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+% Created 2021-07-20 mar. 14:23
+% Intended LaTeX compiler: pdflatex
+\documentclass[aspectratio=169, t]{clean-beamer}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{graphicx}
+\usepackage{grffile}
+\usepackage{longtable}
+\usepackage{wrapfig}
+\usepackage{rotating}
+\usepackage[normalem]{ulem}
+\usepackage{amsmath}
+\usepackage{textcomp}
+\usepackage{amssymb}
+\usepackage{capt-of}
+\usepackage{hyperref}
+\usepackage[most]{tcolorbox}
+\usepackage{bm}
+\usepackage{booktabs}
+\usepackage{tabularx}
+\usepackage{array}
+\usepackage{siunitx}
+\usepackage{mathtools}
+\author[shortname]{Thomas Dehaeze \inst{1,2}, Julien Bonnefoy \inst{1} \and Christophe Collette \inst{2,3}}
+\institute[shortinst]{\inst{1} European Synchrotron Radiation Facility, Grenoble, France \and %
+\inst{2} Precision Mechatronics Laboratory, University of Liege, Belgium \and %
+\inst{3} BEAMS Department, Free University of Brussels, Belgium}
+\vspace{-0.5em}
+\titlegraphic{\includegraphics[height=1.5cm]{figs/logo_pml_full.pdf} \hspace{5em} %
+\includegraphics[height=1.5cm]{figs/logo_esrf.pdf} \hspace{5em} %
+\includegraphics[height=1.5cm]{figs/logo_medsi.pdf}}
+\beamertemplatenavigationsymbolsempty
+\addtobeamertemplate{navigation symbols}{}{%
+\usebeamerfont{footline}%
+\usebeamercolor[fg]{footline}%
+\hspace{1em}%
+\insertframenumber/\inserttotalframenumber
+}
+\setbeamertemplate{itemize items}[circle]
+\usefonttheme[onlymath]{serif}
+\AtBeginSection[]{
+\begin{frame}<beamer>{Outline}
+\tableofcontents[currentsection, hideothersubsections, sectionstyle=show/shaded]
+\end{frame}
+}
+\makeatletter
+\preto\Gin@extensions{gif,}
+\DeclareGraphicsRule{.gif}{png}{.png}{\noexpand\Gin@base.png}
+\preto\Gin@extensions{png,}
+\DeclareGraphicsRule{.png}{pdf}{.pdf}{\noexpand\Gin@base.pdf}
+\makeatother
+\setbeamertemplate{bibliography item}[text]
+\DeclareSIUnit\rms{rms}
+\usetheme{default}
+\author{Dehaeze Thomas, Bonnefoy Julien and Collette Christophe}
+\date{}
+\title{Mechatronics Approach for the Development of a Nano-Active-Stabilization-System}
+\subtitle{MEDSI2020, July 26-29, 2021}
+\hypersetup{
+ pdfauthor={Dehaeze Thomas, Bonnefoy Julien and Collette Christophe},
+ pdftitle={Mechatronics Approach for the Development of a Nano-Active-Stabilization-System},
+ pdfkeywords={},
+ pdfsubject={},
+ pdfcreator={Emacs 27.2 (Org mode 9.5)}, 
+ pdflang={English}}
+\begin{document}
+
+\maketitle
+\section*{Introduction}
+\begin{frame}[label={sec:org4b0545d}]{The ID31 Micro Station}
+\begin{center}
+\includegraphics[scale=1,width=\linewidth]{figs/assemblage.png}
+\end{center}
+
+\textbf{Objective}: Position samples along complex trajectories with high precision\newline
+\textbf{Stacked Positioning Stages}: \(\approx 10\,\mu m\) precision limited by stages vibrations, thermal effects, ground motion, \ldots{}
+\end{frame}
+
