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talk/dehaeze21_mechatronics_approach_nass_talk.org
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talk/dehaeze21_mechatronics_approach_nass_talk.pdf
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talk/dehaeze21_mechatronics_approach_nass_talk.tex
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% Created 2021-07-20 mar. 14:23
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% Intended LaTeX compiler: pdflatex
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\documentclass[aspectratio=169, t]{clean-beamer}
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\usepackage[utf8]{inputenc}
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\usepackage[T1]{fontenc}
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\usepackage{graphicx}
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\usepackage{grffile}
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\usepackage{longtable}
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\usepackage{wrapfig}
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\usepackage{rotating}
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\usepackage[normalem]{ulem}
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\usepackage{amsmath}
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\usepackage{textcomp}
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\usepackage{amssymb}
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\usepackage{capt-of}
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\usepackage{hyperref}
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\usepackage[most]{tcolorbox}
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\usepackage{bm}
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\usepackage{booktabs}
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\usepackage{tabularx}
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\usepackage{array}
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\usepackage{siunitx}
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\usepackage{mathtools}
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\author[shortname]{Thomas Dehaeze \inst{1,2}, Julien Bonnefoy \inst{1} \and Christophe Collette \inst{2,3}}
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\institute[shortinst]{\inst{1} European Synchrotron Radiation Facility, Grenoble, France \and %
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\inst{2} Precision Mechatronics Laboratory, University of Liege, Belgium \and %
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\inst{3} BEAMS Department, Free University of Brussels, Belgium}
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\vspace{-0.5em}
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\titlegraphic{\includegraphics[height=1.5cm]{figs/logo_pml_full.pdf} \hspace{5em} %
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\includegraphics[height=1.5cm]{figs/logo_esrf.pdf} \hspace{5em} %
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\includegraphics[height=1.5cm]{figs/logo_medsi.pdf}}
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\beamertemplatenavigationsymbolsempty
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\addtobeamertemplate{navigation symbols}{}{%
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\usebeamerfont{footline}%
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\usebeamercolor[fg]{footline}%
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\hspace{1em}%
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\insertframenumber/\inserttotalframenumber
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}
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\setbeamertemplate{itemize items}[circle]
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\usefonttheme[onlymath]{serif}
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\AtBeginSection[]{
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\begin{frame}<beamer>{Outline}
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\tableofcontents[currentsection, hideothersubsections, sectionstyle=show/shaded]
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\end{frame}
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}
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\makeatletter
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\preto\Gin@extensions{gif,}
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\DeclareGraphicsRule{.gif}{png}{.png}{\noexpand\Gin@base.png}
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\preto\Gin@extensions{png,}
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\DeclareGraphicsRule{.png}{pdf}{.pdf}{\noexpand\Gin@base.pdf}
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\makeatother
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\setbeamertemplate{bibliography item}[text]
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\DeclareSIUnit\rms{rms}
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\usetheme{default}
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\author{Dehaeze Thomas, Bonnefoy Julien and Collette Christophe}
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\date{}
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\title{Mechatronics Approach for the Development of a Nano-Active-Stabilization-System}
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\subtitle{MEDSI2020, July 26-29, 2021}
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\hypersetup{
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pdfauthor={Dehaeze Thomas, Bonnefoy Julien and Collette Christophe},
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pdftitle={Mechatronics Approach for the Development of a Nano-Active-Stabilization-System},
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pdfkeywords={},
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pdfsubject={},
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pdfcreator={Emacs 27.2 (Org mode 9.5)},
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pdflang={English}}
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\begin{document}
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\maketitle
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\section*{Introduction}
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\begin{frame}[label={sec:org4b0545d}]{The ID31 Micro Station}
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\begin{center}
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\includegraphics[scale=1,width=\linewidth]{figs/assemblage.png}
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\end{center}
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\textbf{Objective}: Position samples along complex trajectories with high precision\newline
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\textbf{Stacked Positioning Stages}: \(\approx 10\,\mu m\) precision limited by stages vibrations, thermal effects, ground motion, \ldots{}
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\end{frame}
