diff --git a/doc/beamer.pdf b/doc/beamer.pdf new file mode 100644 index 0000000..55e6542 Binary files /dev/null and b/doc/beamer.pdf differ diff --git a/doc/compte_rendu/LogoCS.png b/doc/compte_rendu/LogoCS.png new file mode 100644 index 0000000..fad0ef4 Binary files /dev/null and b/doc/compte_rendu/LogoCS.png differ diff --git a/doc/compte_rendu/biblio.bib b/doc/compte_rendu/biblio.bib new file mode 100644 index 0000000..6bd418a --- /dev/null +++ b/doc/compte_rendu/biblio.bib @@ -0,0 +1,50 @@ +@misc{photo_drone, + title = {Fotogallery {\textbar} {Parrot} {Bebop} {Drone}}, + howpublished = "\url{https://www.thedigeon.com/it/robot/fotogallery-parrot-bebop-drone.html}", + url = {https://www.thedigeon.com/it/robot/fotogallery-parrot-bebop-drone.html}, + abstract = {Parrot Bebop Drone pesa appena 390 grammi, è del 25 per cento più compatto del modello AR.Drone, è robusto, grazie al corpo in abs che contiene il 15\% di fibra di vetro ed è dotato di 11 + 11 minuti di autonomia di volo, grazie alle due batterie ai polimeri di litio di serie (1.200 mAh).Cliccate sul simbolo a X nella barra di controllo grigia della fotogallery per vedere le foto a tutto schermo}, + urldate = {2019-05-25}, + journal = {The Digeon}, + keywords = {projet2a} +} + +@misc{zieg_nic, + title = {PI Controller Design (Ziegler-Nichols) and Unit Step Response Graphing for 4th order system}, + howpublished = "\url{https://electronics.stackexchange.com/questions/396028/pi-controller-design-ziegler-nichols-and-unit-step-response-graphing-for-4th-o}", + urldate = {2019-05-25}, + } + +@misc{wiki_ros, + title = {Documentation ROS}, + howpublished = "\url{http://wiki.ros.org/}", + } + +@misc{scipy, + title = {Documentation Scipy}, + howpublished = "\url{https://docs.scipy.org/doc/}", + } + +@misc{sav_gol, + title = {Savitzky-Golay filter}, + howpublished = "\url{https://en.wikipedia.org/wiki/Savitzky\%E2\%80\%93Golay_filter}", + } + +@misc{freq_ech, + title = {Reading from Bebop}, + howpublished = "\url{https://bebop-autonomy.readthedocs.io/en/latest/reading.html}", +} + +@misc{zieg_nic_premier, + title = {Ziegler-Nichols Tuning Rules for PID}, + howpublisehd = "\url{http://www.mstarlabs.com/control/znrule.html}", +} + +@misc{gitlab_frezza, + title= {Gitlab du projet initial}, + howpublisehd = "\url{https://gitlab.centralesupelec.fr/frezza/drone_demo}" +} + +@misc{julia, + title={Langage Julia}, + howpublished = "\url{https://julialang.org}" +} \ No newline at end of file diff --git a/doc/compte_rendu/chap_conclusion.tex b/doc/compte_rendu/chap_conclusion.tex new file mode 100644 index 0000000..03f4c3f --- /dev/null +++ b/doc/compte_rendu/chap_conclusion.tex @@ -0,0 +1,14 @@ +\chapter{Conclusion} + +L'objectif du projet est atteint. L'asservissement en position du drone est désormais bien plus stable. En outre, le script \verb|control_compute.py| peut aisément être réutilisé dans d'autres projets avec ROS pour implémenter facilement des modules de contrôle. + +Ce projet a également été l'occasion pour nous de découvrir et de nous familiariser avec ROS, en plus de mettre en pratique de nombreux cours de Supélec (Génie logiciel, Signaux et Systèmes, Automatique et Commande d'entraînements à vitesse variable notamment). + +Nous souhaitons en particulier remercier messieurs \bsc{Frezza-Buet} et \bsc{Gutzwiller} pour leur accompagnement et leurs conseils tout au long du projet. + +L'intégralité du travail réalisé pour ce projet peut être retrouvé à cette adresse : \url{https://gitlab.rezometz.org/klafyvel/drone-rigide}. Les codes ont été testés sous Ubuntu 18.04 avec la version de ROS "melodic" sous une architecture 64 bits. Si à l'avenir le dépôt se trouvait indisponible, les auteurs peuvent être contactés : + +\begin{description} + \item[Joanne \bsc{Steiner}] \verb|joannesteiner@hotmail.fr| + \item[Hugo \bsc{Levy--Falk}] \verb|me@klafyvel.me| +\end{description} \ No newline at end of file diff --git a/doc/compte_rendu/chap_configuration.tex b/doc/compte_rendu/chap_configuration.tex new file mode 100644 index 0000000..c12641e --- /dev/null +++ b/doc/compte_rendu/chap_configuration.tex @@ -0,0 +1,20 @@ +\chapter{Utilisation et génération des fichiers de configuration} +\label{chap:configuration} +À plusieurs reprises lors de notre projet, nous avons eu à utiliser des fichiers de configuration. + +Ce type de fichier nous a permis de définir des paramètres et de générer une fenêtre dans laquelle nous pouvons les régler en direct. Nos fichiers de configuration débutent par : +\begin{minted}{python} +#!/usr/bin/env python +PACKAGE = "detect_targets" + +from dynamic_reconfigure.parameter_generator_catkin import * + +gen = ParameterGenerator() +\end{minted} + +Nous allons donc utiliser dynamic\_reconfigure afin de créer un générateur de paramètres. Dans ce fichier, l'ajout d'un paramètre dans le générateur se déroulera toujours de la même façon : +\begin{minted}{python} + gen.add("name",type,0,"description",default value, min, max) +\end{minted} + +Cela nous a permis de générer de nouveaux paramètres et de les régler à la main tout au long du projet. \ No newline at end of file diff --git a/doc/compte_rendu/chap_export.tex b/doc/compte_rendu/chap_export.tex new file mode 100644 index 0000000..0f16456 --- /dev/null +++ b/doc/compte_rendu/chap_export.tex @@ -0,0 +1,37 @@ +\chapter{Export du relevé de position} +\label{chap:export} +\section{Relevé} +ROS permet, grâce à la commande \verb|rosbag| d'exporter les données publiées sur un topic ROS pour les jouer plus tard. Pour cela on peut utiliser la commande : + +\begin{minted}{bash} +rosbag record -O record.bag +\end{minted} + +où \verb|| est le topic à enregistrer. + +Après avoir lancé \mintinline{bash}|roscore|, on enregistre la sortie dans un format que le script de l'annexe \ref{chap:test_filter} accepte. +\begin{minted}{bash} +rostopic echo | python3 parse_topic.py +\end{minted} + +Le script \verb|parse_topic.py| accepte plusieurs arguments. + +\begin{minted} +Usage: parse_topic.py [OPTIONS] + +Options: + --output TEXT Output file + --time / --no-time Add the number of seconds + --field TEXT YAML field to store + --help Show this message and exit. +\end{minted} + +On peut alors, dans un autre terminal, jouer l'enregistrement avec la commande suivante. +\begin{minted}{bash} +rosbag play record.bag +\end{minted} + +Enfin, on peut arrêter le script \mintinline{bash}|parse_topic.py| en pressant \verb|Ctrl + C|. + +\section{Script \mintinline{bash}|parse_topic.py|} +\inputminted[frame=lines,linenos,breaklines=true]{python}{scripts/parse_topic.py} \ No newline at end of file diff --git a/doc/compte_rendu/chap_generation.tex b/doc/compte_rendu/chap_generation.tex new file mode 100644 index 0000000..04f4866 --- /dev/null +++ b/doc/compte_rendu/chap_generation.tex @@ -0,0 +1,3 @@ +\chapter{Génération des images afin de vérifier le script pour trouver la cible, script \mintinline{bash}{test_find_targets.py}} +\label{chap:test_find_targets} +\inputminted[frame=lines,linenos,breaklines=true]{python}{scripts/test_find_targets.py} \ No newline at end of file diff --git a/doc/compte_rendu/chap_installation.tex b/doc/compte_rendu/chap_installation.tex new file mode 100644 index 0000000..c83b382 --- /dev/null +++ b/doc/compte_rendu/chap_installation.tex @@ -0,0 +1,92 @@ +\chapter{Installation de ROS et du projet} +\label{chap:installation_projet} + +Tout d'abord, il faut installer ROS sur votre machine \cite{wiki_ros}. Afin d'installer ROS et les modules nécessaires à l'utilisation du projet, nous allons nous référer au tutoriel de M. Frezza-Buet disponible sur son site. + +Suivez le lien suivant http://wiki.ros.org/ROS/Installation afin d'installer ROS sur votre machine. Lors de notre projet, nous avons utilisé la version suivante : ROS Melodic Morenia qui était alors la plus récente disponible. + +Une fois ROS installé, installez les "catkins tools" qui permettront de créer des espaces de travail ROS +\begin{minted}{bash} +sudo apt install python-catkin-tools +\end{minted} + +Créez un workspace sur lequel vous enregistrerez le projet : +\begin{minted}{bash} +cd ~ +mkdir -p drone-rigide/src +cd drone-rigide/src +\end{minted} + +Procédez à l'installation de bebop\_autonomy : +\begin{minted}{bash} +sudo apt-get install build-essential python-rosdep +\end{minted} + +Récupérez également le dépôt teleop-tools, nécessaire à l'utilisation de bebop\_autonomy : +\begin{minted}{bash} +git clone https://github.com/ros-teleop/teleop_tools +\end{minted} + +Procédez à l'installation de Parrot-ARSDK et indiquez enfin le chemin de Parrot-ARSDK pour bebop\_autonomy : +\begin{minted}{bash} +sudo apt install ros-melodic-parrot-arsdk +export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/opt/ros/melodic/lib/parrot_arsdk +git clone https://github.com/AutonomyLab/bebop_autonomy.git bebop_autonomy +\end{minted} + +Pensez à copier le répertoire \verb|bebop_driver| qui se trouve dans \verb|bebop_autonomy| dans le répertoire \verb|src|. + +\begin{minted}{bash} +cp -r bebop_autonomy/bebop_driver ./ +\end{minted} + +Attention à la version de ROS qui n'est pas forcément melodic. + +Installez vq2 + +\begin{minted}{bash} +https://github.com/HerveFrezza-Buet/vq2 +\end{minted} + +Ramenez les modules du projet sur votre workspace : +\begin{minted}{bash} +git clone https://gitlab.rezometz.org/klafyvel/drone-rigide +\end{minted} + +Récupérez le dépôt Gitlab de M. Frezza-Buet suivant : +\begin{minted}{bash} +git clone https://github.com/HerveFrezza-Buet/demo-teleop +git clone https://github.com/HerveFrezza-Buet/vqimg +\end{minted} +Ce module permet de contrôler le drone à l'aide du clavier et de reprendre la main sur ce dernier à tout instant. + +Il faut maintenant procéder à la compilation. Tout d'abord, indiquez sous quelle version de ROS vous travaillez (à adapter à votre version) : +\begin{minted}{bash} +source /opt/ros/melodic/setup.bash +\end{minted} + +Puis compilez votre workspace : +\begin{minted}{bash} +cd ~/drone-rigide +catkin build +\end{minted} + +Désormais, à chaque fois que vous ouvrirez un nouveau terminal pour travailler sous ROS, il faudra indiquer au terminal sous quel version de ROS vous voulez travailler et dans quel workspace. Pour cela, écrivez la commande suivante : +\begin{minted}{bash} +source ~/drone-rigide/devel/setup.bash +\end{minted} + +Ouvrez un terminal et lancez : +\begin{minted}{bash} +roscore +\end{minted} + +Dans un nouveau terminal, placez-vous dans drone-rigide/src : +\begin{minted}{bash} +cd drone-rigide/src +\end{minted} + +Et lancez le fichier \verb|simple_loop.launch| par l'instruction suivante : +\begin{minted}{bash} +roslaunch detect_targets/launch/simple_loop.launch +\end{minted} \ No newline at end of file diff --git a/doc/compte_rendu/chap_introduction.tex b/doc/compte_rendu/chap_introduction.tex new file mode 100644 index 0000000..c17d6a0 --- /dev/null +++ b/doc/compte_rendu/chap_introduction.tex @@ -0,0 +1,7 @@ +\chapter{Introduction} + +Le campus de Metz de CentraleSupélec dispose de drones quadricoptères Bebop 2 (Parrot). Ces derniers sont capables de réaliser des mouvements brusques ce qui rend leur pilotage complexe. Il faut donc les manipuler avec précautions, ce qui revient à sous-exploiter leurs capacités. + +Jusqu'à présent, le drone était asservi à l'aide d'une cible présente dans son champ visuel. Le drone suivait la cible (bleue) et se positionnait en face de cette dernière. Toutefois, le drone se déplaçait lentement et se montrait prudent. De plus, une fois face à la cible, le drone n'était pas stable. Il oscillait verticalement face à la cible. Ce résultat avait été obtenu suite à un projet d'élèves. + +L'objectif de ce projet est donc de rendre l'asservissement du drone plus "rigide" afin de mieux exploiter les capacités de ce dernier. \ No newline at end of file diff --git a/doc/compte_rendu/chap_modelisation.tex b/doc/compte_rendu/chap_modelisation.tex new file mode 100644 index 0000000..82c07fa --- /dev/null +++ b/doc/compte_rendu/chap_modelisation.tex @@ -0,0 +1,115 @@ + +\chapter{Modélisation du problème} + +\section{Modélisation mécanique} + + +\begin{figure}[h!] + \centering + \includegraphics[width=\linewidth]{images/modelisation/drone_axes.png} + \caption{Axes du drone parrot \cite{photo_drone}} + \label{fig:drone_axes} +\end{figure} + +Le contrôle du drone selon les différents axes (figure \ref{fig:drone_axes}) n'est pas identique. Ainsi on contrôle le drone en vitesse pour la translation et la rotation sur l'axe z, alors que le contrôle sur les axes x et y s'effectue par l'inclinaison de la machine. + +\subsection{Axe z} + +Les drones BeBop nous permettent de spécifier directement une vitesse en rotation et en translation sur l'axe $z$. L'asservissement interne du drone se chargeant de faire respecter la consigne. On a donc une une réponse fréquencielle de la forme de celle de la figure \ref{fig:bode_z}. On peut alors assimiler la fonction de transfert sur cet axe à un simple intégrateur dans notre domaine fréquentiel de travail. Pour la correction, on pourra utiliser un simple PID. + +\begin{figure}[h!] + \centering + \includegraphics[width=0.5\linewidth]{images/modelisation/bode_z.eps} + \caption{Diagramme de Bode simplifié de la réponse sur l'axe $z$} + \label{fig:bode_z} +\end{figure} + +\subsection{Axes x et y} + +Les