+\begin{frame}[label={sec:orgb7c2959}]{Introduction - The Nano Active Stabilization System}
+\textbf{Objective}: Improve the position accuracy from \(\approx 10\,\mu m\) down to \(\approx 10\,nm\) \newline
+\textbf{Design approach}: ``Model based design'' (extensive use of models and test benches)
+
+\begin{center}
+\includegraphics[scale=1,width=\linewidth]{figs/nass-concept.pdf}
+\end{center}
+\end{frame}
+
+\begin{frame}[label={sec:orgaf8e005}]{The Nano-Hexapod - Why such mechanical architecture?}
+\begin{itemize}
+\item Why stewart architecture
+\begin{itemize}
+\item 6 DoF to control / 6 actuators
+\end{itemize}
+\item Only flexible elements
+\begin{itemize}
+\item no backlash
+\item no play
+\end{itemize}
+\item How it is working
+\begin{itemize}
+\item Jacobian matrix both for actuation and sensing
+\end{itemize}
+\item Forward / Inverse kinematics : meaning. Easy to compute for small displacements
+\item[{$\square$}] Schematic of Stewart platform
+\end{itemize}
+
+\begin{center}
+\includegraphics[scale=1,width=\linewidth]{figs/nano_hexapod_elements.red.pdf}
+\end{center}
+\end{frame}
+
+\begin{frame}[label={sec:orgb9ee458}]{Stewart Platforms Architecture}
+\vspace{-2em}
+
+\begin{columns}
+\begin{column}{0.5\columnwidth}
+\begin{figure}[htbp]
+\centering
+\includegraphics[scale=1,width=\linewidth]{figs/stewart_schematic.png}
+\caption{\label{fig:stewart_schematic}Geometry of a Stewart Platform}
+\end{figure}
+
+\vspace{-1em}
+
+\begin{tcolorbox}[title=Advantages]
+\begin{itemize}
+\item Compact
+\item Allows 6dof motion
+\item Can be ``monolithic''
+\end{itemize}
+\end{tcolorbox}
+\end{column}
+
+\begin{column}{0.5\columnwidth}
+\begin{tcolorbox}[title=Definition of the Geomtry]
+\begin{itemize}
+\item \(\bm{a}_i\): position of the attachment points on the fixed base
+\item \(\bm{b}_i\): position of moving attachment points
+\item \(l_i\): length of each limb
+\item \(\hat{\bm{s}}_i\): unit vector representing the direction of each limb
+\end{itemize}
+\end{tcolorbox}
+\end{column}
+\end{columns}
+\end{frame}
+
+\begin{frame}[label={sec:org09981cc}]{Stewart Platform Architecture - Kinematics}
+\begin{itemize}
+\item \(\bm{\mathcal{L}} = \left[ l_1, l_2, \ldots, l_6 \right]^T\): vector of actuated joint coordinates
+\item \(\bm{\mathcal{X}} = \left[ {}^A\bm{P}, \bm{}^A\hat{\bm{s}} \right]^T\): vector of platform motion variables
+\end{itemize}
+
+\begin{align*}
+\bm{\mathcal{X}} & \xrightarrow[\text{Simple}]{\text{Inverse Kinematics}}  \bm{\mathcal{L}} \\
+\bm{\mathcal{L}} & \xrightarrow[\text{Complex}]{\text{Forward Kinematics}} \bm{\mathcal{X}}
+\end{align*}
+
+For small displacements: \textbf{Jacobian} matrix
+\begin{equation*}
+  \bm{J} = \begin{bmatrix}
+    {\hat{\bm{s}}_1}^T & (\bm{b}_1 \times \hat{\bm{s}}_1)^T \\
+    {\hat{\bm{s}}_2}^T & (\bm{b}_2 \times \hat{\bm{s}}_2)^T \\
+    {\hat{\bm{s}}_3}^T & (\bm{b}_3 \times \hat{\bm{s}}_3)^T \\
+    {\hat{\bm{s}}_4}^T & (\bm{b}_4 \times \hat{\bm{s}}_4)^T \\
