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[AMR] Various fixes, error propagation, more explanations

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janishutz
2026-07-24 16:09:47 +02:00
parent 1f4727d9f3
commit 2dabc055f0
8 changed files with 15 additions and 10 deletions
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electives/amr/parts/02_Sensors-Actuators/00_intro.tex
+4 -2
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@@ -1,5 +1,7 @@
\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
\label{sec:sensors}
\bi{Meas. Model}: $\vec{z} = \vec{h}(\vec{x}) + \vec{v} + \vec{o}$, with $\vec{h}(\vec{x})$ determ. mean,
$\vec{v}$ zero-mean noise, $\vec{o}$ unmodelled effects, $\vec{x}$ true state.
$\vec{h}(\vec{x})$ describes how to compute $x$ from known values.
\bi{Motor encoders} Typ. 64-2048 incrm. per rev; Estim. rot
electives/amr/parts/02_Sensors-Actuators/02_actuators.tex
+1 -1
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@@ -13,5 +13,5 @@
(Induced V, Faraday) $U_i = k_i \omega$
(Mech. pow. eq. el. pow)\\
(Mech. pow. $=$ electric power)\\
$U_i I_a = k_i \omega I_a = T_\omega = k_T I_a \omega \Rightarrow k_i = k_T =: k$
electives/amr/parts/02_Sensors-Actuators/03_cameras.tex
+3 -5
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@@ -7,12 +7,10 @@ $\begin{bmatrix}
\begin{bmatrix}
x & y
\end{bmatrix}^\top$
with $f$ the distance to the lens and $z$ the full distance
with $f$ the distance to the lens and $z$ the distance from object
\newpage
$u = c_u + f \cdot x'$ and $v = c_v + f \cdot y'$ where $x' = t_x \div t_z$ and $y' = t_y \div t_z$
where $u, v$ are the pixel $x, y$ coords, $\vec{c} = [c_u, c_v]^\top$ is optical centre of cam in pixel coords, $f$ scale factor,
% and $\vec{{_C}\vec{t}_P} = [t_x, t_y, t_z]^\top$
where $u, v$ are the pixel $x, y$ coords, $\vec{c} = [c_u, c_v]^\top$ is optical centre of cam in pixel coords, $f$ scale factor.
The full proj:
$\vec{u} =
@@ -34,7 +32,7 @@ $\vec{u} =
}
= \mat{K}\; {_C}\vec{t}_P$
If p. in diff frame ${_W} \vec{t}_P$, then $\vec{u} = \mat{K}[\mat{R}_{CW}\; {_C}\vec{t}_{CW}] {_W}\vec{t}_P$
If p. in diff frame, e.g. $W$-frame then $\vec{u} = \mat{K}[\mat{R}_{CW}\; {_C}\vec{t}_{CW}] {_W}\vec{t}_P$
\subsubsection{Pinhole Camera Projection with distortion}
\shortdefinition Model: $\vec{u} = \vec{k}(\vec{d}(\vec{p}({_C}\vec{t}_P)))$, with ($\vec{c}$ as above):