axes x et y ayant des comportements similaires, nous pouvons les assimiler à un axe $u$ pour les calculs. On suppose que les moteurs du drone fournissent une force de portance constante $\vec{F}_m$ et que le drone doit faire face à une force de frottements fluides $\vec{F}_f=-\alpha \dot{u}$. + +\begin{figure}[h!] + \centering + \includegraphics[width=\linewidth]{images/modelisation/forces.eps} + \caption{Modélisation des forces appliquées au drone dans le cas d'une translation dans le sens positif de $\vec{u}$} + \label{fig:forces} +\end{figure} + +En appliquant le principe fondamental de la dynamique dans le cadre des forces appliquées dans le schéma de la figure \ref{fig:forces}, on a : + +\begin{eqnarray} + m \ddot{u} &=& \sin{(\theta)} F_{m} - \alpha \dot{u} +\end{eqnarray} + +Dans le domaine de Laplace, et en se plaçant dans le domaine des faibles inclinaisons, on a donc : + +\begin{eqnarray} + m p^2 u &=& \theta F_{m} - \alpha p u \\ + u &=& \frac{F_{m}}{\alpha p(\frac{m}{\alpha}p + 1)} \theta +\end{eqnarray} + +Ce qui donne un diagramme de Bode similaire à celui de la figure \ref{fig:bode_u}. + +\begin{figure}[h!] + \centering + \includegraphics[width=0.5\linewidth]{images/modelisation/bode_u.eps} + \caption{Diagramme de Bode simplifié de la réponse sur l'axe $u$} + \label{fig:bode_u} +\end{figure} + +Malheureusement, nous ne connaissons pas le paramètre $\alpha$. Cependant, d'après M. Frezza, à pleine vitesse, le drone met plusieurs seconde à atteindre sa vitesse limite (correspondant à la fréquence à laquelle la fonction de transfert peut être assimilée à un simple intégrateur). On peut donc supposer que pour les fréquences de travail du cadre de ce projet, les axes $x$ et $y$ se comportent comme des doubles intégrateurs. C'est pourquoi le correcteur qui semble adapté pour ces deux axes est un correcteur Proportionnel Dérivé. + +\section{Modélisation primaire de l'asservissement} + +On peut dans un premier temps modéliser l'asservissement de la manière de la figure \ref{fig:model_simple}. + +\begin{figure}[h!] +\centering +\begin{tikzpicture}[auto, node distance=2cm,>=latex'] +% We start by placing the blocks +\node [input, name=input] {}; +\node [sum, right of=input, node distance=3cm] (sum) {}; +\node [block, right of=sum] (controller) {Correcteur}; +\node [block, right of=controller, +node distance=3cm] (system) {Drone}; +% We draw an edge between the controller and system block to +% calculate the coordinate u. We need it to place the measurement block. +\draw [->] (controller) -- node[name=u] {$u$} (system); +\node [output, right of=system, node distance=5cm] (output) {}; +\node [block, below of=u] (measurements) {Mesure}; + +% Once the nodes are placed, connecting them is easy. +\draw [draw,->] (input) -- node {position attendue} (sum); +\draw [->] (sum) -- node {$\epsilon$} (controller); +\draw [->] (system) -- node [name=y] {position réelle du drone}(output); +\draw [->] (y) |- (measurements); +\draw [->] (measurements) -| node[pos=0.99] {$-$} +node [near end] {mesure de la position} (sum); +\end{tikzpicture} +\caption{Modélisation simple de l'asservissement} +\label{fig:model_simple} +\end{figure} + +Le drone diffuse un flux optique, qui permet de calculer sa position vis-à-vis d'une cible. La mesure peut se décomposer en trois éléments, comme le montre la figure \ref{fig:decomp_mesure}. + +\begin{figure}[h!] + \centering + \begin{tikzpicture}[auto, node distance=3cm,>=latex'] + % We start by placing the blocks + \node [input, name=input] {}; + \node [block, right of=input] (cam) {Caméra}; + \node [block, right of=cam] (transm) {Transmission}; + \node [block, right of=transm] (trait) {Traitement}; + \node [output, right of=system] (output) {}; + % We draw an edge between the controller and system block to + % calculate the coordinate u. We need it to place the measurement block. + \draw [->] (input) -- (cam); + \draw [->] (cam) -- (transm); + \draw [->] (transm) -- (trait); + \draw [->] (trait) -- (output); + \end{tikzpicture} + \caption{Décomposition de la mesure} + \label{fig:decomp_mesure} +\end{figure} + +Comme le traitement ne se fait pas directement sur le drone, il existe des retards aléatoires dûs au temps de transit sur le réseau, ainsi qu'au temps de calcul sur le poste de contrôle. Ces retards limitent la fréquence des mesures à environ 20Hz\cite{freq_ech}. \ No newline at end of file diff --git a/doc/compte_rendu/chap_probleme.tex b/doc/compte_rendu/chap_probleme.tex new file mode 100644 index 0000000..76c340b --- /dev/null +++ b/doc/compte_rendu/chap_probleme.tex @@ -0,0 +1,9 @@ +\chapter{Problèmes connus} +\label{chap:chap_probleme} + +Lors de notre projet, nous avons rencontré quelques difficultés liés à des problèmes rencontrés avec le matériel : +\begin{itemize} + \item les batteries sont peu performantes, elles ont une autonomie très faible (de l'ordre de la dizaine de minutes maximum lorsque le drone est en vol) ce qui implique d'avoir à redémarrer le drone de façon répétée; + \item sur les quatre drones présents dans la Smart Room, trois voient flou; + \item il arrive que l'image de la caméra se fige, il faut alors redémarrer le drone. +\end{itemize} \ No newline at end of file diff --git a/doc/compte_rendu/chap_realisation.tex b/doc/compte_rendu/chap_realisation.tex new file mode 100644 index 0000000..1844860 --- /dev/null +++ b/doc/compte_rendu/chap_realisation.tex @@ -0,0 +1,474 @@ +\chapter{Réalisation du projet} +\section{Prise en main de ROS et du drone présent à la smartroom} +Pour la prise en main de ROS, nous avons suivi les étapes du tutoriel de M. \bsc{Frezza-Buet}. Cela nous a permis de comprendre comment fonctionne ROS et de pouvoir l'utiliser de manière basique et simple. + +Pour installer et utiliser ROS, ainsi que notre projet, on pourra se référer à l'annexe \ref{chap:installation_projet}. + +\section{Réduction du bruit} +\subsection{Problème et solution liés au bruit causé par le calcul de la position du drone par rapport à l'image} +Nous avons constaté qu'une forte incertitude existait lors du calcul de la position du drone par rapport au panneau. En effet, celle-ci, même si le drone était immobile, bougeait beaucoup et faisait des "sauts". Il s'agissait d'un bruit de type de Poisson, difficile, voire impossible, à traiter en automatique pour obtenir un asservissement satisfaisant. En effet, le drone, avec ce bruit, y aurait été asservi, rendant impossible l'obtention d'une position fixe. Notre drone aurait fait de grands écarts par rapport à la position attendue. + +Afin de régler ce problème, l'idée proposée a été de modifier l'algorithme en place. Ce dernier calcule la position des trois carrés bleus dans l'image renvoyée par le drone par les position H, R et L. Cette détermination se faisait par gngt. Nous avons donc développé un nouveau script Python qui utilise la labellisation \cite{scipy} afin de déterminer la position des panneaux. + + +Dans cette partie, nous ne nous intéresserons qu'au fichier +\verb|find_targets.py|. Il permet, à partir d'un seuil RGB défini, de trouver les parties "bleues" de l'image\footnote{On pourrait cependant chercher d'autres couleurs en changeant les valeurs des seuils.}. Une fois ces positions trouvées, on ne garde que les trois plus grandes parties et on en calcule le centre de masse. Les résultats obtenus sont plutôt satisfaisants. +\subsection{Détails des fonctions exposées par \mintinline{bash}|find_targets.py|} +Le module contient deux fonctions. +\subsubsection{\mintinline{python}|find_targets|} + +Cette fonction prend en argument l'image dont on souhaite extraire la cible, des valeurs de seuil bleu, rouge et vert minimales et maximales, un booléen \verb|return_slices| qui indique s'il faut, ou non, retourner les slices localisant les limites de la cible et un booléen \verb|return_binary| qui indique s'il faut, ou non, retourne l'image binaire. Ce dernier sera utile pour régler des seuils lorsque, pas exemple, la couleur des cibles est modifiée. + +La fonction retourne les coordonnées des centres de masse des trois carrés de la cible sous la forme d'un tuple \verb|(H,L,R)| avec \verb|H| le point le plus haut, \verb|L| le point le plus à gauche et \verb|R| le point le plus à droite ainsi que les slices correspondant aux zones bleues le cas échéant\footnote{Cela permet de dessiner les rectangles, ce qui est utile lorsqu'on souhaite procéder à des vérifications}. + +La première étape de l'algorithme consiste à détecter tous les points répondant aux conditions de seuil définis dans les arguments de la fonction. Lorsqu'un pixel de l'image remplit les conditions, un 1 est placé sur ce pixel, sinon on y place un 0. On construit ainsi une matrice de 0 et de 1 correspondant aux points satisfaisant les critères de seuil. + +On définit ensuite une structure de labellisation. Pour cela, on utilise la matrice suivante : +$$ + \begin{bmatrix} +0 & 1 & 0 \\ +1 & 1 & 1 \\ +0 & 1 & 0 +\end{bmatrix} +$$ +Cette matrice permet de demander à l'algorithme de labellisation de considérer que deux pixels A et B sont dans la même surface si et seulement si le pixel B se trouve à gauche, à droite, au-dessus ou en-dessous du pixel B. L'algorithme numérote ensuite ces surfaces de manière unique. Nous récupérons ainsi l'image labellisée ainsi que le nombre de zones détectées. + +Dans le cas où moins de trois zones sont trouvées, on considère que la détection s'est mal déroulée et une erreur est levée. + +On récupère ensuite les zones détectées sous la forme d'une liste de 3-uplets \verb|(a[0],a[1],i)| où \verb|a[0]| et \verb|a[1]| sont les slices des zones (elles délimitent le parallélépipède le plus petit contenant la zone) et \verb|i| est le numéro de la zone. + +On trie ensuite les zones par aire et on ne garde que les trois zones ayant les aires les plus grandes. On suppose ici qu'aucune autre surface bleue importante, qui pourrait être confondue avec les cibles, ne sera présente sur notre image. + +Nous déterminons ensuite les centres de masse des zones trouvées grâce à \verb|center_of_mass|. + +Enfin, on trie les centre de masse selon l'axe vertical et on définit \verb|H| comme le point le plus haut. On trie les centres de masse restants selon l'axe horizontal et on définit \verb|L| par le point le plus à gauche et \verb|R| comme le point le plus à droite. On retrouve ainsi les trois centres de masse de la cible. On retourne ces derniers, avec leurs slices le cas échéant. +\subsubsection{\mintinline{python}|normalize_coordinates|} +Cette fonction prend en argument un point, la largeur et la hauteur d'une image et retourne des coordonnées \verb|(x,y)| normalisés. Cette fonction nous permet d'adapter le format des coordonnées renvoyés au code qui existait déjà. Il s'agit donc d'un changement de repère : on place l'origine au centre de l'image, on inverse l'axe y\footnote{Dans une image classique, l'axe y est orienté "vers le bas"} et on normalise les positions de manière à ce que la plus grande dimension (hauteur ou largeur) de l'image vaille 1. + +En posant $w$ la largeur, $h$ la hauteur et $j = max(w, h)$, cela revient à calculer les nouvelles coordonnées $(x', y')$ par la transformation affine de l'équation \ref{eq:normalisation}. +\begin{equation} + (x',y') = (x,y)\cdot\begin{pmatrix} +\frac{1}{j} & 0 \\ +0 & -\frac{1}{j} +\end{pmatrix}+ \left(-\frac{w}{2j}, \frac{h}{2j}\right) \label{eq:normalisation} +\end{equation} +\subsection{Conclusion et résultats} +Nous obtenons désormais une position bien plus stable du drone. Évidemment, le bruit n'a pas été totalement supprimé, mais il ne provoque plus de "sauts" dans la position et reste, en moyenne, autour de la position du drone. Le bruit restant est probablement causé par la qualité de l'image renvoyée par le drone et par le seuil que nous avons défini. Des résultats de l'algorithme sont donnés figure \ref{result}. Les positions des cibles seront ensuite publiées grâce au nœud \mintinline{bash}|target_publisher.py| dans un format compréhensible des nœuds de triangularisation. + +Ces résultats ont été obtenu à l'aide du script \verb|test_find_targets.py| donné en annexe \ref{chap:test_find_targets}. + +\begin{figure} + \centering + \includegraphics[width=\linewidth]{images/realisation/target.png} + \caption{Résultat de l'algorithme} + \label{result} +\end{figure} + +\FloatBarrier +\section{Premier asservissement sommaire} + + +Le premier asservissement qui a été réalisé n'utilisait qu'une seule boucle et asservissait la position du drone. On se référera à la modélisation mécanique réalisée précédemment. + +Pour ce premier asservissement sommaire, nous avons estimé la courbe de la réponse fréquentielle de notre drone afin d'en déduire le type de correcteur à utiliser. + +Nous savons que selon l'axe z, le drone répond seulement en vitesse. On peut approximer sa réponse fréquentielle par une pente nulle en basse fréquence, puis une pente \verb|[-1]| en haute fréquence. Afin d'asservir le drone, nous aurons donc besoin d'un correcteur de type proportionnel-intégral +\begin{equation} + C(p)=K_p + \frac{K_i}{p} +\end{equation} +Concernant les axes x et y, nous savons que le drone ne peut être correctement asservi en vitesse. En effet, le réglage de la vitesse et de l'accélération du drone se fait selon un angle d'inclinaison : le