+    {\hat{\bm{s}}_5}^T & (\bm{b}_5 \times \hat{\bm{s}}_5)^T \\
+    {\hat{\bm{s}}_6}^T & (\bm{b}_6 \times \hat{\bm{s}}_6)^T
+  \end{bmatrix}
+\end{equation*}
+
+\begin{align*}
+  \delta\bm{\mathcal{L}} &= \bm{J}      \delta\bm{\mathcal{X}} \\
+  \delta\bm{\mathcal{X}} &= \bm{J}^{-1} \delta\bm{\mathcal{L}}
+\end{align*}
+
+As an example, for the Nano-Hexapod:
+\begin{equation*}
+\bm{J} = \begin{bmatrix*}[r]
+ 0.69 & -0.38 & 0.61 & -0.13 & -0.10 &  0.08 \\
+-0.69 & -0.38 & 0.61 & -0.13 &  0.10 & -0.08 \\
+-0.02 &  0.80 & 0.61 &  0.15 & -0.06 &  0.08 \\
+ 0.68 & -0.41 & 0.61 & -0.02 & -0.16 & -0.08 \\
+-0.68 & -0.41 & 0.61 & -0.02 &  0.16 &  0.08 \\
+ 0.02 &  0.80 & 0.61 &  0.15 &  0.06 & -0.08
+\end{bmatrix*}, \quad \bm{J}^{-1} = \begin{bmatrix*}[r]
+ 0.84 & -0.84 & -1.00 & -0.15 &  0.15 &  1.00 \\
+ 0.66 &  0.66 &  0.39 & -1.06 & -1.06 &  0.39 \\
+ 0.27 &  0.27 &  0.27 &  0.27 &  0.27 &  0.27 \\
+-4.51 & -4.51 &  0.12 &  4.39 &  4.39 &  0.12 \\
+ 2.46 & -2.46 & -5.14 & -2.67 &  2.67 &  5.14 \\
+ 1.96 & -1.96 &  1.96 & -1.96 &  1.96 & -1.96
+\end{bmatrix*}
+\end{equation*}
+
+\begin{itemize}
+\item[{$\square$}] Control architecture in the frame of the legs with the Jacobian matrix
+\end{itemize}
+\end{frame}
+
+\begin{frame}[label={sec:orgec6681e}]{Control Challenges - Analogy}
+\vspace{-2em}
+
+\only<1>{
+
+\begin{center}
+\includegraphics[scale=1,width=\linewidth]{figs/001_Room.pdf}
+\end{center}
+
+}\only<2>{
+
+\begin{center}
+\includegraphics[scale=1,width=\linewidth]{figs/002_Analogies.pdf}
+\end{center}
+
+}\only<3>{
+
+\begin{center}
+\includegraphics[scale=1,width=\linewidth]{figs/003_Laser.pdf}
+\end{center}
+
+}\only<4>{
+
+\begin{center}
+\includegraphics[scale=1,width=\linewidth]{figs/004_Top-Platform.pdf}
+\end{center}
+
+}\only<5>{
+
+\begin{center}
+\includegraphics[scale=1,width=\linewidth]{figs/005_Candle.pdf}
+\end{center}
+
+}\only<6>{
+
+\begin{center}
+\includegraphics[scale=1,width=\linewidth]{figs/006_Objective and Challenges.pdf}
+\end{center}
+
+}\only<7>{
+
+\begin{center}
+\includegraphics[scale=1,width=\linewidth]{figs/007_Truck.pdf}
+\end{center}
+
+}\only<8>{
+
+\begin{center}
+\includegraphics[scale=1,width=\linewidth]{figs/008_Trampoline.pdf}
+\end{center}
+
+}\only<9>{
+
+\begin{center}
+\includegraphics[scale=1,width=\linewidth]{figs/009_Spindle.pdf}
+\end{center}
+
+}\only<10>{
+
+\begin{center}
+\includegraphics[scale=1,width=\linewidth]{figs/010_Metrology.pdf}
+\end{center}
+
+}\only<11>{
+
+\begin{center}
+\includegraphics[scale=1,width=\linewidth]{figs/011_Flame.pdf}
+\end{center}
+
+}
+\end{frame}
+
+\begin{frame}[label={sec:orgd25c78f}]{Overview of the Mechatronic Approach - Model Based Design}
+\vspace{-1em}
+
+\begin{center}
+\includegraphics[scale=1,width=\linewidth]{figs/nass-mechatronics-approach.png}
+\end{center}
+\end{frame}
+
+\begin{frame}[label={sec:org4f4bab3}]{Outline}
+\tableofcontents
+\end{frame}
+\end{document}