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\usepackage{amsmath, amssymb} +\usepackage{tikz} +\usepackage{multicol} +\usetikzlibrary{arrows.meta, backgrounds, calc, fit, positioning, scopes, shadows} + + \mode \usetheme{Dresden} \definecolor{vulm}{HTML}{7d1dd3} \definecolor{yulm}{HTML}{ffe500} -\AtBeginSection[]{\begin{frame}{Plan}\tableofcontents[subsectionstyle=shaded/hide,sectionstyle=show/shaded]\end{frame}} +\AtBeginSection[]{\begin{frame}{Plan}\tableofcontents[sectionstyle=show/shaded]\end{frame}} \setbeamercolor{structure}{fg = vulm} \setbeamercolor{section in head/foot}{fg = yulm} @@ -27,43 +32,189 @@ \begin{frame} \frametitle{Petite Machine à Bois} - + \begin{figure} + \centering + \includegraphics[width=.9\textwidth]{images/cnc} + \caption{Une Petite Machine à Bois} + \label{fig:cnc} + \end{figure} \end{frame} \begin{frame} \frametitle{Format d'Entrée} - + On convertit un fichier \texttt{.svg} en fichier \texttt{.gc} qui est une abstraction des commandes à exécuter. + \begin{figure} + \centering + \begin{tikzpicture} + \draw[vulm, fill=yulm!30] (0, 0) rectangle +(2, 2) node[pos=.5] {\texttt{.svg}}; + \draw[vulm, ->] (2, 1) -- (3, 1); + \draw[vulm, fill=yulm!30] (3, 0) rectangle +(2, 2) node[pos=.5] {\texttt{.gc}}; + \draw[vulm, ->] (5, 1) -- (6, 1); + \draw[vulm, fill=yulm!30, double] (6, 0) rectangle +(2, 2) node[pos=.5] {\texttt{CNC}}; + \end{tikzpicture} + \end{figure} + \visible<2->{Le format GCode est standardisé, et indépendant des capacités de la machine.} \end{frame} +\tikzset{ + comp/.style = { + minimum width = 8cm, + minimum height = 4.5cm, + text width = 8cm, + inner sep = 0pt, + text = green, + align = center, + font = \Huge, + transform shape, + thick + }, + monitor/.style = {draw = none, xscale = 18/16, yscale = 11/9}, + display/.style = {shading = axis, left color = black!60, right color = black}, + ut/.style = {fill = gray} +} + +\tikzset{ + computer/.pic = { + % screen (with border) + \node(-m) [comp, pic actions, monitor] + {\phantom{\parbox{\linewidth}{\tikzpictext}}}; + % display (without border) + \node[comp, pic actions, display] {\tikzpictext}; + \begin{scope}[x = (-m.east), y = (-m.north)] + % filling the lower part + \path[pic actions, draw = none] + ([yshift=2\pgflinewidth]-0.1,-1) -- (-0.1,-1.3) -- (-1,-1.3) -- + (-1,-2.4) -- (1,-2.4) -- (1,-1.3) -- (0.1,-1.3) -- + ([yshift=2\pgflinewidth]0.1,-1); + % filling the border of the lower part + \path[ut] + (-1,-2.4) rectangle (1,-1.3) + (-0.9,-1.4) -- (-0.7,-2.3) -- (0.7,-2.3) -- (0.9,-1.4) -- cycle; + % drawing the frame of the whole computer + \path[pic actions, fill = none] + (-1,1) -- (-1,-1) -- (-0.1,-1) -- (-0.1,-1.3) -- (-1,-1.3) -- + (-1,-2.4) coordinate(sw)coordinate[pos=0.5] (-b west) -- + (1,-2.4) -- (1,-1.3) coordinate[pos=0.5] (-b east) -- + (0.1,-1.3) -- (0.1,-1) -- (1,-1) -- (1,1) -- cycle; + % node around the whole computer + \node(-c) [fit = (sw)(-m.north east), inner sep = 