drone accélère en permanence s'il conserve le même angle ce qui ne permet pas le maintien d'une vitesse constante. La réponse fréquentielle selon ses axes est donc représentée par une pente de \verb|[-1]| dans les basses fréquence et une pente de \verb|[-2]| dans les hautes fréquences. Afin de corriger ces axes, nous allons donc utiliser une correction de type Proportionnelle-Dérivée : +\begin{equation} + C(p)=K_p+K_d p +\end{equation} + +\subsection{Script \mintinline{bash}|triangle_control.py|} + +Ce script reprend, en partie, le script provenant du projet initial qu'il est possible de retrouver sur le Gitlab de M. \bsc{Frezza-Buet} \cite{gitlab_frezza}. Nous l'avons adapté à notre projet et en avons repris les éléments principaux. Il utilise le fichier de configuration (Voir Annexe \ref{chap:configuration}) \verb|triangle_control.cfg| qui a également été repris, en partie, du projet initial. +La classe \verb|TriangleControl| implémente 6 méthodes : +\begin{description} + \item[\mintinline{python}|on_reconf|] Cette méthode permet, à partir du fichier de configuration, de définir les valeurs à donner aux différents paramètres des 4 PID, ainsi que les valeurs limites de l'accélération et de la vitesse du drone, l'angle de la caméra, la largeur et la longueur de la cible et la distance à laquelle on souhaite que le drone se trouve par rapport à la cible; + \item[\mintinline{python}|clear_controls|] : remet les erreurs à 0; + \item[\mintinline{python}|saturate_twist|] : limite la vitesse selon tous les axes; + \item[\mintinline{python}|on_comp|] : méthode qui n'a pas été modifié et qui permet de définir la position des trois rectangles bleus de la cible; + \item[\mintinline{python}|triangle|] : prend en paramètre les trois points de la cible et calcule la consigne de sortie à l'aide de la bibliothèque SimplePID de Python. +\end{description} + +\subsection{Conclusion sur l'utilisation d'une simple boucle} + +La régulation simple donne des résultats satisfaisants. Cependant quelques problèmes subsistent. Tout d'abord celui du dépassement. En effet la régulation étant linéaire, le dépassement est proportionnel à la consigne. Or si le drone se trouve à grande distance de la cible, le dépassement est tel que cette dernière finit par se trouver hors champ de la caméra, provoquant un comportement chaotique du drone. Une solution pour cela serait de saturer la vitesse du drone afin de limiter l'inertie, et donc le dépassement. D'autre part le système reste "assez lent", dans le sens où il ne donne pas vraiment le sentiment d'un asservissement rigide à la cible. Enfin, il serait intéressant de rendre notre code plus modulaire afin de pouvoir facilement changer la régulation dans un fichier \verb|.launch| de ROS. Afin de régler les deux premiers problèmes, nous choisissons d'implémenter une double régulation en vitesse pour laquelle nous développons une bibliothèque pour effectuer de l'automatique simple sous ROS + +\section{Développement de la bibliothèque d'automatique sous ROS} + +Nous avons développer une bibliothèque permettant de créer d'implémenter des PID sous ROS et de les régler dynamiquement par un protocole expérimental simple. Afin d'implémenter les correcteurs, nous avons créé des nœuds ROS que nous avons ensuite connectés dans des fichiers \verb|.launch|. + +L'idée est de créer plusieurs classes de nœuds dans un script Python dont les paramètres seront obtenus à l'aide de fichiers \verb|.cfg|. + +\subsection{Mesure de la vitesse} + +Afin d'implémenter la partie dérivée de nos PID, il faut pouvoir calculer la vitesse du drone. + +La mesure de vitesse doit se faire en dérivant la mesure de position. Cependant le bruit présent sur cette mesure empêche d'utiliser une dérivation naïve: en effet, on aurait alors de brusques sauts sur la valeur mesurée dus aux hautes fréquences dans le spectre du bruit. Afin d'obtenir une valeur lissée de la vitesse, on se propose d'utiliser un filtre de \bsc{Savitzky–Golay}. + +\subsubsection{Principe} + +Un filtre de \bsc{Savitzky–Golay} \cite{sav_gol} est un filtre à réponse impulsionnelle finie, qui correspond à une approximation locale du signal par un polynôme de degré faible. Ainsi, un filtre moyenneur est un filtre de \bsc{Savitzky–Golay} simple. Afin d'obtenir la réponse indicielle $[b_0, \dots b_n ]$ du filtre, on utilise la méthode des moindres carrés. En posant $((x_i,y_i))_{i\in\intervalleEntier{1}{n}}$ les $n$ points de la fenêtre, et en écrivant le polynôme d'approximation $a_0 + a_1 X + \dots + a_k X^k$, Cela revient donc à déterminer le jeu de coefficients $(a_0,\dots, a_k)$ qui minimise la grandeur de l'équation \ref{eq:moindrecarres_raw}. + +\begin{equation} +\left \| + \begin{pmatrix} + y_1 \\ + y_2 \\ + \vdots \\ + y_n + \end{pmatrix} + - + \begin{pmatrix} + 1 & x_1 & x_1 ^2 & \cdots & x_1 ^ k \\ + 1 & x_2 & x_2 ^2 & \cdots & x_2 ^ k \\ + \vdots & \vdots & \vdots & & \vdots \\ + 1 & x_n & x_n ^2 & \cdots & x_n ^ k + \end{pmatrix} + \cdot + \begin{pmatrix} + a_0 \\ + a_1 \\ + \vdots \\ + a_k + \end{pmatrix} +\right \| ^2 +\label{eq:moindrecarres_raw} +\end{equation} + +En supposant de plus que la fenêtre de points $((x_i,y_i))_{i\in\intervalleEntier{1}{k}}$ que l'on souhaite lisser est centrée en 0 (on peut toujours se ramener à ce cas par changement de variable), telle que les $x_i$ soient espacés régulièrement d'un pas $h$, et $k$ impair, on peut s'affranchir des valeurs prises par $(x_i)$ en calculant les $(a'_0,\dots, a'_k)$ qui minimisent +\begin{eqnarray} + L((y_k),(a_k)) &=& + \left \| + \underbrace{ + \begin{pmatrix} + y_1 \\ + y_2 \\ + \vdots \\ + y_n + \end{pmatrix}}_{=Y} + - + \underbrace{ + \begin{pmatrix} + 1 & -\floor{\frac{n}{2}} & \left(-\floor{\frac{n}{2}}\right) ^2 & \cdots & \left(-\floor{\frac{n}{2}}\right) ^ k \\ + 1 & \left(-\floor{\frac{n-1}{2}}\right) & \left(-\floor{\frac{n-1}{2}}\right) ^2 & \cdots & \left(-\floor{\frac{n-1}{2}}\right) ^ k \\ + \vdots & \vdots & \vdots & \vdots & \vdots \\ + 1 & -1 & \left(-1\right) ^2 & \cdots & \left(-1\right) ^ k \\ + 1 & 0 & 0 & \cdots & 0 \\ + 1 & \left(1\right) & \left(1\right) ^2 & \cdots & \left(1\right) ^ k \\ + \vdots & \vdots & \vdots & \vdots & \vdots \\ + 1 & \left(\floor{\frac{n-1}{2}}\right) & \left(\floor{\frac{n-1}{2}}\right) ^2 & \cdots & \left(\floor{\frac{n-1}{2}}\right) ^ k \\ + 1 & \left(\floor{\frac{n}{2}}\right) & \left(\floor{\frac{n}{2}}\right) ^2 & \cdots & \left(\floor{\frac{n}{2}}\right) ^ k + \end{pmatrix}}_{=M} + \cdot + \underbrace{ + \begin{pmatrix} + a'_0 \\ + a'_1 \\ + \vdots \\ + a'_k + \end{pmatrix}}_{=A} +\right \| ^2 \\ +&=& \left( + Y + - M \cdot A + \right)^\intercal \cdot + \left( + Y + - M \cdot A + \right) +\label{eq:moindrecarres} +\end{eqnarray} +On a donc : +\begin{eqnarray} + \frac{\partial L}{\partial (A)}(A) &=& -2 \cdot M^\intercal \cdot (Y - M \cdot A) +\end{eqnarray} +Et finalement, en cherchant le point où cette dérivée s'annule : +\begin{eqnarray} + A = \underbrace{(M^\intercal\cdot M)^{-1} \cdot M^\intercal}_{=B} \cdot Y +\end{eqnarray} + +On peut ainsi obtenir facilement les valeurs "lissées" en chaque point $i$ : en effet, la valeur de la fonction en un point est donné par le coefficient $a_0$, celle de sa dérivée par $\frac{a_1}{h}$ etc. Plus formellement, pour approximer la dérivée d'ordre $d$, on peut convoluer le signal par le filtre RIF $[b_1, \dots b_n ]$, avec +\begin{equation} + \forall i \in \intervalleEntier{0}{n}, b_i = B_{d,n-i} +\end{equation} + +Dans le cas de notre projet, on ne s'intéresse qu'a la vitesse (donc $d=1$). Il faut maintenant déterminer la taille du filtre ($n$) et le degré $k$ du polynôme d'approximation. En effet on souhaite minimiser $n$ car la mesure de vitesse induit un retard de $\frac{n}{2} \times h$. + +\subsubsection{Protocole expérimental} + +Afin de déterminer le filtre que nous utiliserons, nous choisissons d'en tester plusieurs sur le même relevé de position. Pour relever la position, on se contente de tenir le drone allumé face à la cible puis de marcher dans sa direction. On se référera à l'annexe \ref{chap:export} pour la méthode employée pour exporter les données depuis ROS vers un fichier \verb|output.txt|. On peut ensuite traiter les données avec le script Julia \verb|test_filter.jl| (annexe \ref{chap:test_filter}). + + +\subsubsection{Choix du filtre} +Les résultats obtenus sont donnés figures \ref{fig:savgol_quad}, \ref{fig:savgol_cub} et \ref{fig:savgol_big_quad}. On remarque que la vitesse est mieux lissée lorsqu'un filtre quadratique est utilisé. En effet, plus le degré du polynôme est élevé, plus il sera proche du signal mesuré et donc lissera moins bien. + +Sans surprise, le fait d'augmenter la taille du filtre permet de mieux lisser la vitesse. Toutefois, pour éviter de causer un retard trop important dû à l'attente des points pour calculer la dérivée, il sera nécessaire de trouver un compromis entre signal lissé et retard inhérent au filtre, ceci afin d'augmenter la stabilité du système. + +Après étude des courbes obtenues, nous avons choisis de commencer les expérimentations d'asservissement avec un filtre quadratique de 19 points, ce qui semble assurer un bien meilleur lissage. Cependant il faut prendre en compte le retard induit par la taille de fenêtre. + +Lors de l'implémentation du filtre, il faut également s'assurer que la fréquence d'échantillonage du signal d'entrée correspond à celle pour lequel le filtre est calculé\footnote{Nos expérimentations ont montré la très mauvaise stabilité du filtre dans les cas où la fréquence d'échantillonage n'est pas constante.}. + +\begin{figure}[h!] + \centering + \includegraphics[width=\linewidth]{images/realisation/mesure_vitesse_quadratique.eps} + \caption{Performance des filtres quadratiques} + \label{fig:savgol_quad} +\end{figure} +\begin{figure}[h!] + \centering + \includegraphics[width=\linewidth]{images/realisation/mesure_vitesse_cubique.eps} + \caption{Performance des filtres cubiques} + \label{fig:savgol_cub} +\end{figure} +\begin{figure}[h!] + \centering + \includegraphics[width=\linewidth]{images/realisation/mesure_vitesse_big_quadra.eps} + \caption{Performance des filtres quadratiques pour des nombres de points élevés} + \label{fig:savgol_big_quad} +\end{figure} +\FloatBarrier + +\subsection{Création de fichiers de configuration} +Les fichiers de configuration vont nous permettre de régler, à l'aide d'une interface graphique, les paramètres de nos correcteurs dans la double boucle. Pour une explication plus détaillée du fonctionnement des fichiers de configuration, on se réfèrera à l'annexe \ref{chap:configuration}. + +Nous avons créé les fichiers de configurations suivants : +\begin{description} + \item[\mintinline{python}|DerivativeNode.cfg|] : permet de choisir le gain de la partie dérivée du correcteur et le filtre de Savitzky-Golay adapté (ordre et taille du polynôme à utiliser); + \item[\mintinline{python}|IntegralNode.cfg|] : permet de choisir le gain de la partie intégrale du correcteur et les valeurs minimale et maximale de l'intégrale; + \item[\mintinline{python}|ProportionalNode.cfg|] : permet de choisir le gain de la partie proportionnelle du correcteur; + \item[\mintinline{python}|InputNode.cfg|] : contient la valeur d'une entrée; + \item[\mintinline{python}|SaturateNode.cfg|] : permet de choisir les valeurs de saturation (max et min); + \item[\mintinline{python}|RateNode.cfg|] : permet de forcer une fréquence d'échantillonage constante. +\end{description} +\subsection{Création des classes de nœuds dans un script Python} +L'idée du script est de créer une classe de n\oe ud \verb|ControlNode| qui se spécialise en d'autres n\oe uds utiles pour notre PID. Chacun des noeuds héritant de \verb|ControlNode| prendra alors une ou plusieures entrées afin de générer une sortie. On peut également leur appliquer un reset afin de mettre la sortie à 0. + +Dans la classe \verb|ControlNode|, on définit un Publisher \verb|output_topic| qui publie sur le topic "output" ainsi qu'un Subscriber qui s'inscrit au topic "reset". + +Le diagramme d'héritage de notre script est donné figure \ref{fig:diag_pid}, page \pageref{fig:diag_pid}. + +\begin{landscape} +\begin{figure}[h!] + \centering + \includegraphics[width=\linewidth]{images/realisation/uml.png} + \caption{Diagramme UML} + \label{fig:diag_pid} +\end{figure} +\end{landscape} + +Les méthodes de la classe mère sont les suivantes : +\begin{description} + \item[\mintinline{python}|on_reset(self, value)|] : la valeur de l'output est remise à 0. Certaines classes filles comme \verb|DerivativeNode| surchargent cette méthode pour remettre d'autres valeurs à 0; + \item[\mintinline{python}|on_reconf(self, config, level)|] : permet de récupérer la configuration, réalise également un appel à \mintinline{python}|on_reset|; + \item[\mintinline{python}|on_compute(self, value)|] : publie sur le topic "output" et met à jour la date du dernier calcul pour la limitation de fréquence; + \item[\mintinline{python}|check_time(self, delta_time=0.0)|] : permet de vérifier qu'on ne réalise pas de calculs trop souvent et donc de manière irrégulière\footnote{En effet, comme il est dit dans la section portant sur le filtre dérivateur, ce dernier nécessite un pas d'échantillonage constant.