From 9ea73f249690d8d9a29b9f58cce007834b4c83ed Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Sun, 26 Jul 2026 08:48:28 +0200 Subject: [PATCH] [AMR] Fix errors --- .../autonomous-mobile-robots-cheatsheet.pdf | Bin 653494 -> 653546 bytes .../amr/parts/00_basics/02_trigonometry.tex | 2 ++ .../parts/00_basics/03_error-propagation.tex | 1 + .../parts/02_Sensors-Actuators/00_intro.tex | 3 ++- .../02_Sensors-Actuators/04_depth-range.tex | 1 + .../05_kalman-filter.tex | 1 - .../amr/parts/04_vision/00_keypoints.tex | 2 +- electives/amr/parts/04_vision/03_mapping.tex | 1 - 8 files changed, 7 insertions(+), 4 deletions(-) diff --git a/electives/amr/autonomous-mobile-robots-cheatsheet.pdf b/electives/amr/autonomous-mobile-robots-cheatsheet.pdf index 93567cca69083033be5c70bb12b821c7db2637da..566745c4da5bd070126957ca08b094b6c4236401 100644 GIT binary patch delta 56283 zcmV)1K+V6l@h9r>C$Je20y#F5u?8o9?R{yJ8#j{Zcl`>^zK9)mSga}BC_B9IWckwA 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a/electives/amr/parts/00_basics/02_trigonometry.tex +++ b/electives/amr/parts/00_basics/02_trigonometry.tex @@ -5,3 +5,5 @@ \shortdefinition[Orthogonal vec] $v^\top w = 0$ \shortdefinition[Determinant] $ad - bc$ for mat $[a, b; c, d]$ + +\shortdefinition[Vec Line Eq] $\vec{p} + \lambda \vec{d}$ diff --git a/electives/amr/parts/00_basics/03_error-propagation.tex b/electives/amr/parts/00_basics/03_error-propagation.tex index 2870350..cf0482f 100644 --- a/electives/amr/parts/00_basics/03_error-propagation.tex +++ b/electives/amr/parts/00_basics/03_error-propagation.tex @@ -1,3 +1,4 @@ \subsection{Error Propagation} +\label{sec:error-propagation} For functions $\vec{f}(\vec{x}) = \mat{A}\vec{x}$, the \bi{linear error propagation} is given by $\Sigma^f = A \Sigma^x \A^\top$, with $\Sigma^x$ the uncertanty of $\vec{x}$ (covariance mat.) diff --git a/electives/amr/parts/02_Sensors-Actuators/00_intro.tex b/electives/amr/parts/02_Sensors-Actuators/00_intro.tex index 500cfca..acd91e8 100644 --- a/electives/amr/parts/02_Sensors-Actuators/00_intro.tex +++ b/electives/amr/parts/02_Sensors-Actuators/00_intro.tex @@ -1,7 +1,8 @@ \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. +$\vec{h}(\vec{x})$ describes how to compute $x$ from known values (e.g. Intercept-Theorem). +Probabilistic M.M: use rand var in def, and s. \ref{sec:error-propagation} \bi{Motor encoders} Typ. 64-2048 incrm. per rev; Estim. rot diff --git a/electives/amr/parts/02_Sensors-Actuators/04_depth-range.tex b/electives/amr/parts/02_Sensors-Actuators/04_depth-range.tex index 9a76fb6..9981261 100644 --- a/electives/amr/parts/02_Sensors-Actuators/04_depth-range.tex +++ b/electives/amr/parts/02_Sensors-Actuators/04_depth-range.tex @@ -1,4 +1,5 @@ \subsection{Depth and Range sensing} +Typ. derive D.M. with sensor dir param (as vec line eq) \subsubsection{Triangulation-based} \bi{Struct. Light} Single cam, single projector: {\color{ForestGreen}Spatial acc}, {\color{red} no worky in bright light, interference with other IR depth cams} diff --git a/electives/amr/parts/03_multi-sensor-estimation/05_kalman-filter.tex b/electives/amr/parts/03_multi-sensor-estimation/05_kalman-filter.tex index b3372f7..5ae652e 100644 --- a/electives/amr/parts/03_multi-sensor-estimation/05_kalman-filter.tex +++ b/electives/amr/parts/03_multi-sensor-estimation/05_kalman-filter.tex @@ -9,7 +9,6 @@ $\vec{x}_k = \mat{F}\vec{x}_{k - 1} + \mat{G}\vec{u}_k + \mat{L}\vec{w}_k$ with \item \bi{Covariance} $\mat{P}_{k | k - 1} = \mat{F} \mat{P}_{k - 1 | k - 1} \mat{F}^\top + \mat{L} \mat{Q}_{k} \mat{L}^\top$ \end{itemize} \bi{Update} Lin. meas.: $\tilde{\vec{z}}_k = \mat{H}\vec{x}_k + \vec{v}_k$ with $\vec{v_k} \sim \cN(\vec{0}, \mat{R}_k)$: -\newpage \begin{itemize} \item \bi{Meas. residual}: $\vec{y}_k = \tilde{\vec{z}}_k - \mat{H} \hat{\vec{x}}_{k | k - 1}$ \item \bi{Resid. Cov}: $\mat{S}_k = \mat{H}\mat{P}_{k | k - 1} \mat{H}^\top \mat{R}_k$ diff --git a/electives/amr/parts/04_vision/00_keypoints.tex b/electives/amr/parts/04_vision/00_keypoints.tex index 690460a..01eeaa5 100644 --- a/electives/amr/parts/04_vision/00_keypoints.tex +++ b/electives/amr/parts/04_vision/00_keypoints.tex @@ -1,6 +1,6 @@ \subsection{Keypoints} \bi{Corner det.} $SSD(\Delta x, \Delta y) \approx [\Delta_x \; \Delta_y] \mat{M} [\Delta_x \; \Delta_y]^\top$ -with $\mat{M} = \mat{R}^\top \text{diag}(\lambda_1, \lambda_2) \mat{R}$; $\lambda_i$ E.V. of $M$; $\kappa$ const 0.04-0.15; +with $\mat{M} = \mat{R}^\top \text{diag}(\lambda_1, \lambda_2) \mat{R}$; $\lambda_i$ E.V. of $M$; $\kappa$ const 0.04-0.15;\\ $\mat{R} = \det(M) - \kappa \cdot \text{TR}(M)^2 = \lambda_1\lambda_2 - \kappa(\lambda_1 + \lambda_2)^2$;\\ $M = \sum_{x, y \in P} {\scriptsize diff --git a/electives/amr/parts/04_vision/03_mapping.tex b/electives/amr/parts/04_vision/03_mapping.tex index 9c5fb0c..e1980ad 100644 --- a/electives/amr/parts/04_vision/03_mapping.tex +++ b/electives/amr/parts/04_vision/03_mapping.tex @@ -1,4 +1,3 @@ -\newpage \subsection{Mapping} \bi{Problem Formulations} \textit{Localisation} {\scriptsize (always static given map)}:\\ $\vec{x}^*_{R, k} = \text{argmax}\; \P(x_{R, k} \divider \vec{x}_M, \vec{z}_{1 : k}, \vec{u}_{1 : k})$ (recursive)\\