0pt] {}; + \end{scope} + } +} + \begin{frame} \frametitle{Communication} - + \begin{figure} + \centering + \hfill + \begin{minipage}{.5\textwidth} + \begin{tikzpicture} + \pic(comp0) [ + draw, fill = gray!30, pic text = {Contrôleur de Petite Machine à Bois}, scale=.3 + ] {computer}; + \coordinate (cnc) at ($(comp0-c.south) + (0, -1)$); + \path (comp0-c.east) edge [loop right, min distance=.7cm, in=330, out=30, looseness=8, -{Latex[width=3mm]}, vulm] node[right, vulm, rectangle, fill=yulm!30, draw=vulm] {GCode} (comp0-c.east); + \draw[vulm, fill=yulm!30] ($(cnc) + (-1, 0)$) rectangle +(2, -1) node[pos=0.5] {Socket}; + \draw[vulm, ->, double] ($(comp0-c.south) + (0.2, 0)$) --node[anchor=west, vulm]{$\omega_{c}$} ($(cnc.north) + (0.2, 0)$); + \draw[vulm, <-, double] ($(comp0-c.south) + (-0.2, 0)$) --node[anchor=east, vulm]{$\theta$} ($(cnc.north) + (-0.2, 0)$); + \draw[vulm, ->, double] ($(cnc) + (0.2, -1)$) -- node[anchor=west, vulm]{$\omega_{c}$} ($(cnc) + (0.2, -2)$);; + \draw[vulm, <-, double] ($(cnc) + (-0.2, -1)$) -- node[anchor=east, vulm]{$\theta$} ($(cnc) + (-0.2, -2)$);; + \draw[vulm, fill=yulm!30] ($(cnc) + (-2, -2)$) rectangle +(4, -1) node[pos=0.5] {Petite Machine à Bois}; + \end{tikzpicture} + \end{minipage} + \hfill + \begin{minipage}{.4\textwidth} + \begin{tikzpicture}[scale=.5] + \node[vulm, font=\small] (top) at (0, 0) {\parbox{.9\linewidth}{\textbf{Contrôleur:} traduit le GCode et envoie les vitesses de commande $\omega_{c}$ pour les moteurs.}}; + \node[vulm, font=\small] (mid) at ($(top.south) + (0, -2)$) {\parbox{.9\linewidth}{\textbf{Socket:} sert d'intermédiaire pour la connexion (CNC).}}; + \node[vulm, font=\small] (bot) at ($(mid.south) + (0, -2)$) {\parbox{.9\linewidth}{\textbf{Petite Machine à Bois:} envoie les positions $\theta$ de ses moteurs pas-à-pas.}}; + \node[draw=vulm, thick, fit={(top) (mid) (bot)}, inner sep=3pt] (box) {}; + \end{tikzpicture} + \end{minipage} + \hfill + \end{figure} \end{frame} \section{Implémentation}\label{sec:l'implementation} \begin{frame} - \frametitle{Contrôleur} + \frametitle{Traducteur} + On agit simplement ligne par ligne, voici quelques commandes: + \begin{center} + \begin{minipage}{.95\textwidth} + \begin{multicols}{2} + \begin{itemize} + \item[G0:] Aller au point donné; + \item[G1:] Aller au point donné, en coupant au passage; + \item[G2,G3:] Faire un arc de cercle, en sens trigonométrique ou non; + \item[G4:] Dormir; + \item[G5:] Suivre une courbe de Bézier cubique. Permet d'en suivre plusieurs d'affilée de manière dérivable; + \item[G20:] WTF IS A KILOMETER; + \item[G21:] Changer d'unité en mm; + \item[G28:] Retourner à la maison; + \item[G30:] Retourner à la maison, en passant par un point donné. + \end{itemize} +\end{multicols} +\end{minipage} +\end{center} +\end{frame} +\begin{frame} + \frametitle{Module de Contrôle Hardware} + Le module Hardware du contrôleur maintient une représentation mémoire de la position \emph{théorique} de la tête, transmise au