}. On vérifie que le temps passé depuis le dernier calcul est supérieur au \verb|refresh_time| que l'on s'est imposé. +\end{description} + +On définit une classe fille \verb|InputControlNode| qui hérite de \verb|ControlNode|. Ceci a été l'occasion d'expérimenter un effet de bord intéressant de l'héritage en environnement multi-threadé. En effet, \verb|ControlNode| lance le Subscriber sur \verb|on_reset| dès l'appel à la méthode \verb|__init__| de la classe mère, mais c'est la méthode \verb|on_reset| de la classe fille qui est appelée, méthode qui n'est possiblement pas encore correctement initialisée, menant à des erreurs d'exécutions. Cette classe fille nous permet de rajouter un Subscriber qui récupère un input d'un topic "input". + +Toutes les classes filles de \verb|InputControlNode| s'inscriront donc à un topic pour récupérer une entrée et publieront sur un topic "output". Les classes héritant de \verb|InputControlNode| sont : +\begin{description} + \item[\mintinline{python}|ProportionalNode|] : partie proportionnelle du correcteur, permet de définir la valeur du gain et de publier l'output sur un topic avec \verb|on_compute| après vérification du temps; + \item[\mintinline{python}|SaturateNode|] : permet d'imposer une valeur maximale et minimale à l'output. La classe \verb|IntegralNode| en hérite. Cette classe permet de définir la valeur du gain de l'intégrale et de publier l'output sur un topic (output qui sera donc saturé). Ceci permet d'éviter des instabilités dûes à l'action intégrale. L'intégration est réalisée avec la méthode des rectangles\footnote{Il serait intéressant d'étudier l'effet de méthodes d'intégration plus performantes, notamment sur la stabilité.}; + \item[\mintinline{python}|DerivativeNode|] : partie dérivée du correcteur, permet de définir la valeur du gain, la façon de calculer la valeur de la dériver et de publier l'output de la correction dérivée sur un output. La valeur de la dérivée est calculée à l'aide d'un filtre de \bsc{Savitzky-Golay} dont on récupère le paramètre dans la configuration; + \item[\mintinline{python}|DifferenciateNode|] : permet de faire la différence entre une valeur d'entrée et une valeur mesurée; + \item[\mintinline{python}|InputNode|] : permet de définir un nœud publiant une sortie; + \item[\mintinline{python}|RateNode|] : permet de forcer une fréquence d'échantillonage fixe sur la sortie. +\end{description} + +Enfin, \verb|SumNode| hérite de \verb|ControlNode|. Il va permettre de faire la somme des différentes parties du correcteur PID. Nous ne le faisons pas hériter de \verb|InputControlNode| car il ne prendra pas toujours une seule entrée. La classe prend donc en paramètre un nombre de topics auxquels elle s'inscrit et qui seront les entrées de la somme. + +Ces classes permettront la création de nos nœuds ROS et à terme devraient permettre l'implémentation de la double boucle d'asservissement. + +Le script que nous avons écrit prend en paramètre le type de nœud que l'utilisateur souhaite créer (\verb|sum|, \verb|differenciate|, \verb|input|, \verb|saturate|, \verb|derivative|, \verb|integral|, \verb|rate| ou \verb|proportional|) afin de pouvoir aisément lancer beaucoup de nœuds en les organisant dans un fichier \verb|.launch| + +\subsection{Fichier \mintinline{bash}|control.launch|} + + +Puisque dans la suite nous aurons régulièrement à créer des régulateurs PID, nous décidons d'ajouter à notre bibliothèque un fichier \verb|launch| permettant d'en inclure un facilemetn. Ce fichier utilise 8 paramètres : \verb|input|, \verb|output|, \verb|measure|, \verb|reset|, \verb|param_P|, \verb|param_I|, \verb|param_D| et \verb|param_input|. Les quatre premiers paramètres permettent de régler les topics sur lesquels le block doit publier ou s'inscrire, tandis que les quatre derniers donnent les chemin relatif vers les fichiers de configuration des différents nœuds par rapport au répertoire \verb|params| de notre projet. + +Le bloc est composé des noeuds suivants : une entrée, une différence qui entre l'entrée et la mesure, les parties proportionnelle, intégrale et dérivée du PID qui font leurs calculs et les publie sur des topics de sorties et une somme sur ces sorties et publie le résultat sur le topic \verb|output|. + +On crée les nœuds de la manière suivante : +\begin{minted}{xml} + + + ... + +\end{minted} + +Le remap permet de relier les noeuds entre eux. Par exemple, la sortie de la différence est remapé sur un epsilon et les entrées du PID sont remapées sur epsilon. La sortie de la somme devient donc l'entrée du PID. + +Durant les phases de test, nous avons rencontré des problèmes lors du remap, notamment lors de l'utilisation du noeud de somme. Nous avons donc décidé de simplifier notre diagramme d'héritage en ne faisant pas hériter \verb|SumNode| de \verb|InputControlNode| ce qui nous permettait de définir plusieurs inputs et de régler le problème de remap. Nous ne savons toutefois pas pourquoi le problème existait au préalable. + +Le fichier \verb|control.lauch| permet ainsi de générer le graphe de nœuds de la figure \ref{fig:control_block}. + +\begin{figure}[!h] + \centering + \includegraphics[width=\linewidth]{images/realisation/control_launch.png} + \caption{Nœuds ROS du block control} + \label{fig:control_block} +\end{figure} + +\section{Nœuds divers réalisés pour mettre en place l'asservissement} + +Afin d'interfacer notre bibliothèque avec les drones BeBop, divers nœuds ont étés réalisés ou adaptés du projet existant de M. \bsc{Frezza}. + +\subsection{Script \mintinline{bash}|safe_drone_teleop.py|} + +Ce script a été presque entièrement repris du projet initial, à l'exception de l'ajout d'une publication sur le topic \verb|reset_pid| lors du passage en mode automatique afin de déclencher la remise à zéro des régulateurs, par exemple pour désaturer les actions intégrales. Il s'agit donc de l'interface de contrôle principale des drones. + +\subsection{Script \mintinline{bash}|triangle.py|} + +Ce script a pour mission de calculer la position du drone à partir de la position normalisée des cibles dans l'image. Il publie ensuite les positions au format \verb|Float64| de ROS, que les nœuds de notre bibliothèque comprennent. + +\subsection{Script \mintinline{bash}{twist_controls.py}} + +Ce script est destiné à lire la sortie des différents contrôleurs afin de générer un objet \verb|Twist| qui sera envoyé à \mintinline{bash}|safe_drone_teleop.py| pour être interprété comme la consigne à donner au drone. + +\section{Asservissement simple boucle avec la bibliothèque} +\subsection{Méthode de \bsc{Ziegler-Nichols}} +Afin de déterminer les paramètres des correcteurs PID (axes $z$ et angle $z$), nous avons utilisé la méthode de \bsc{Ziegler-Nichols} \cite{zieg_nic_premier}. Pour réguler les boucles selon les quatre axes, nous allons générer des oscillations (qui sont faciles à voir) en augmentant progressivement le gain proportionnel. Une fois des oscillations d'amplitude et de fréquence constantes obtenues, nous allons pouvoir calculer le régulateur à utiliser en fonction de $K_u$ le gain proportionnel obtenu et $T_u$ la fréquence des oscillations. +\begin{center} +\begin{tabular}{|c|c|} + \hline + Type de contrôle & Paramètres de réglage \\ + \hline + P.I.D & $K_p=0.6 K_u$ $K_i=\frac{T_u}{2}$ $K_d=\frac{T_u}{8}$ \\ + \hline + P.I.D peu de dépassement & $K_p=0.33 K_u$ $K_i=\frac{T_u}{2}$ $K_d=\frac{T_u}{3}$ \\ + \hline + P.I.D aucun dépassement & $K_p=0.2 K_u$ $K_i=\frac{T_u}{2}$ $K_d=\frac{T_u}{3}$ \\ + \hline +\end{tabular} +\end{center} +\subsection{Méthode empirique} +Pour les deux autres axes ($x$ et $y$), nous avons utilisé une méthode empirique de réglage. Tous les autres gains étant par ailleurs nuls, on augmente progressivement le gain D\footnote{Pour rappel, cela revient à augmenter le gain P du PI équivalent du fait du comportement double intégrateur du système.}. Lorsque l'on atteint la limite du comportement oscillant du système, on augmente alors le gain D\footnote{Pour les mêmes raisons que précédemment, cela revient à augmenter le I du PI équivalent.}. + +\subsection{Protocole de réglage} + +Afin de faciliter le réglage du drone, il convient de régler les différents axes dans le "bon" ordre. Pour appliquer la méthode de \bsc{Ziegler-Nichols}, on pourra filmer les oscillations du drone (par exemple avec un téléphone portable) afin de mesurer la période des oscillations \textit{a posteriori}\footnote{Il existe de nombreux logiciels de relevé de position à partir d'une vidéo, par exemple avimeca.}. + +Nous conseillons donc de procéder au réglage du drone dans cet ordre : +\begin{enumerate} + \item Axe $z$; + \item Lacet (angle selon $z$); + \item Axe $y$; + \item Axe $x$. +\end{enumerate} + +Cependant on notera que l'asservissement des différents axes n'est pas totalement indépendant. En particulier, nous avons pu nous rendre compte que le réglage de l'axe $x$ a tendance à instabiliser le lacet. De plus, il est difficile de régler correctement l'axe $y$ si l'axe $x$ est instable, et \textit{vice-versa}. On procédera donc à un réglage par itérations successives. Enfin on notera que du fait de la mesure de l'erreur, il est nécessaire de donner des gains négatifs pour les axes $x$ et de lacet. + +\subsection{Fichier \mintinline{bash}{launch}} + +Nous avons créé un fichier \verb|simple_loop.launch| qui permet de lancer la simple boucle tout en chargeant les paramètres de drone que nous avons déterminé. Ce fichier fait usage du fichier \verb|control.launch| de notre bibliothèque. + +\section{Asservissement double boucle avec la bibliothèque} + +Afin d'améliorer les performances, on souhaite intégrer une boucle de régulation interne sur la vitesse. En outre, cette boucle devrait nous permettre d'ajouter une saturation en vitesse limitant le dépassement lorsque le drone arrive depuis une grande distance vers la cible. On modélise la nouvelle régulation avec la figure \ref{fig:double_boucle} (page \pageref{fig:double_boucle}). + +\begin{figure}[h!] +\centering +\begin{tikzpicture}[auto, node distance=2cm,>=latex'] +% We start by placing the blocks +\node [input, name=input] {}; +\node [sum, right of=input] (sum) {}; +\node [block, right of=sum] (controller) {$C_p(p)$}; +\node [sum, right of=controller, node distance=3cm] (sum_speed) {}; +\node [block, right of=sum_speed] (controller_speed) {$C_v(p)$}; +\node [block, right of=controller_speed, +node distance=3cm] (system) {Drone}; +\node [block, right of=system, +node distance=3cm] (integrate) {$\frac{1}{p}$}; +\node [block, below of=controller_speed] (measurements_speed) {Mesure}; +% We draw an edge between the controller and system block to +% calculate the coordinate u. We need it to place the measurement block. +\draw [->] (controller) -- node[pos=0.99] {$+$} +node [near end] {$u$} (sum_speed); +\node [output, right of=system, node distance=5cm] (output) {}; +\node [block, below of=measurements_speed] (measurements) {Mesure}; + +% Once the nodes are placed, connecting them is easy. +\draw [draw,->] (input) -- node {consigne +} (sum); +\draw [->] (sum) -- node {$\epsilon_p$} (controller); +\draw [->] (sum_speed) -- node {$\epsilon_v$} (controller_speed); +\draw [->] (controller_speed) -- node [name=x] {} (system); +\draw [->] (system) -- node [name=v] {} (integrate); +\draw [->] (measurements_speed) -| node[pos=0.99] {$-$} +node [near end] {mesure de la vitesse} (sum_speed); +\draw [->] (integrate) -- node [name=y] {position }(output); +\draw [->] (v) |- (measurements_speed); +\draw [->] (y) |- (measurements); +\draw [->] (measurements) -| node[pos=0.99] {$-$} +node [near end] {} (sum); +\end{tikzpicture} +\caption{Modélisation simple de l'asservissement} +\label{fig:double_boucle} +\end{figure} + +\subsection{Réglage de la double boucle} +\subsubsection{Méthode} +Afin de régler la double boucle, on utilisera la méthode de \bsc{Ziegler-Nichols}. Cette méthode permet de déterminer les paramètres du PID à implémenter de deux façons possibles. +\begin{itemize} + \item On peut générer des oscillations d'amplitudes et de fréquence constante sur la mesure à régler en augmentant doucement le gain proportionnel. Avec les valeurs du gain $K_u$ et de la période des oscillations $T_u$, on calcule les paramètres du PID de la façon suivante : $K_i=2/T_u,$ $K_p=0.6K_u$, $K_d=T_u/8$; + \item On enregistre la réponse du système non régulé à un échelon et on en déduit la valeur des paramètres par analyse de cette réponse comme donné sur la \ref{fig:ziegnic}. + \begin{figure}[h!] + \centering + \includegraphics[width=\linewidth]{zieg_nic.jpg} + \caption{Méthode de Ziegler-Nichols pour déterminer les paramètres d'un PID \cite{zieg_nic}} + \label{fig:ziegnic} +\end{figure} +\end{itemize} +\subsubsection{Réglage de la boucle interne} +Nous allons commencer par régler la boucle interne, soit la boucle asservissant la vitesse. Pour cela, nous allons utiliser la réponse du système non régulé à un échelon afin de trouver les paramètres du PID interne. + +Pour cela, non envoie un échelon en inclinaison à notre drone (il s'agit donc d'une accélération) car nous ne pouvons pas directement lui donner une commande en vitesse, et on enregistre la réponse indicielle en boucle ouverte. Pour la calculer, nous avons utilisé un filtre de \bsc{Savitsky-Golay} quadratique de 19 points (avoir beaucoup de retard dans les calculs ne pose, ici, aucun problème, car