[AMR] Summarize W4 content

electives/others/amr/parts/01_kinematics/04_rigid-body-imu-kinematics.tex

@@ -46,5 +46,5 @@ $\displaystyle \vec{\dot{q}}_{WS} = \frac{1}{2} \vec{q}_{WS} \otimes
     where {\color{gray} gray parts} only IRL (in theor. models, leave out), with $\vec{\dot{b}}_g = \vec{w}_{b_g}$ and $\vec{\dot{b}}_a = \vec{w}_{b_a}$
 
 \bi{IMU Sensor Model}: $\vec{\tilde{z}} = \vec{b}_C + s\mat{M}\vec{z} + \vec{b} + \vec{n} + \vec{o}$
-where bias $\vec{b}$ and scale $s$ often modled as time-varying state $\dot{b}(t) = \sigma_C n(t)$.
-$\vec{b}_C$ const. calib. and $\vec{n}$ the model.
+where bias $\vec{b}$ and scale $s$ often modelled time-varying $\dot{b}(t) = \sigma_C n(t)$.
+$\vec{b}_C$ const. calib; $\mat{M}$ Misalignment; $\vec{n}$ noise; $\vec{o}$ other infl.

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

@@ -40,6 +40,7 @@
 \bi{Gen. eq. of Motion} $\dot{x}_1 = v\cos(\theta)$, $\dot{x}_2 = v\sin(\theta)$, $\dot{\theta} = \Omega$,
 with $v = 0.5\cdot(\omega_l r_l + \omega_r + r_r)$, $\Omega = \frac{\omega_r r_r - \omega_l r_l}{w}$
 
+% TODO: Consider adding wheel constraints (planar) here as well (from W05 slides)
 \textit{Straight}: $v = \omega_l r_l = \omega_r r_r$, $\Omega = 0$, $D = v\Delta t$.\\
 $\vec{b}_s = \begin{bmatrix}
         D \cos(\theta) \\

electives/others/amr/parts/02_Sensors-Actuators/00_intro.tex

@@ -0,0 +1,6 @@
+\bi{Meas. Model}: $\vec{z} = \vec{h}(\vec{x}) + \vec{v} + \vec{o}$, with $\vec{h}(\vec{x})$ deterministic mean, 
+$\vec{v}$ zero-mean noise, $\vec{o}$ unmodelled effects, $\vec{x}$ true state
+
+\bi{Motor encoders} Typ. 64-2048 incrm. per rev; Estim. rot
+
+\bi{Rolling-Shutter} Most CMOS sensors don't take full image at once, need time stamp for each row

electives/others/amr/parts/02_Sensors-Actuators/01_gps.tex

@@ -0,0 +1,7 @@
+\subsection{GNSS}
+Need ultra-precise time sync ($c \approx 0.3\; m/ns$). \bi{Errors}
+\begin{itemize}
+    \item Multipath problem (signal bounce) (0.5 - 100m)
+    \item Ionosphere delays (10m)
+    \item Satellite pos. err, trop. delay (1m)
+\end{itemize}

electives/others/amr/parts/02_Sensors-Actuators/02_actuators.tex

@@ -0,0 +1,17 @@
+\subsection{Actuators}
+\bi{Hydraulic} {\color{ForestGreen} acc., easy control, power}; {\color{red} maint., speed, price}
+
+\bi{Pneumatic} {\color{ForestGreen} price, shock abs., speed}; {\color{red} acc., loud, maint.}
+
+\subsubsection{DC Motor}
+\begin{wrapfigure}[4]{r}{0.32\columnwidth}
+    \includegraphics[width=0.32\columnwidth]{assets/dc-motor.png}
+\end{wrapfigure}
+(Kirchoff) $U_a = L_a \dot{I_a} + R_a I_a + U_i$
+
+(Torque, Lorenz Force) $T = k_T I_a$
+
+(Induced V, Faraday) $U_i = k_i \omega$
+
+(Mech. pow. eq. el. pow)\\
+$U_i I_a = k_i \omega I_a = T_\omega = k_T I_a \omega \Rightarrow k_i = k_T =: k$