contrôleur. + Il demande à la socket (et donc au \emph{vrai} hardware) les positions mesurées des moteurs pas-à-pas. + \begin{figure} + \centering + \begin{tikzpicture} + \draw[vulm, fill=yulm!30] (0, 0) rectangle +(2, 1) node[pos=0.5] (h) {Hardware}; + \draw[vulm, fill=yulm!30] (6, 0) rectangle +(2, 1) node[pos=0.5] (c) {Contrôleur}; + \draw[vulm, fill=yulm!30] (0, -2) rectangle +(2, 1) node[pos=0.5] (s) {Socket}; + \draw[vulm, ->] ($(h.east) + (.2, 0.1)$) -- node[above, vulm] {Position $\rho$ \& Cible $\tau$} ($(c.west) + (-0.1, 0.1)$); + \draw[vulm, <-] ($(h.east) + (.2, -0.1)$) -- node[below, vulm] {Déplacement $\Gamma_{c}$} ($(c.west) + (-0.1, -0.1)$); + \draw[vulm, ->] ($(h.south) + (.1, -.3)$) -- node[right, vulm] {$\omega_{c}$} ($(s.north) + (.1, 0.3)$); + \draw[vulm, <-] ($(h.south) + (-.1, -.3)$) -- node[left, vulm] {$\theta$} ($(s.north) + (-.1, 0.3)$); + \end{tikzpicture} + \end{figure} + Il envoie ensuite à la socket pour envoyer les vitesses de commandes traduites dans la spécification des moteurs. +\end{frame} + +\begin{frame} + \frametitle{Contrôleur en Vitesse} + Dans une première approximation, on poursuit le point de contrôle à vitesse constante. + On calcule $\delta = \rho - \tau$. + Selon le signe de $\delta_{x}$ (resp. $y, z$) on définit $\omega_{c}$ la vitesse de commande de sorte que: + \begin{equation*} + \norm{\omega_{c}} = 1 \text{ et } \left(\omega_{c}\right)_{x} \leq \texttt{FAST_XY_FEEDRATE} \text{(resp. $y, z$)} + \end{equation*} + Un contrôleur plus poussé est obtenu en ajoutant une proportionnalité par rapport à l'écart \emph{théorie - mesure}. \end{frame} \begin{frame} \frametitle{Simulateur} - + Pour modéliser la Petite Machine à Bois, on construit un simulateur physique simple. + On discrétise le temps par: + \begin{equation*} + \Delta t = t\left( \text{dernière requête reçue} \right) - t\left( \text{dernière requête traitée} \right) + \end{equation*} + On a ensuite par le PFD: + \begin{equation*} + \dot{J_{\omega}} = \underset{\text{Inertie}}{-f\omega} + \underset{\text{Couple Commande}}{\left( \omega_{c} - \omega_{t} \right)}, \text{d'où } \omega_{t + 1} = \omega_{t} + \Delta t \left( -f\omega + \left( \omega_{c} - \omega_{t} \right) \right) + \end{equation*} + On introduit par ailleurs un terme d'erreur lié aux frottements, et on peut encore raffiner le modèle. \end{frame} \section{Réalisme} \begin{frame} - \frametitle{Connexion} - -\end{frame} - -\begin{frame} - \frametitle{Précision} - + \frametitle{Connexion et Précision} + L'utilisation d'une socket et d'un modèle théorique restreint comme intermédiaire permet de prendre en compte, durant les phases de test, les différents facteurs d'erreurs pouvant intervenir durant l'exécution: + \begin{itemize} + \item Une connexion trop volatile; + \item Des erreurs liées au glissement des moteurs pas-à-pas; + \item Des erreurs liées à la dureté du matériau à couper, et à son anisotropie. + \end{itemize} \end{frame} \end{document}