nous ne cherchons pas à avoir une réponse rapide, mais une réponse la plus lissée possible pour déterminer au plus juste les paramètres découlant de la méthode de \bsc{Ziegler-Nichols}. + +Afin de déterminer la réponse indicielle de la vitesse en boucle ouverte, nous avions besoin d'un grand espace. Nous avons donc déterminé cette réponse dans le gymnase en modifiant la couleur des cibles (jaunes) pour que le drone ne soit pas perturbé par le sol qui est bleu. + +Cependant nos essais n'ont pas été très concluants pour plusieurs raisons. Tout d'abord parce que le drone a tendance à perdre la cible lorsqu'il est à grande distance, et à cause des changements de luminosité. Cependant un réglage à proximité de la cible n'est pas envisageable car le drone met quelques secondes à atteindre sa vitesse maximale : il dépasse donc la cible. La régulation en double boucle n'est donc pas fonctionnelle à l'heure de la cloture de ce rapport. + + +\subsection{Création du fichier launch et connection des noeuds} + +Pour réaliser la double boucle, on crée un fichier \verb|launch| dédié. + +On crée des noeuds afin de récupérer la position du drone +\begin{minted}{xml} + + + + + + +\end{minted} + +On organise grâce à des groupes : +\begin{minted}{xml} + + ... + +\end{minted} + +À l'intérieur de ces groupes, on récupère les noeuds crées avec \verb|control.launch| en incluant le fichier : +\begin{minted}{xml} + +\end{minted} + +Et on donne les bonnes valeurs aux arguments grâce à \begin{minted}{xml} + +\end{minted} + +Pour les boucles en x et en y, on crée deux boucles, tandis que pour les boucles en z, on en crée qu'une seule (car on ne régulera pas cet axe avec une double boucle, ce dernier n'étant pas soumis aux problèmes de lenteur et de dépassement étant donné les faibles déplacements sur cet axe). + +Il "suffit" ensuite de bien relier les entrées et les sorties des noeuds. Nous obtenu le résultat de nos noeuds \ref{fig:noeuds}. +\begin{figure}[h!] + \centering + \includegraphics[width=\linewidth]{noeuds.png} + \caption{Nœuds ROS pour la double boucle} + \label{fig:noeuds} +\end{figure} diff --git a/doc/compte_rendu/chap_testfilter.tex b/doc/compte_rendu/chap_testfilter.tex new file mode 100644 index 0000000..24a97a6 --- /dev/null +++ b/doc/compte_rendu/chap_testfilter.tex @@ -0,0 +1,6 @@ +\chapter{Script \mintinline{bash}|test_filter.jl|} +\label{chap:test_filter} + +Ce script teste différents filtres de \bsc{Savitsky-Golay} à l'aide du langage Julia\cite{julia}. Outre le fait qu'il illustre la souplesse et la simplicité d'utilisation du langage, il permet de donner un exemple de calcul des coefficients du filtre. + +\inputminted[frame=lines,linenos,breaklines=true]{julia}{scripts/test_filter.jl} diff --git a/doc/compte_rendu/chap_utilisation.tex b/doc/compte_rendu/chap_utilisation.tex new file mode 100644 index 0000000..f53a7fd --- /dev/null +++ b/doc/compte_rendu/chap_utilisation.tex @@ -0,0 +1,60 @@ +\chapter{Utilisation du livrable} + +\section{Installation du module} + +Pour l'installation du module, se référer à l'annexe \ref{chap:installation_projet}. + +\section{Utilisation} + +\subsection{Lancement} +Le lancement du projet est décrit dans l'annexe \ref{chap:installation_projet}. Pour rappel : + +\begin{enumerate} + \item Connectez-vous au réseau WiFi du drone; + \item Ouvrez un terminal et lancez : +\begin{minted}{bash} +roscore +\end{minted} + \item Dans un nouveau terminal: +\begin{minted}{bash} +source ~/drone-rigide/devel/setup.bash +roslaunch detect_targets simple_loop.launch +\end{minted} +\end{enumerate} + +Cinq fenêtres s'ouvrent : un terminal, deux fenêtres de visualisation, un graphe des nœuds et une fenêtre de configuration. + +\subsection{Contrôle manuel} +Dans la fenêtre de terminal (figure \ref{fig:terminal}) qui s'est ouverte, il est possible de contrôler manuellement le drone. Au bout de quelques secondes après le décollage, si aucun ordre n'est donné le contrôle automatique prend la main. + +\begin{figure}[h!] + \centering + \includegraphics[width=\linewidth]{images/utilisation/fenetre_control.png} + \caption{Terminal de contrôle manuel} + \label{fig:terminal} +\end{figure} + +\subsection{Fenêtre de visualisation} + +Ces fenêtres (figure \ref{fig:visualisation}) permet de donner un aperçu de la sortie de la caméra, afin notamment de vérifier que le drone est bien en mesure de visualiser la cible. + +La fenêtre en haut à droite permet de régler les seuils de couleur. Il y a également deux options "Binary" qui permet d'afficher l'image binaire (en haut à gauche) et "Targets" qui permet d'afficher la position des cibles trouvée. Il faut bien penser à décocher ces deux options lorsque le drone est en vol, car leur génération provoque beaucoup de calculs et induit donc un retard, source d'instabilités. + + +\begin{figure}[h!] + \centering + \includegraphics[width=\linewidth]{images/utilisation/targets.png} + \caption{Visualisation de la sortie de la caméra} + \label{fig:visualisation} +\end{figure} + +\subsection{Fenêtre de paramétrage} + +La dernière fenêtre qui s'ouvre (figure \ref{fig:parametrage}) est la fenêtre de paramétrage. Elle permet de paramétrer tous les nœuds qui utilisent \verb|dynamic_reconfigure|. Ainsi, pour donner une consigne de distance sur l'axe $x$, il suffit de changer le paramètre \verb|value| de \verb|controller_linear_x/external_loop/input|. + +\begin{figure} + \centering + \includegraphics[width=\linewidth]{images/utilisation/capture_rqt.png} + \caption{Fenêtre de paramétrage} + \label{fig:parametrage} +\end{figure} \ No newline at end of file diff --git a/doc/compte_rendu/compte_rendu.pdf b/doc/compte_rendu/compte_rendu.pdf deleted file mode 100644 index 1a8a557..0000000 Binary files a/doc/compte_rendu/compte_rendu.pdf and /dev/null differ diff --git a/doc/compte_rendu/compte_rendu.tex b/doc/compte_rendu/compte_rendu.tex deleted file mode 100644 index de4f7cd..0000000 --- a/doc/compte_rendu/compte_rendu.tex +++ /dev/null @@ -1,164 +0,0 @@ -\documentclass[]{report} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{tikz} -\usepackage[french]{babel} - -\usepackage{geometry} % Required for adjusting page dimensions - -\geometry{ - top=2cm, % Top margin - bottom=2cm, % Bottom margin - left=2cm, % Left margin - right=2cm, % Right margin - includehead, % Include space for a header - includefoot, % Include space for a footer - %showframe, % Uncomment to show how the type block is set on the page -} - - -\usetikzlibrary{shapes,arrows} -\tikzstyle{block} = [draw, fill=blue!20, rectangle, -minimum height=3em, minimum width=6em] -\tikzstyle{sum} = [draw, fill=blue!20, circle, node distance=1cm] -\tikzstyle{input} = [coordinate] -\tikzstyle{output} = [coordinate] -\tikzstyle{pinstyle} = [pin edge={to-,thin,black}] - -% Title Page -\title{Projet double :\\ Asservissement "rigide" de drone} -\author{Joanne \bsc{Steiner}, Hugo \bsc{Levy-{}-Falk}} -\date{2019} - -\begin{document} -\maketitle - -\begin{abstract} -\end{abstract} - -\tableofcontents - -\chapter{Introduction} - -Le campus de Metz de CentraleSupélec dispose de drones appelés les quadricoptères Bebop 2 (Parrot). Ces derniers sont capables de réaliser des mouvements brusques ce qui rend leur pilotage complexe. Il faut donc les manipuler avec précautions, ce qui revient à sous-exploiter leurs capacités.\\ -Jusqu'à présent, le drone était asservi à l'aide d'une cible présente dans son champ visuel. Le drone suivait la cible (bleu) et se positionnait en face de cette dernière. Toutefois, le drone se déplaçait lentement et se montrait prudent. De plus, une fois face à la cible, le drone n'était pas stable. Il oscillait verticalement face à la cible. Ce résultat avait été obtenu suite à un projet d'élèves.\\ -L'objectif de ce projet est donc de rendre l'asservissement du drone plus "rigide" et donc d'améliorer et de mieux exploiter l'utilisation de ce dernier. - -\chapter{Déroulement du projet} -Le projet comporte les étapes suivantes : -\begin{itemize} -\item Etape 1 : Prise en main de ROS et du drone présent à la smartroom; -\item Etape 2 : Réduction du bruit causé par le calcul de la position du drone par rapport à l'image -\item Etape 3 : Choix du correcteur simple boucle -\item Etape 4 : Choix du correcteur double boucle -\item Etape 5 : Ecriture d'un guide de fonctionnement -\end{itemize} - -\chapter{Modélisation du problème} - -Le drone diffuse un flux optique, qui permet de calculer sa position vis-à-vis d'une cible. On peut donc dans un premier temps modéliser l'asservissement de cette manière : - -\begin{figure}[h!] -\centering -\begin{tikzpicture}[auto, node distance=2cm,>=latex'] -% We start by placing the blocks -\node [input, name=input] {}; -\node [sum, right of=input, node distance=3cm] (sum) {}; -\node [block, right of=sum] (controller) {Correcteur}; -\node [block, right of=controller, -node distance=3cm] (system) {Drone}; -% We draw an edge between the controller and system block to -% calculate the coordinate u. We need it to place the measurement block. -\draw [->] (controller) -- node[name=u] {$u$} (system); -\node [output, right of=system, node distance=5cm] (output) {}; -\node [block, below of=u] (measurements) {Mesure}; - -% Once the nodes are placed, connecting them is easy. -\draw [draw,->] (input) -- node {position attendue} (sum); -\draw [->] (sum) -- node {$\epsilon$} (controller); -\draw [->] (system) -- node [name=y] {position réelle du drone}(output); -\draw [->] (y) |- (measurements); -\draw [->] (measurements) -| node[pos=0.99] {$-$} -node [near end] {mesure de la position} (sum); -\end{tikzpicture} -\caption{Modélisation simple de l'asservissement} -\end{figure} - -La mesure peut se décomposer en trois éléments : - -\begin{figure}[h!] - \centering - \begin{tikzpicture}[auto, node distance=3cm,>=latex'] - % We start by placing the blocks - \node [input, name=input] {}; - \node [block, right of=input] (cam) {Caméra}; - \node [block, right of=cam] (transm) {Transmission}; - \node [block, right of=transm] (trait) {Traitement}; - \node [output, right of=system] (output) {}; - % We draw an edge between the controller and system block to - % calculate the coordinate u. We need it to place the measurement block. - \draw [->] (input) -- (cam); - \draw [->] (cam) -- (transm); - \draw [->] (transm) -- (trait); - \draw [->] (trait) -- (output); - \end{tikzpicture} - \caption{Décomposition de la mesure} -\end{figure} - -Comme le traitement ne se fait pas directement sur le drone, il existe des retards aléatoires dûs au temps de transit sur le réseau, ainsi qu'au temps de calcul sur le poste de contrôle. Ces retards limitent la fréquence des mesures à environ 5Hz. -\chapter{Réalisation du projet} -\section{Prise en main de ROS et du drone présent à la smartroom} -Pour la prise en main de ROS, nous avons suivi les étapes du tutoriel de M. Frezza-Buet. Cela nous a permis de comprendre comment fonctionne ROS et de pouvoir l'utiliser de manière basique et simple.\\ -\section{Réduction du bruit causé par le calcul de la position du drone par rapport à l'image} -Nous avons constaté qu'une forte incertitude existait lors du calcul de la position du drone par rapport au panneau. En effet, celle-ci, même si le drone était immobile, bougeait beaucoup et faisait des "sauts". Il s'agissait d'un bruit de type de Poisson, difficile, voire impossible, à traiter en automatique pour obtenir un asservissement satisfaisant. En effet, le drone, avec ce bruit, aurait été asservi à ce dernier, rendant impossible l'obtention d'une position fixe. Notre drone aurait fait de grands écarts par rapport à la position attendue.\\ -Afin de régler ce problème, l'idée proposée a été de modifier l'algorithme en place. Ce dernier calcul la position des trois carrés bleus dans l'image renvoyée par le drone par les position H, R et L. Cette détermination se faisait par gngt, qui faisait beaucoup de bruit. Nous avons donc utilisé un nouveau script Python qui profite de la labellisation afin de déterminer la position des panneaux.\\ -Dans cette partie, nous ne nous intéresserons qu'au script donné dans le fichier -\textbf{src$\backslash$detect\_targets$\backslash$script$\backslash$find\_targets.py}. Il permet, à partir d'un seuil RGB défini, de trouver les parties "bleues" de l'image. Une fois ces positions trouvées, on ne garde que les trois plus grandes parties et on en calcule le centre de masse. Les résultats obtenus sont plutôt satisfaisants. -\section{Premier asservissement sommaire} -Le premier asservissement qui a été réalisé n'utilisait qu'une seule boucle et asservissait la position du drone.\\ -Pour ce premier asservissement sommaire, nous avons estimé la courbe de la réponse fréquentielle de notre drone afin d'en déduire le type de correcteur à utiliser.