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\begin{frame}[label={sec:orgb7c2959}]{Introduction - The Nano Active Stabilization System}
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\textbf{Objective}: Improve the position accuracy from \(\approx 10\,\mu m\) down to \(\approx 10\,nm\) \newline
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\textbf{Design approach}: ``Model based design'' (extensive use of models and test benches)
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\begin{center}
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\includegraphics[scale=1,width=\linewidth]{figs/nass-concept.pdf}
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\end{center}
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\end{frame}
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\begin{frame}[label={sec:orgaf8e005}]{The Nano-Hexapod - Why such mechanical architecture?}
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\begin{itemize}
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\item Why stewart architecture
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\begin{itemize}
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\item 6 DoF to control / 6 actuators
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\end{itemize}
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\item Only flexible elements
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\begin{itemize}
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\item no backlash
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\item no play
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\end{itemize}
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\item How it is working
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\begin{itemize}
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\item Jacobian matrix both for actuation and sensing
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\end{itemize}
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\item Forward / Inverse kinematics : meaning. Easy to compute for small displacements
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\item[{$\square$}] Schematic of Stewart platform
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\end{itemize}
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\begin{center}
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\includegraphics[scale=1,width=\linewidth]{figs/nano_hexapod_elements.red.pdf}
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\end{center}
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\end{frame}
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\begin{frame}[label={sec:orgb9ee458}]{Stewart Platforms Architecture}
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\vspace{-2em}
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\begin{columns}
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\begin{column}{0.5\columnwidth}
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\begin{figure}[htbp]
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\centering
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\includegraphics[scale=1,width=\linewidth]{figs/stewart_schematic.png}
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\caption{\label{fig:stewart_schematic}Geometry of a Stewart Platform}
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\end{figure}
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\vspace{-1em}
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\begin{tcolorbox}[title=Advantages]
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\begin{itemize}
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\item Compact
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\item Allows 6dof motion
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\item Can be ``monolithic''
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\end{itemize}
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\end{tcolorbox}
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\end{column}
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\begin{column}{0.5\columnwidth}
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\begin{tcolorbox}[title=Definition of the Geomtry]
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\begin{itemize}
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\item \(\bm{a}_i\): position of the attachment points on the fixed base
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\item \(\bm{b}_i\): position of moving attachment points
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\item \(l_i\): length of each limb
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\item \(\hat{\bm{s}}_i\): unit vector representing the direction of each limb
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\end{itemize}
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\end{tcolorbox}
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\end{column}
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\end{columns}
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\end{frame}
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\begin{frame}[label={sec:org09981cc}]{Stewart Platform Architecture - Kinematics}
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\begin{itemize}
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\item \(\bm{\mathcal{L}} = \left[ l_1, l_2, \ldots, l_6 \right]^T\): vector of actuated joint coordinates
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\item \(\bm{\mathcal{X}} = \left[ {}^A\bm{P}, \bm{}^A\hat{\bm{s}} \right]^T\): vector of platform motion variables
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\end{itemize}
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\begin{align*}
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\bm{\mathcal{X}} & \xrightarrow[\text{Simple}]{\text{Inverse Kinematics}} \bm{\mathcal{L}} \\
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\bm{\mathcal{L}} & \xrightarrow[\text{Complex}]{\text{Forward Kinematics}} \bm{\mathcal{X}}
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\end{align*}
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For small displacements: \textbf{Jacobian} matrix
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\begin{equation*}
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\bm{J} = \begin{bmatrix}
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{\hat{\bm{s}}_1}^T & (\bm{b}_1 \times \hat{\bm{s}}_1)^T \\
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{\hat{\bm{s}}_2}^T & (\bm{b}_2 \times \hat{\bm{s}}_2)^T \\
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{\hat{\bm{s}}_3}^T & (\bm{b}_3 \times \hat{\bm{s}}_3)^T \\
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{\hat{\bm{s}}_4}^T & (\bm{b}_4 \times \hat{\bm{s}}_4)^T \\
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{\hat{\bm{s}}_5}^T & (\bm{b}_5 \times \hat{\bm{s}}_5)^T \\
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{\hat{\bm{s}}_6}^T & (\bm{b}_6 \times \hat{\bm{s}}_6)^T
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\end{bmatrix}
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\end{equation*}
