefinition[Jac.] $\mat{J}_{\vec{f}}$ rows for eq of $\vec{f}$ cols for vars of each eq.
+\shortdefinition[Jac.] $\mat{J}_{\vec{f}}$ rows for eq of $\vec{f}$; cols for vars of each eq.
 
 Part. diff; Approx. using finite differences $\frac{f(\overline{x} + h) - f(\overline{x})}{h}$,\\
 or central differences (vector of $\frac{\vec{f}(\vec{\overline{x}}) + h_i \vec{e_i}}{h_i}$, with $\vec{e_i}$ unit vec)