\\ -Nous savons que selon l'axe z, le drone répond seulement en vitesse. On peut approximer sa réponse fréquence par une pente nulle en basse fréquence, puis une pente [-1] en haute fréquence. Afin d'asservir le drone, nous aurons donc besoin d'un correcteur de type proportionnel-intégrale -\[C(p)=K_p + \frac{K_i}{p}\] -Concernant les axes x et y, nous savons que le drone ne peut être correctement asservi en vitesse. En effet, le réglage de la vitesse et de l'accélération du drone se fait selon un angle d'inclinaison : le drone accélère en permanence s'il conserve le même angle ce qui ne permet pas le maintien d'une vitesse constante. La réponse fréquentielle selon ses axes est donc représentée par une pente de [-1] dans les basses fréquence et une pente de [-2] dans les hautes fréquences. Afin de corriger ces axes, nous allons donc utiliser une correction de type Proportionnelle-Dérivée : -\[C(p)=K_p+K_d p\] -\begin{figure}[h!] -\centering -\begin{tikzpicture}[auto, node distance=2cm,>=latex'] -% We start by placing the blocks -\node [input, name=input] {}; -\node [sum, right of=input, node distance=3cm] (sum) {}; -\node [block, right of=sum] (controller) {$C_p(p)$}; -\node [sum, right of=controller, node distance=3cm] (sum_speed) {}; -\node [block, right of=sum_speed] (controller_speed) {$C_v(p)$}; -\node [block, right of=controller_speed, -node distance=3cm] (system) {Drone}; -\node [block, right of=system, -node distance=3cm] (integrate) {$\frac{1}{p}$}; -\node [block, below of=controller_speed] (measurements_speed) {Mesure}; -% We draw an edge between the controller and system block to -% calculate the coordinate u. We need it to place the measurement block. -\draw [->] (controller) -- node[pos=0.99] {$+$} -node [near end] {$u$} (sum_speed); -\node [output, right of=system, node distance=5cm] (output) {}; -\node [block, below of=measurements_speed] (measurements) {Mesure}; - -% Once the nodes are placed, connecting them is easy. -\draw [draw,->] (input) -- node {position attendue +} (sum); -\draw [->] (sum) -- node {$\epsilon_p$} (controller); -\draw [->] (sum_speed) -- node {$\epsilon_v$} (controller_speed); -\draw [->] (controller_speed) -- node [name=x] {} (system); -\draw [->] (system) -- node [name=v] {} (integrate); -\draw [->] (measurements_speed) -| node[pos=0.99] {$-$} -node [near end] {mesure de la vitesse} (sum_speed); -\draw [->] (integrate) -- node [name=y] {position }(output); -\draw [->] (v) |- (measurements_speed); -\draw [->] (y) |- (measurements); -\draw [->] (measurements) -| node[pos=0.99] {$-$} -node [near end] {mesure de la position} (sum); -\end{tikzpicture} -\caption{Modélisation simple de l'asservissement} -\end{figure} -\section{Deuxième asservissement utilisant une double-boucle d'asservissement} -\section{Installation du module et utilisation de l'interface graphique} -Modules pour régler les seuils de couleur (on pourrait songer à utiliser des cibles rouges, à condition de modifier les seuils) et le correcteur : la valeur de la saturation en vitesse et en accélération peuvent se régler ainsi que les différentes valeurs du PID (il est toutefois déconseillé de modifier les valeurs, celles-ci ayant été adaptés au problème). -\end{document} \ No newline at end of file diff --git a/doc/compte_rendu/images/modelisation/bode_u.eps b/doc/compte_rendu/images/modelisation/bode_u.eps new file mode 100644 index 0000000..5f9cb51 --- /dev/null +++ b/doc/compte_rendu/images/modelisation/bode_u.eps @@ -0,0 +1,327 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: cairo 1.15.10 (http://cairographics.org) +%%CreationDate: Sat May 25 18:04:18 2019 +%%Pages: 1 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glyphshow +39.796875 0.000000 m /a glyphshow +44.699219 0.000000 m /space glyphshow +47.242188 0.000000 m /four glyphshow +52.332031 0.000000 m /one glyphshow +57.421875 0.000000 m /space glyphshow +59.964844 0.000000 m /p glyphshow +65.042969 0.000000 m /o glyphshow +69.937500 0.000000 m /i glyphshow +72.160156 0.000000 m /n glyphshow +77.230469 0.000000 m /t glyphshow +80.367188 0.000000 m /s glyphshow +grestore +0.676 0.556 0.094 setrgbcolor +gsave +602.987229 139.452229 m +618.987229 139.452229 l +stroke +grestore +0.000 setgray +gsave +625.387229 136.652229 translate +0.000000 rotate +0.000000 0.000000 m /b glyphshow +5.078125 0.000000 m /i glyphshow +7.300781 0.000000 m /g glyphshow +12.378906 0.000000 m /underscore glyphshow +16.378906 0.000000 m /q glyphshow +21.457031 0.000000 m /u glyphshow +26.527344 0.000000 m /a glyphshow +31.429688 0.000000 m /d glyphshow +36.507812 0.000000 m /r glyphshow +39.796875 0.000000 m /a glyphshow +44.699219 0.000000 m /space glyphshow +47.242188 0.000000 m /five glyphshow +52.332031 0.000000 m /one glyphshow +57.421875 0.000000 m /space glyphshow +59.964844 0.000000 m /p glyphshow +65.042969 0.000000 m /o glyphshow +69.937500 0.000000 m /i glyphshow +72.160156 0.000000 m /n glyphshow +77.230469 0.000000 m /t glyphshow +80.367188 0.000000 m /s glyphshow +grestore + +end +showpage diff --git a/doc/compte_rendu/images/realisation/mesure_vitesse_cubique.eps b/doc/compte_rendu/images/realisation/mesure_vitesse_cubique.eps new file mode 100644 index 0000000..2e854ba --- /dev/null +++ b/doc/compte_rendu/images/realisation/mesure_vitesse_cubique.eps @@ -0,0 +1,3466 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: matplotlib version 2.2.3, http://matplotlib.org/ +%%CreationDate: Sun May 26 14:47:35 2019 +%%Orientation: portrait +%%BoundingBox: -54 180 666 612 +%%EndComments +%%BeginProlog +/mpldict 9 dict def +mpldict begin +/m { moveto } bind def +/l { lineto } bind def +/r { rlineto } bind def +/c { curveto } bind def +/cl { closepath } bind def +/box { +m +1 index 0 r +0 exch r +neg 0 r +cl +} bind def +/clipbox { +box +clip +newpath +} bind def +%!PS-Adobe-3.0 Resource-Font +%%Title: DejaVu Sans Oblique +%%Copyright: Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. Copyright (c) 2006 by Tavmjong Bah. All Rights Reserved. DejaVu changes are in public domain +%%Creator: Converted from TrueType to type 3 by PPR +25 dict begin +/_d{bind def}bind def +/_m{moveto}_d +/_l{lineto}_d +/_cl{closepath eofill}_d +/_c{curveto}_d +/_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d +/_e{exec}_d +/FontName /DejaVuSans-Oblique def +/PaintType 0 def +/FontMatrix[.001 0 0 .001 0 0]def +/FontBBox[-1016 -350 1659 1068]def +/FontType 3 def +/Encoding [ /m /s ] def +/FontInfo 10 dict dup begin +/FamilyName (DejaVu Sans) def +/FullName (DejaVu Sans Oblique) def +/Notice (Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. Copyright (c) 2006 by Tavmjong Bah. All Rights Reserved. DejaVu changes are in public domain ) def +/Weight (Oblique) def +/Version (Version 2.35) def +/ItalicAngle -11.0 def +/isFixedPitch false def +/UnderlinePosition -130 def +/UnderlineThickness 90 def +end readonly def +/CharStrings 3 dict dup begin +/.notdef 0 def +/m{{974 0 35 0 906 560 _sc +898 330 _m +834 0 _l +744 0 _l +807 327 _l +809 341 811 353 813 363 _c +814 373 815 381 815 389 _c +815 418 806 441 790 457 _c +774 473 751 482 722 482 _c +678 482 639 465 605 433 _c +571 400 549 357 539 305 _c +479 0 _l +389 0 _l +453 327 _l +455 339 457 350 459 360 _c +460 370 461 380 461 388 _c +461 418 452 441 436 457 _c +420 473 397 482 369 482 _c +}_e{325 482 285 465 251 433 _c +217 400 195 357 185 305 _c +125 0 _l +35 0 _l +142 547 _l +232 547 _l +215 462 _l +239 494 267 518 300 535 _c +333 551 368 560 406 560 _c +445 560 477 549 503 529 _c +529 508 544 479 550 442 _c +577 480 609 510 645 530 _c +681 550 719 560 759 560 _c +805 560 841 546 867 519 _c +893 492 906 454 906 405 _c +906 394 905 382 904 369 _c +}_e{902 356 900 343 898 330 _c +_cl}_e}_d +/s{{521 0 11 -13 500 560 _sc +500 531 _m +483 446 _l +459 458 433 468 407 475 _c +381 481 354 485 326 485 _c +278 485 241 477 214 461 _c +187 445 174 423 174 395 _c +174 363 205 338 269 321 _c +273 319 277 318 279 318 _c +308 309 _l +368 292 408 274 428 256 _c +448 238 458 213 458 182 _c +458 124 435 77 389 41 _c +343 5 282 -13 208 -13 _c +179 -13 149 -10 117 -5 _c +}_e{85 0 49 8 11 20 _c +29 113 _l +61 95 94 82 126 74 _c +158 65 188 61 218 61 _c +262 61 297 70 325 89 _c +352 108 366 132 366 161 _c +366 192 330 217 258 237 _c +249 239 _l +218 247 _l +172 259 138 274 117 294 _c +96 314 86 339 86 370 _c +86 428 107 475 151 509 _c +195 543 254 560 330 560 _c +360 560 389 557 417 552 _c +445 547 472 540 500 531 _c +_cl}_e}_d +end readonly def + +/BuildGlyph + {exch begin + CharStrings exch + 2 copy known not{pop /.notdef}if + true 3 1 roll get exec + end}_d + +/BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec +}_d + +FontName currentdict end definefont pop +%!PS-Adobe-3.0 Resource-Font +%%Title: DejaVu Sans +%%Copyright: Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. Copyright (c) 2006 by Tavmjong Bah. All Rights Reserved. DejaVu changes are in public domain +%%Creator: Converted from TrueType to type 3 by PPR +25 dict begin +/_d{bind def}bind def +/_m{moveto}_d +/_l{lineto}_d +/_cl{closepath eofill}_d +/_c{curveto}_d +/_sc{7 -1 roll{setcachedevice}{pop pop pop pop pop pop}ifelse}_d +/_e{exec}_d +/FontName /DejaVuSans def +/PaintType 0 def +/FontMatrix[.001 0 0 .001 0 0]def +/FontBBox[-1021 -463 1793 1232]def +/FontType 3 def +/Encoding [ /space /parenleft /parenright /hyphen /period /zero /one /two /three /five /seven /nine /P /T /V /b /c /e /i /m /n /o /p /q /r /s /t /u /acute /eacute /minus ] def +/FontInfo 10 dict dup begin +/FamilyName (DejaVu Sans) def +/FullName (DejaVu Sans) def +/Notice (Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. Copyright (c) 2006 by Tavmjong Bah. All Rights Reserved. DejaVu changes are in public domain ) def +/Weight (Book) def +/Version (Version 2.35) def +/ItalicAngle 0.0 def +/isFixedPitch false def +/UnderlinePosition -130 def +/UnderlineThickness 90 def +end readonly def +/CharStrings 32 dict dup begin +/.notdef 0 def +/space{318 0 0 0 0 0 _sc +}_d +/parenleft{390 0 86 -131 310 759 _sc +310 759 _m +266 683 234 609 213 536 _c +191 463 181 389 181 314 _c +181 238 191 164 213 91 _c +234 17 266 -56 310 -131 _c +232 -131 _l +183 -54 146 20 122 94 _c +98 168 86 241 86 314 _c +86 386 98 459 122 533 _c +146 607 182 682 232 759 _c +310 759 _l +_cl}_d +/parenright{390 0 80 -131 304 759 _sc +80 759 _m +158 759 _l +206 682 243 607 267 533 _c +291 459 304 386 304 314 _c +304 241 291 168 267 94 _c +243 20 206 -54 158 -131 _c +80 -131 _l +123 -56 155 17 177 91 _c +198 164 209 238 209 314 _c +209 389 198 463 177 536 _c +155 609 123 683 80 759 _c +_cl}_d +/hyphen{361 0 49 234 312 314 _sc +49 314 _m +312 314 _l +312 234 _l +49 234 _l +49 314 _l +_cl}_d +/period{318 0 107 0 210 124 _sc +107 124 _m +210 124 _l +210 0 _l +107 0 _l +107 124 _l +_cl}_d +/zero{636 0 66 -13 570 742 _sc +318 664 _m +267 664 229 639 203 589 _c +177 539 165 464 165 364 _c +165 264 177 189 203 139 _c +229 89 267 64 318 64 _c +369 64 407 89 433 139 _c +458 189 471 264 471 364 _c +471 464 458 539 433 589 _c +407 639 369 664 318 664 _c +318 742 _m +399 742 461 709 505 645 _c +548 580 570 486 570 364 _c +570 241 548 147 505 83 _c +461 19 399 -13 318 -13 _c +236 -13 173 19 130 83 _c +87 147 66 241 66 364 _c +66 486 87 580 130 645 _c +173 709 236 742 318 742 _c +_cl}_d +/one{636 0 110 0 544 729 _sc +124 83 _m +285 83 _l +285 639 _l +110 604 _l +110 694 _l +284 729 _l +383 729 _l +383 83 _l +544 83 _l +544 0 _l +124 0 _l +124 83 _l +_cl}_d +/two{{636 0 73 0 536 742 _sc +192 83 _m +536 83 _l +536 0 _l +73 0 _l +73 83 _l +110 121 161 173 226 239 _c +290 304 331 346 348 365 _c +380 400 402 430 414 455 _c +426 479 433 504 433 528 _c +433 566 419 598 392 622 _c +365 646 330 659 286 659 _c +255 659 222 653 188 643 _c +154 632 117 616 78 594 _c +78 694 _l +118 710 155 722 189 730 _c +223 738 255 742 284 742 _c +}_e{359 742 419 723 464 685 _c +509 647 532 597 532 534 _c +532 504 526 475 515 449 _c +504 422 484 390 454 354 _c +446 344 420 317 376 272 _c +332 227 271 164 192 83 _c +_cl}_e}_d +/three{{636 0 76 -13 556 742 _sc +406 393 _m +453 383 490 362 516 330 _c +542 298 556 258 556 212 _c +556 140 531 84 482 45 _c +432 6 362 -13 271 -13 _c +240 -13 208 -10 176 -4 _c +144 1 110 10 76 22 _c +76 117 _l +103 101 133 89 166 81 _c +198 73 232 69 268 69 _c +330 69 377 81 409 105 _c +441 129 458 165 458 212 _c +458 254 443 288 413 312 _c +383 336 341 349 287 349 _c +}_e{202 349 _l +202 430 _l +291 430 _l +339 430 376 439 402 459 _c +428 478 441 506 441 543 _c +441 580 427 609 401 629 _c +374 649 336 659 287 659 _c +260 659 231 656 200 650 _c +169 644 135 635 98 623 _c +98 711 _l +135 721 170 729 203 734 _c +235 739 266 742 296 742 _c +370 742 429 725 473 691 _c +517 657 539 611 539 553 _c +539 513 527 479 504 451 _c +481 423 448 403 406 393 _c +_cl}_e}_d +/five{{636 0 77 -13 549 729 _sc +108 729 _m +495 729 _l +495 646 _l +198 646 _l +198 467 _l +212 472 227 476 241 478 _c +255 480 270 482 284 482 _c +365 482 429 459 477 415 _c +525 370 549 310 549 234 _c +549 155 524 94 475 51 _c +426 8 357 -13 269 -13 _c +238 -13 207 -10 175 -6 _c +143 -1 111 6 77 17 _c +77 116 _l +106 100 136 88 168 80 _c +199 72 232 69 267 69 _c +}_e{323 69 368 83 401 113 _c +433 143 450 183 450 234 _c +450 284 433 324 401 354 _c +368 384 323 399 267 399 _c +241 399 214 396 188 390 _c +162 384 135 375 108 363 _c +108 729 _l +_cl}_e}_d +/seven{636 0 82 0 551 729 _sc +82 729 _m +551 729 _l +551 687 _l +286 0 _l +183 0 _l +432 646 _l +82 646 _l +82 729 _l +_cl}_d +/nine{{636 0 63 -13 566 742 _sc +110 15 _m +110 105 _l +134 93 159 84 185 78 _c +210 72 235 69 260 69 _c +324 69 374 90 408 134 _c +442 178 462 244 468 334 _c +448 306 424 284 396 269 _c +367 254 335 247 300 247 _c +226 247 168 269 126 313 _c +84 357 63 417 63 494 _c +63 568 85 628 129 674 _c +173 719 232 742 306 742 _c +390 742 455 709 499 645 _c +543 580 566 486 566 364 _c +}_e{566 248 