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\begin{align*}
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\delta\bm{\mathcal{L}} &= \bm{J} \delta\bm{\mathcal{X}} \\
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\delta\bm{\mathcal{X}} &= \bm{J}^{-1} \delta\bm{\mathcal{L}}
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\end{align*}
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As an example, for the Nano-Hexapod:
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\begin{equation*}
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\bm{J} = \begin{bmatrix*}[r]
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0.69 & -0.38 & 0.61 & -0.13 & -0.10 & 0.08 \\
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-0.69 & -0.38 & 0.61 & -0.13 & 0.10 & -0.08 \\
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||||
-0.02 & 0.80 & 0.61 & 0.15 & -0.06 & 0.08 \\
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||||
0.68 & -0.41 & 0.61 & -0.02 & -0.16 & -0.08 \\
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-0.68 & -0.41 & 0.61 & -0.02 & 0.16 & 0.08 \\
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0.02 & 0.80 & 0.61 & 0.15 & 0.06 & -0.08
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\end{bmatrix*}, \quad \bm{J}^{-1} = \begin{bmatrix*}[r]
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0.84 & -0.84 & -1.00 & -0.15 & 0.15 & 1.00 \\
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0.66 & 0.66 & 0.39 & -1.06 & -1.06 & 0.39 \\
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0.27 & 0.27 & 0.27 & 0.27 & 0.27 & 0.27 \\
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-4.51 & -4.51 & 0.12 & 4.39 & 4.39 & 0.12 \\
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2.46 & -2.46 & -5.14 & -2.67 & 2.67 & 5.14 \\
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1.96 & -1.96 & 1.96 & -1.96 & 1.96 & -1.96
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\end{bmatrix*}
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\end{equation*}
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\begin{itemize}
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\item[{$\square$}] Control architecture in the frame of the legs with the Jacobian matrix
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\end{itemize}
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\end{frame}
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\begin{frame}[label={sec:orgec6681e}]{Control Challenges - Analogy}
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\vspace{-2em}
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\only<1>{
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\begin{center}
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\includegraphics[scale=1,width=\linewidth]{figs/001_Room.pdf}
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\end{center}
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}\only<2>{
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\begin{center}
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\includegraphics[scale=1,width=\linewidth]{figs/002_Analogies.pdf}
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\end{center}
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}\only<3>{
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\begin{center}
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\includegraphics[scale=1,width=\linewidth]{figs/003_Laser.pdf}
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\end{center}
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}\only<4>{
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\begin{center}
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\includegraphics[scale=1,width=\linewidth]{figs/004_Top-Platform.pdf}
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\end{center}
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}\only<5>{
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\begin{center}
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\includegraphics[scale=1,width=\linewidth]{figs/005_Candle.pdf}
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\end{center}
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}\only<6>{
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\begin{center}
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\includegraphics[scale=1,width=\linewidth]{figs/006_Objective and Challenges.pdf}
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\end{center}
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}\only<7>{
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\begin{center}
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\includegraphics[scale=1,width=\linewidth]{figs/007_Truck.pdf}
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\end{center}
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}\only<8>{
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\begin{center}
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\includegraphics[scale=1,width=\linewidth]{figs/008_Trampoline.pdf}
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\end{center}
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}\only<9>{
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\begin{center}
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\includegraphics[scale=1,width=\linewidth]{figs/009_Spindle.pdf}
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\end{center}
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}\only<10>{
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\begin{center}
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\includegraphics[scale=1,width=\linewidth]{figs/010_Metrology.pdf}
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\end{center}
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}\only<11>{
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\begin{center}
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\includegraphics[scale=1,width=\linewidth]{figs/011_Flame.pdf}
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\end{center}
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}
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\end{frame}
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\begin{frame}[label={sec:orgd25c78f}]{Overview of the Mechatronic Approach - Model Based Design}
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\vspace{-1em}
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\begin{center}
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\includegraphics[scale=1,width=\linewidth]{figs/nass-mechatronics-approach.png}
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\end{center}
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\end{frame}
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\begin{frame}[label={sec:org4f4bab3}]{Outline}
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\tableofcontents
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\end{frame}
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\end{document}
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