538 157 484 89 _c +429 21 356 -13 264 -13 _c +239 -13 214 -10 189 -6 _c +163 -2 137 5 110 15 _c +306 324 _m +350 324 385 339 411 369 _c +437 399 450 441 450 494 _c +450 546 437 588 411 618 _c +385 648 350 664 306 664 _c +262 664 227 648 201 618 _c +175 588 162 546 162 494 _c +162 441 175 399 201 369 _c +227 339 262 324 306 324 _c +_cl}_e}_d +/P{603 0 98 0 569 729 _sc +197 648 _m +197 374 _l +321 374 _l +367 374 402 385 427 409 _c +452 433 465 467 465 511 _c +465 555 452 588 427 612 _c +402 636 367 648 321 648 _c +197 648 _l +98 729 _m +321 729 _l +402 729 464 710 506 673 _c +548 636 569 582 569 511 _c +569 439 548 384 506 348 _c +464 311 402 293 321 293 _c +197 293 _l +197 0 _l +98 0 _l +98 729 _l +_cl}_d +/T{611 0 -2 0 614 729 _sc +-2 729 _m +614 729 _l +614 646 _l +355 646 _l +355 0 _l +256 0 _l +256 646 _l +-2 646 _l +-2 729 _l +_cl}_d +/V{684 0 8 0 676 729 _sc +286 0 _m +8 729 _l +111 729 _l +342 115 _l +573 729 _l +676 729 _l +398 0 _l +286 0 _l +_cl}_d +/b{{635 0 91 -13 580 760 _sc +487 273 _m +487 339 473 390 446 428 _c +418 466 381 485 334 485 _c +286 485 249 466 222 428 _c +194 390 181 339 181 273 _c +181 207 194 155 222 117 _c +249 79 286 61 334 61 _c +381 61 418 79 446 117 _c +473 155 487 207 487 273 _c +181 464 _m +199 496 223 520 252 536 _c +281 552 316 560 356 560 _c +422 560 476 533 518 481 _c +559 428 580 359 580 273 _c +}_e{580 187 559 117 518 65 _c +476 13 422 -13 356 -13 _c +316 -13 281 -5 252 10 _c +223 25 199 49 181 82 _c +181 0 _l +91 0 _l +91 760 _l +181 760 _l +181 464 _l +_cl}_e}_d +/c{{550 0 55 -13 488 560 _sc +488 526 _m +488 442 _l +462 456 437 466 411 473 _c +385 480 360 484 334 484 _c +276 484 230 465 198 428 _c +166 391 150 339 150 273 _c +150 206 166 154 198 117 _c +230 80 276 62 334 62 _c +360 62 385 65 411 72 _c +437 79 462 90 488 104 _c +488 21 _l +462 9 436 0 410 -5 _c +383 -10 354 -13 324 -13 _c +242 -13 176 12 128 64 _c +}_e{79 115 55 185 55 273 _c +55 362 79 432 128 483 _c +177 534 244 560 330 560 _c +358 560 385 557 411 551 _c +437 545 463 537 488 526 _c +_cl}_e}_d +/e{{615 0 55 -13 562 560 _sc +562 296 _m +562 252 _l +149 252 _l +153 190 171 142 205 110 _c +238 78 284 62 344 62 _c +378 62 412 66 444 74 _c +476 82 509 95 541 113 _c +541 28 _l +509 14 476 3 442 -3 _c +408 -9 373 -13 339 -13 _c +251 -13 182 12 131 62 _c +80 112 55 181 55 268 _c +55 357 79 428 127 481 _c +175 533 241 560 323 560 _c +397 560 455 536 498 489 _c +}_e{540 441 562 377 562 296 _c +472 322 _m +471 371 457 410 431 440 _c +404 469 368 484 324 484 _c +274 484 234 469 204 441 _c +174 413 156 373 152 322 _c +472 322 _l +_cl}_e}_d +/i{278 0 94 0 184 760 _sc +94 547 _m +184 547 _l +184 0 _l +94 0 _l +94 547 _l +94 760 _m +184 760 _l +184 646 _l +94 646 _l +94 760 _l +_cl}_d +/m{{974 0 91 0 889 560 _sc +520 442 _m +542 482 569 511 600 531 _c +631 550 668 560 711 560 _c 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118 _c +219 80 257 62 306 62 _c +354 62 392 80 420 118 _c +448 156 462 207 462 273 _c +462 337 448 389 420 427 _c +392 465 354 484 306 484 _c +306 560 _m +384 560 445 534 490 484 _c +534 433 557 363 557 273 _c +557 183 534 113 490 63 _c +445 12 384 -13 306 -13 _c +227 -13 165 12 121 63 _c +77 113 55 183 55 273 _c +55 363 77 433 121 484 _c +165 534 227 560 306 560 _c +_cl}_d +/p{{635 0 91 -207 580 560 _sc +181 82 _m +181 -207 _l +91 -207 _l +91 547 _l +181 547 _l +181 464 _l +199 496 223 520 252 536 _c +281 552 316 560 356 560 _c +422 560 476 533 518 481 _c +559 428 580 359 580 273 _c +580 187 559 117 518 65 _c +476 13 422 -13 356 -13 _c +316 -13 281 -5 252 10 _c +223 25 199 49 181 82 _c +487 273 _m +487 339 473 390 446 428 _c +418 466 381 485 334 485 _c +}_e{286 485 249 466 222 428 _c +194 390 181 339 181 273 _c +181 207 194 155 222 117 _c +249 79 286 61 334 61 _c +381 61 418 79 446 117 _c +473 155 487 207 487 273 _c +_cl}_e}_d +/q{{635 0 55 -207 544 560 _sc +148 273 _m +148 207 161 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index 0000000..c1c732e Binary files /dev/null and b/doc/compte_rendu/images/utilisation/targets.png differ diff --git a/doc/compte_rendu/images/utilisation/targets_yellow.png b/doc/compte_rendu/images/utilisation/targets_yellow.png new file mode 100644 index 0000000..2c0c9ff Binary files /dev/null and b/doc/compte_rendu/images/utilisation/targets_yellow.png differ diff --git a/doc/compte_rendu/main.tex b/doc/compte_rendu/main.tex new file mode 100644 index 0000000..0709685 --- /dev/null +++ b/doc/compte_rendu/main.tex @@ -0,0 +1,107 @@ +\documentclass[]{report} +\usepackage[utf8]{inputenc} +\usepackage{fontenc} +\usepackage{tikz} +\usepackage{nameref} +\usepackage[french]{babel} +\usepackage{minted} +\usepackage{amsmath,amsmath,amsfonts,amssymb} +\usepackage{graphicx} +\usepackage{verbatim} +\usepackage{stmaryrd} +\usepackage{placeins} +\usepackage{mdframed} +\usepackage{url} +\usepackage{pdflscape} + +\usepackage{geometry} % Required for adjusting page dimensions + +\geometry{ + top=2cm, % Top margin + bottom=2cm, % Bottom margin + left=2cm, % Left margin + right=2cm, % Right margin + includehead, % Include space for a header + includefoot, % Include space for a footer + %showframe, % Uncomment to show how the type block is set on the page +} + +\newcommand*\intervalleEntier[2]{\intervalle{\llbracket}{#1}{#2}{\rrbracket}} +\newcommand*\intervalle[4]{\left#1 #2 \, ; #3 \right#4} +\newcommand*\floor[1]{\left \lfloor{#1}\right \rfloor} + +\surroundwithmdframed{minted} + +\usetikzlibrary{shapes,arrows} +\tikzstyle{block} = [draw, fill=blue!20, rectangle, minimum height=3em, minimum width=6em] +\tikzstyle{sum} = [draw, fill=blue!20, circle, node distance=1cm] +\tikzstyle{input} = [coordinate] +\tikzstyle{output} = [coordinate] +\tikzstyle{pinstyle} = [pin edge={to-,thin,black}] + + +\begin{document} +\begin{titlepage} +\begin{center} + +\includegraphics[width=0.6\textwidth]{LogoCS.png}\\[1cm] + +{\large Projet double de deuxième année}\\[0.5cm] + +% Title +\rule{\linewidth}{0.5mm} \\[0.4cm] +{ \huge \bfseries Asservissement "rigide" de drone \\[0.4cm] } +\rule{\linewidth}{0.5mm} \\[1.5cm] + +% Author and supervisor +\noindent +\begin{minipage}{0.4\textwidth} + \begin{flushleft} \large + \emph{Auteurs :}\\ + M. Hugo \textsc{Levy--Falk}\\ + M\up{lle} Joanne \textsc{Steiner}\\ + \end{flushleft} +\end{minipage}% +\begin{minipage}{0.4\textwidth} + \begin{flushright} \large + \emph{Encadrants :} \\ + M Jean-Louis \textsc{Gutzwiller}\\ + M. Hervé \textsc{Frezza-Buet} + \end{flushright} +\end{minipage} + +\vfill + +% Bottom of the page +{\large Version du \today} + +\end{center} +\end{titlepage} + +\newpage\null\thispagestyle{empty}\newpage + +\begin{abstract} +Dans ce rapport, nous détaillons la mise en place d'un asservissement en position d'un drone BeBop en utilisant le flux optique qu'il fournit. Pour cela nous utilisons diverses corrections (PI, PD, PID) et le framework RobotOS. +\end{abstract} + +\tableofcontents +%\listoffigures + +\input{chap_introduction.tex} +\input{chap_modelisation.tex} +\input{chap_realisation.tex} +\input{chap_utilisation.tex} +\input{chap_conclusion.tex} + +\appendix + +\input{chap_probleme.tex} +\input{chap_installation.tex} +\input{chap_export.tex} +\input{chap_testfilter.tex} +\input{chap_generation.tex} +\input{chap_configuration.tex} + +\bibliographystyle{plain} +\bibliography{biblio} +\end{document} diff --git a/doc/compte_rendu/noeuds.png b/doc/compte_rendu/noeuds.png new file mode 100644 index 0000000..f73a9de Binary files /dev/null and b/doc/compte_rendu/noeuds.png differ diff --git a/doc/compte_rendu/presentation.tex b/doc/compte_rendu/presentation.tex new file mode 100644 index 0000000..50b82e3 --- /dev/null +++ b/doc/compte_rendu/presentation.tex @@ -0,0 +1,360 @@ +\documentclass[aspectratio=169]{beamer} \usepackage[utf8]{inputenc} +\usepackage[french]{babel} +\usepackage{minted} +\usepackage{xcolor} +\usepackage{tikz} + \usepackage{appendixnumberbeamer} + + +\definecolor{boxcolor}{HTML}{23373B} + + +\usetikzlibrary{shapes,arrows} +\tikzstyle{block} = [draw, fill=boxcolor!30, rectangle, minimum height=3em, minimum width=6em] +\tikzstyle{sum} = [draw, fill=boxcolor!30, circle, node distance=1cm] +\tikzstyle{input} = [coordinate] +\tikzstyle{output} = [coordinate] +\tikzstyle{pinstyle} = [pin edge={to-,thin,black}] + +\usepackage{amsmath,amsmath,amsfonts,amssymb} + \usetheme{metropolis} + \setbeamertemplate{footline}[frame number] + +\newcommand*\intervalleEntier[2]{\intervalle{\llbracket}{#1}{#2}{\rrbracket}} +\newcommand*\intervalle[4]{\left#1 #2 \, ; #3 \right#4} +\newcommand*\floor[1]{\left \lfloor{#1}\right \rfloor} + + \title{\includegraphics[width=8cm]{LogoCS.png}\\Asservissement rigide de drones} + \author{Hugo \bsc{Levy--Falk} et Joanne \bsc{Steiner}}\institute{CentraleSupélec} + \date{Soutenance de projet} + + \begin{document} + + \begin{frame} + \titlepage + \end{frame} + + \section{Introduction} + + \begin{frame}{Objectifs du projet} + Asservissement plus "rigide" d'un drone + \begin{itemize} + \item<2-> Stabilité + \item<3-> Rapidité + \end{itemize} + \end{frame} + + \begin{frame}{Livrables} + \begin{itemize} + \item Une bibliothèque d'automatique; + \item Un exemple d'asservissement en simple boucle. + \end{itemize} + \end{frame} + + \section{Utilisation de la bibliothèque} + + \begin{frame}{Pourquoi ?} + \begin{itemize} + \item Faire de l'automatique avec ROS; + \item Utilisable dans des cas plus généraux que l'asservissement d'un drone. + \end{itemize} + \end{frame} + + \begin{frame}{Fonctionnement} + \begin{itemize} + \item Script Python permettant de créer des n\oe uds; + \item Fichiers de configuration pour gérer les paramètres dynamiquement; + \item Fichiers launch pour relier les n\oe uds entre eux. + \end{itemize} + \begin{center} + \includegraphics[width=0.3\linewidth]{images/presentation/brique.jpg} + \end{center} + \end{frame} + + \begin{frame}{Différents n\oe uds} + \begin{itemize} + \item On a les n\oe uds suivants : + \begin{itemize} + \item \mintinline{python}|ProportionalNode|; + \item \mintinline{python}|SaturateNode|; + \item \mintinline{python}|DerivativeNode|; + \item \mintinline{python}|DifferenciateNode|; + \item \mintinline{python}|SumNode|; + \item \mintinline{python}|InputNode|; + \item \mintinline{python}|RateNode|. + \end{itemize} + \item Calcul de la vitesse du n\oe ud \mintinline{python}|DerivativeNode| grâce à un filtre de \bsc{Savitzky-Golay}. + \end{itemize} + \end{frame} + + \begin{frame}{Performances de \bsc{Savitzky-Golay}} + \begin{figure} + \centering + \includegraphics[height=0.7\textheight]{images/realisation/mesure_vitesse_big_quadra.eps} + \caption{Filtre de \bsc{Savitsky-Golay}} + \end{figure} + \end{frame} + + \begin{frame}[fragile]{Utilisation du script} + \begin{minted}{bash} +python control_compute.py derivative +python control_compute.py proportional +python control_compute.py sum 3 +... + \end{minted} + \end{frame} + \begin{frame}{Utilisation du script} + \includegraphics[width=\linewidth]{images/realisation/control_launch.png} + \end{frame} + + \section{Interface avec le drone} + + \begin{frame}{Rappels} + \begin{itemize} + \item Objectif : Asservir le drone; + \item Livrable : Une bibliothèque pour faire de l'automatique. + \end{itemize} + \end{frame} + + \begin{frame}{Détection des cibles} + \begin{itemize} + \item Idée du script : Détecter les zones d'une couleur choisie; + \item Possibilité de modifier dynamiquement la couleur. + \end{itemize} + \end{frame} + + \begin{frame}{Détection du bleu} + \begin{figure} + \centering + \includegraphics[height=0.7\textheight]{images/utilisation/targets.png} + \caption{Cibles bleues} + \end{figure} + \end{frame} + + \begin{frame}{Détection du jaune} + \begin{figure} + \centering + \includegraphics[height=0.7\textheight]{images/utilisation/targets_yellow.png} + \caption{Cibles jaunes} + \end{figure} + \end{frame} + \begin{frame}{Interface avec le contrôleur} + \centering + \includegraphics[width=\linewidth]{images/presentation/schema_mesure.png} + \end{frame} + + \begin{frame}{Simple boucle : Principe} +\centering +\begin{tikzpicture}[auto, node distance=2cm,>=latex'] +% We start by placing the blocks +\node [input, name=input] {}; +\node [sum, right of=input, node distance=3cm] (sum) {}; +\node [block, right of=sum] (controller) {$C(p)$}; +\node [block, right of=controller, +node distance=3cm] (system) {Drone}; +% We draw an edge between the controller and system block to +% calculate the coordinate u. We need it to place the measurement block. +\node [output, right of=system, node distance=5cm] (output) {}; +\node [block, below of=system] (measure) {Mesure}; + +% Once the nodes are placed, connecting them is easy. +\draw [draw,->] (input) -- node[pos=0.99] {$+$} (sum); +\draw [->] (sum) -- node {$\epsilon$} (controller); +\draw [->] (controller) -- (system); +\draw [->] (system) -- node [name=y] {position }(output); +\draw [->] (y) |- (measure); +\draw [->] (measure) -| node[pos=0.99] {$-$} +node [near end] {mesure de la position} (sum); +\end{tikzpicture} + \end{frame} + + \begin{frame}{Axes du drone} + + \includegraphics[height=\textheight]{images/modelisation/drone_axes.png} + + \end{frame} + + \begin{frame}{Diagramme de bode selon l'axe z et l'angle z} + \begin{figure}[h!] + \centering + \includegraphics[width=0.5\linewidth]{images/modelisation/bode_z.eps} + \caption{Diagramme de Bode simplifié} + $C(p)=K_p+K_i/p + K_d p$ +\end{figure} + \end{frame} + + \begin{frame}{Diagramme de Bode selon les axes x et y} + \begin{figure}[h!] + \centering + \includegraphics[width=0.5\linewidth]{images/modelisation/bode_u.eps} + \caption{Diagramme de Bode simplifié} + $C(p)=K_p+K_d p$ +\end{figure} + \end{frame} + + \begin{frame}{Réglage de la simple boucle} + \begin{itemize} + \item Axe z et angle z : Méthode de \bsc{Ziegler-Nichols} en oscillations entretenues, puis ajustements; + \item Axe x et y : Méthode empirique car \bsc{Ziegler-Nichols} trop instable; + \item Amélioration éventuelle avec une double boucle + \end{itemize} + \end{frame} + \section{Conclusion} + + \begin{frame}{Conclusion} + \begin{itemize} + \item Bibliothèque fonctionnelle; + \item Asservissement fonctionnelle extensible à d'autres applications; + \item Extension éventuelle à une double boucle. + \end{itemize} + \includegraphics[height=0.5\textheight]{images/presentation/marvin.jpg} + \end{frame} + +\appendix + +\begin{frame}{Diagramme UML} + \begin{figure} + \centering + \includegraphics[width=\linewidth]{images/realisation/uml.png} + \caption{Diagramme UML} + \label{fig:uml} + \end{figure} +\end{frame} + +\begin{frame}{Savitzky-Golay} +\begin{columns}[T] +\begin{column}{.48\textwidth} + $((x_i,y_i))_{i\in\intervalleEntier{1}{n}}$ les $n$ points de la fenêtre + + Polynôme $a_0 + a_1 X + \dots + a_k X^k$ + + \begin{equation*} +\left \| + \begin{pmatrix} + y_1 \\ + y_2 \\ + \vdots \\ + y_n + \end{pmatrix} + - + \begin{pmatrix} + 1 & x_1 & x_1 ^2 & \cdots & x_1 ^ k \\ + 1 & x_2 & x_2 ^2 & \cdots & x_2 ^ k \\ + \vdots & \vdots & \vdots & & \vdots \\ + 1 & x_n & x_n ^2 & \cdots & x_n ^ k + \end{pmatrix} + \cdot + \begin{pmatrix} + a_0 \\ + a_1 \\ + \vdots \\ + a_k + \end{pmatrix} +\right \| ^2 +\label{eq:moindrecarres_raw} +\end{equation*} +\end{column} +\begin{column}{.48\textwidth} +En supposant les $x_i$ centrés en 0 et espacés régulièrement d'un pas $h$, et $k$ impair, +\end{column} +\end{columns} +\end{frame} +\begin{frame}{Savitsky-Golay} + \begin{eqnarray*} + L((y_k),(a_k)) &=& + \left \| + \underbrace{ + \begin{pmatrix} + y_1 \\ + y_2 \\ + \vdots \\ + y_n + \end{pmatrix}}_{=Y} + - + \underbrace{ + \begin{pmatrix} + 1 & -\floor{\frac{n}{2}} & \left(-\floor{\frac{n}{2}}\right) ^2 & \cdots & \left(-\floor{\frac{n}{2}}\right) ^ k \\ + 1 & \left(-\floor{\frac{n-1}{2}}\right) & \left(-\floor{\frac{n-1}{2}}\right) ^2 & \cdots & \left(-\floor{\frac{n-1}{2}}\right) ^ k \\ + \vdots & \vdots & \vdots & \vdots & \vdots \\ + 1 & -1 & \left(-1\right) ^2 & \cdots & \left(-1\right) ^ k \\ + 1 & 0 & 0 & \cdots & 0 \\ + 1 & \left(1\right) & \left(1\right) ^2 & \cdots & \left(1\right) ^ k \\ + \vdots & \vdots & \vdots & \vdots & \vdots \\ + 1 & \left(\floor{\frac{n-1}{2}}\right) & \left(\floor{\frac{n-1}{2}}\right) ^2 & \cdots & \left(\floor{\frac{n-1}{2}}\right) ^ k \\ + 1 & \left(\floor{\frac{n}{2}}\right) & \left(\floor{\frac{n}{2}}\right) ^2 & \cdots & \left(\floor{\frac{n}{2}}\right) ^ k + \end{pmatrix}}_{=M} + \cdot + \underbrace{ + \begin{pmatrix} + a'_0 \\ + a'_1 \\ + \vdots \\ + a'_k + \end{pmatrix}}_{=A} +\right \| ^2 \\ +\label{eq:moindrecarres} +\end{eqnarray*} +\end{frame} +\begin{frame}{Savitsky-Golay} + \begin{eqnarray} + \frac{\partial L}{\partial (A)}(A) &=& -2 \cdot M^\intercal \cdot (Y - M \cdot A)\\ + A &=& \underbrace{(M^\intercal\cdot M)^{-1} \cdot M^\intercal}_{=B} \cdot Y +\end{eqnarray} +Dérivée d'ordre $d$, on convolue le signal par le filtre RIF $[b_1, \dots b_n ]$, avec +\begin{equation} + \forall i \in \intervalleEntier{0}{n}, b_i = B_{d,n-i} +\end{equation} +\end{frame} + +\begin{frame}{Méthode de \bsc{Ziegler-Nichols}} +\centering + \begin{tabular}{|c|c|} + \hline + Type de contrôle & Paramètres de réglage \\ + \hline + P.I.D & $K_p=0.6 K_u$ $K_i=\frac{T_u}{2}$ $K_d=\frac{T_u}{8}$ \\ + \hline + P.I.D peu de dépassement & $K_p=0.33 K_u$ $K_i=\frac{T_u}{2}$ $K_d=\frac{T_u}{3}$ \\ + \hline + P.I.D aucun dépassement & $K_p=0.2 K_u$ $K_i=\frac{T_u}{2}$ $K_d=\frac{T_u}{3}$ \\ + \hline +\end{tabular} +\end{frame} + +\begin{frame}{Double boucle} +\begin{tikzpicture}[auto, node distance=2cm,>=latex',scale=0.7, every node/.style={scale=0.7}] +% We start by placing the blocks +\node [input, name=input] {}; +\node [sum, right of=input, node distance=3cm] (sum) {}; +\node [block, right of=sum] (controller) {$C_p(p)$}; +\node [sum, right of=controller, node distance=3cm] (sum_speed) {}; +\node [block, right of=sum_speed] (controller_speed) {$C_v(p)$}; +\node [block, right of=controller_speed, +node distance=3cm] (system) {Drone}; +\node [block, right of=system, +node distance=3cm] (integrate) {$\frac{1}{p}$}; +\node [block, below of=controller_speed] (measurements_speed) {Mesure}; +% We draw an edge between the controller and system block to +% calculate the coordinate u. We need it to place the measurement block. +\draw [->] (controller) -- node[pos=0.99] {$+$} +node [near end] {$u$} (sum_speed); +\node [output, right of=system, node distance=5cm] (output) {}; +\node [block, below of=measurements_speed] (measurements) {Mesure}; + +% Once the nodes are placed, connecting them is easy. +\draw [draw,->] (input) -- node {position attendue +} (sum); +\draw [->] (sum) -- node {$\epsilon_p$} (controller); +\draw [->] (sum_speed) -- node {$\epsilon_v$} (controller_speed); +\draw [->] (controller_speed) -- node [name=x] {} (system); +\draw [->] (system) -- node [name=v] {} (integrate); +\draw [->] (measurements_speed) -| node[pos=0.99] {$-$} +node [near end] {mesure de la vitesse} (sum_speed); +\draw [->] (integrate) -- node [name=y] {position }(output); +\draw [->] (v) |- (measurements_speed); +\draw [->] (y) |- (measurements); +\draw [->] (measurements) -| node[pos=0.99] {$-$} +node [near end] {mesure de la position} (sum); +\end{tikzpicture} +\end{frame} + +\end{document} \ No newline at end of file diff --git a/doc/compte_rendu/scripts/parse_topic.py b/doc/compte_rendu/scripts/parse_topic.py new file mode 100644 index 0000000..d39d16c --- /dev/null +++ b/doc/compte_rendu/scripts/parse_topic.py @@ -0,0 +1,34 @@ +#! /usr/bin/python3 + +import yaml +import sys +import time + +import click + + +@click.command() +@click.option('--output', default="output.csv", help='Output file') +@click.option('--time/--no-time', 'use_time', default=False, help='Add the number of seconds') +@click.option('--field', default="data", help='YAML field to store') +def main(output, use_time, field): + with open(output, 'w') as f: + s = "" + last_line = "" + try: + for line in sys.stdin: + if line == "---\n": + v = yaml.load(s)[field] + print(v) + if use_time: + f.write(str(time.time()) + ',' + str(v) + "\n") + else: + f.write(str(v)+"\n") + s = "" + else: + s += line + '\n' + except KeyboardInterrupt: + print("Output saved to " + output) + +if __name__ == '__main__': + main() diff --git a/doc/compte_rendu/scripts/test_filter.jl b/doc/compte_rendu/scripts/test_filter.jl new file mode 100644 index 0000000..824925a --- /dev/null +++ b/doc/compte_rendu/scripts/test_filter.jl @@ -0,0 +1,68 @@ +using Plots +using DSP +using CSV + +pyplot() + +# Parameters +filename = joinpath(@__DIR__, "data", "walk.csv") # input file +h = 1/22 # sample time +orders = [ + (title="quadratique", order=2, sizes=5:2:11), + (title="cubique", order=3, sizes=5:2:11), + (title="big_quadra", order=2, sizes=11:10:51) +] + + +function savgol(size::Int64, poly_order::Int64, deriv::Int64=0, delta::Float64=1.0, conv::Bool=false) + half_size, rem = divrem(size, 2) + if rem == 0 + throw(ArgumentError("size must be odd.")) + end + M = [-half_size:half_size;] .^ [0:poly_order;]'; + y = zeros(poly_order+1)'; + y[deriv+1] = factorial(deriv) / delta^deriv; + scal = y*inv(M'*M)*M' + if conv + scal = scal[end:-1:1] + end + scal +end + +error = (CSV.read(filename, header=false) |> Matrix{Float64})[:,2] + + +for order in orders + plot( + 0:h:(length(error)-1)*h, + error, + label="erreur mesurée", + layout=(2,1), + subplot=1, + title="Position", + xrotation=60, + xlabel="Temps (s)", + ylabel="Position (m)", + reuse=false, + size=(1000, 600) + ) + plot!( + subplot=2, + title="Vitesse mesurée", + xrotation=60, + xlabel="Temps (s)", + ylabel="Vitesse (\$m.s^{-1}\$)" + ) + for size in order.sizes + filter = savgol(size, order.order, 1, h, true) + speed = conv(filter, error)[size:end-size] + plot!( + size*h/2:h:size*h/2+(length(speed)-1)*h, + speed, + label=string(order.title, " ", size, " points"), + subplot=2 + ) + end + savefig(joinpath(@__DIR__, "results", string("mesure_vitesse_", order.title, ".eps"))) +end +show() diff --git a/doc/compte_rendu/scripts/test_find_targets.py b/doc/compte_rendu/scripts/test_find_targets.py new file mode 100644 index 0000000..2182eaf --- /dev/null +++ b/doc/compte_rendu/scripts/test_find_targets.py @@ -0,0 +1,32 @@ +import matplotlib.pyplot as pl +from matplotlib.patches import Rectangle + +from find_targets import find_targets, normalize_coordinates + +ax = pl.subplot(211) +img = pl.imread('image.jpeg') + + +H, L, R, objects = find_targets(img, return_slices=True) + +for o in objects: + x, y = o + r = Rectangle((y.start, x.start), y.stop-y.start, x.stop-x.start, linewidth=1,edgecolor='r',facecolor='none') + ax.add_patch(r) +ax.imshow(img) +ax.plot([H[0], L[0], R[0]], [H[1], L[1], R[1]], 'o', color='red') + +ax = pl.subplot(212) + +w = len(img[0]) +h = len(img) + +H = normalize_coordinates(H, w, h) +L = normalize_coordinates(L, w, h) +R = normalize_coordinates(R, w, h) +ax.plot([H[0], L[0], R[0]], [H[1], L[1], R[1]], 'o', color='red') +ax.grid() +ax.set_title("Positions normalisées") + + +pl.show() \ No newline at end of file diff --git a/doc/compte_rendu/triangle_control.svg b/doc/compte_rendu/triangle_control.svg new file mode 100644 index 0000000..4572026 --- /dev/null +++ b/doc/compte_rendu/triangle_control.svg @@ -0,0 +1,10 @@ + + + + + + + + + + diff --git a/doc/compte_rendu/uml_control.eps b/doc/compte_rendu/uml_control.eps new file mode 100644 index 0000000..86be78f --- /dev/null +++ b/doc/compte_rendu/uml_control.eps @@ -0,0 +1,4222 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: GIMP PostScript file plugin V 1,17 by Peter Kirchgessner +%%Title: uml_control.eps +%%CreationDate: Fri May 24 17:48:56 2019 +%%DocumentData: Clean7Bit +%%LanguageLevel: 2 +%%Pages: 1 +%%BoundingBox: 14 14 856 610 +%%EndComments +%%BeginProlog +% Use own dictionary to avoid conflicts +10 dict begin +%%EndProlog +%%Page: 1 1 +% Translate for offset +14.173228346456694 14.173228346456694 translate +% Translate to begin of first scanline +0 595.20000000000005 translate +841.60000000000014 -595.20000000000005 scale +% Image geometry +1052 744 8 +% Transformation matrix +[ 1052 0 0 744 0 0 ] +% Strings to hold RGB-samples per scanline +/rstr 1052 string def +/gstr 1052 string def 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a/doc/rapport.pdf b/doc/rapport.pdf new file mode 100644 index 0000000..4281f6a Binary files /dev/null and b/doc/rapport.pdf differ diff --git a/launch/simple_loop.launch b/launch/simple_loop.launch index 5eb1e6a..407f3e8 100644 --- a/launch/simple_loop.launch +++ b/launch/simple_loop.launch @@ -1,10 +1,10 @@ - - - - + + + + diff --git a/utils/parse_topic.py b/utils/parse_topic.py index 94345a2..d39d16c 100755 --- a/utils/parse_topic.py +++ b/utils/parse_topic.py @@ -8,7 +8,7 @@ import click @click.command() -@click.option('--output', default="output.csv", help='Number of greetings.') +@click.option('--output', default="output.csv", help='Output file') @click.option('--time/--no-time', 'use_time', default=False, help='Add the number of seconds') @click.option('--field', default="data", help='YAML field to store') def main(output, use_time, field): diff --git a/utils/results/savgol_bode_plop.eps b/utils/results/savgol_bode_plop.eps index 183f602..aed5f95 100644 --- a/utils/results/savgol_bode_plop.eps +++ b/utils/results/savgol_bode_plop.eps @@ -1,6 +1,6 @@ %!PS-Adobe-3.0 EPSF-3.0 %%Creator: matplotlib version 2.2.4, http://matplotlib.org/ -%%CreationDate: Tue Jun 4 14:06:46 2019 +%%CreationDate: Thu Jun 6 21:14:01 2019 %%Orientation: portrait %%BoundingBox: 90 252 522 540 %%EndComments diff --git a/utils/test_filter_bode.jl b/utils/test_filter_bode.jl index 302bd0b..e0ef729 100644 --- a/utils/test_filter_bode.jl +++ b/utils/test_filter_bode.jl @@ -1,6 +1,7 @@ using Plots using DSP using CSV +using ControlSystems pyplot() @@ -29,19 +30,12 @@ function savgol(size::Int64, poly_order::Int64, deriv::Int64=0, delta::Float64=1 scal end - -filter = savgol(19, 2, 1, h, true) -H = tf(filter, [1], h) -mag, phase, w = bode(H) -plot(w,log.(mag[:,1]), label="mag", title="plop") -savefig(joinpath(@__DIR__, "results", string("savgol_bode_", "plop", ".eps"))) +plot(title="Comparaison de tailles de filtres") +for size in orders[3].sizes + filter = savgol(size, 2, 1, h, true) + H = tf(filter, [1], h) + mag, phase, w = bode(H) + plot!(w,log.(mag[:,1]), label=string(size, " points")) +end +savefig(joinpath(@__DIR__, "results", "savgol_bode.eps")) show() -# for order in orders -# for size in order.sizes -# filter = savgol(size, order.order, 1, h, true) -# H = tf(filter, [1], 0.05) -# bode(H) -# end -# savefig(joinpath(@__DIR__, "results", string("savgol_bode_", order.title, ".eps"))) -# end -# show()