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 # Ignore PDFs on master
 literature/
 
-# Pictures stuff
+# Pictures
 *.png
-# But not the whole scheme
-!teleoperation_overview.png
+# But not the necessary ones
+!docs/figures/**/*
 
 # Presentation stuff
 *.pptx
 
 # fuck apple
 .DS_Store
+
+# Latex Stuff
+build/
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+\documentclass[conference]{IEEEtran}
+
+% \IEEEoverridecommandlockouts
+% The preceding line is only needed to identify funding in the first footnote.
+% If that is unneeded, please comment it out.
+
+\usepackage{cite}
+\usepackage{amsmath,amssymb,amsfonts}
+% \usepackage{algorithmic}
+\usepackage{graphicx}
+\usepackage{textcomp}
+\usepackage{xcolor}
+\usepackage{subcaption}
+\usepackage{todonotes}
+
+\def\BibTeX{{\rm B\kern-.05em{\sc i\kern-.025em b}\kern-.08em
+    T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}
+
+\begin{document}
+
+\title{Humanoid Robotic Systems - ``Teleoperating NAO''}
+
+\author{Pavel Lutskov, Luming Li, Lukas Otter and Atef Kort}
+
+\maketitle
+
+\section{Project Description}
+
+In this semester the task of our group was to program a routine for
+teleoperation of a NAO robot. Using the ArUco markers, placed on the operator's
+chest and hands, the position and the posture of the operator should have been
+determined by detecting the markers' locations with a webcam, and then the
+appropriate commands should have been sent to the robot to imitate the motions
+of the operator. The overview of the
+process can be seen in \ref{fig:overview}. The main takeaway from
+fulfilling this objective was practicing the skills that we acquired during the
+Humanoid Robotic Systems course and to get familiar with the NAO robot as a
+research and development platform.
+
+\begin{figure}[h]
+  \centering
+  \includegraphics[width=\linewidth]{figures/teleoperation_overview.png}
+  \caption{Overview of the defined states and their transistions.}
+  \label{fig:overview}
+\end{figure}
+
+In closer detail, once the markers are detected, their coordinates relative to
+the webcam are extracted. The position and the orientation of the user's
+chest marker is used to control the movement of the NAO around the environment.
+We call this approach a ``Human Joystick'' and we describe it in more detail in
+\ref{ssec:navigation}.
+
+The relative locations of the chest and hand markers can be used to determine
+the coordinates of the user's end effectors (i.e.\ hands) in the user's chest
+frame. In order for the NAO to imitate the arm motions, these coordinates need
+to be appropriately remapped into the NAO torso frame. With the knowledge of the
+desired coordinates of the hands, the commands for the NAO joints can be
+calculated by using the Cartesian control approach. We present a thorough
+discussion of the issues we had to solve and the methods we used for arm motion
+imitation in \ref{ssec:imitation}.
+
+Furthermore, in order to enable the most intuitive teleoperation, a user
+interface was needed to be developed. In our system, we present the operator
+with a current estimation of the operator's pose, a sensor feedback based robot
+pose, as well as with the camera feed from both NAO's cameras and with the
+webcam view of the operator. In order for the user to be able to give explicit
+commands to the robot, such as a request to open or close the hands or to
+temporarily suspend the operation, we implemented a simple voice command system.
+Finally, to be able to accommodate different users and to perform control in
+different conditions, a small calibration routine was developed, which would
+quickly take a user through the process of setting up the teleoperation.
+We elaborate on the tools and approaches that we used for implementation of the
+user-facing features in \ref{ssec:interface}.
+
+An example task, that can be done using our teleoperation package might be the
+following. The operator can safely and precisely navigate the robot through an
+uncharted environment with a high number of obstacles to some lightweight
+object, such as an empty bottle, then make the robot pick up that object and
+bring the object back to the operator. Thanks to the high precision of the arm
+motions and the constant operator input, the robot is able to pick up an object
+of different shapes and sizes, applying different strategies when needed. We
+demonstrate the functioning of our system in the supporting video.
+
+We used ROS as a framework for our implementation. ROS is a well-established
+software for developing robot targeted applications with rich support
+infrastructure and modular approach to logic organization For interacting 
+with the robot we mainly relied on the NAOqi Python API. The advantage of using
+Python compared to C++ is a much higher speed of development and a more concise
+and readable resulting code.
+
+\section{System Overview}
+
+\subsection{Vision}
+
+- Camera calibration
+- Aruco marker extraction
+- TF world coordinate publishing
+
+\begin{figure}
+  \centerline{\includegraphics[width=0.8\linewidth]{figures/aruco.png}}
+  \caption{ArUco marker detection on the operator.}
+  \label{fig:aruco_detection}
+\end{figure}
+
+\subsection{Interface}\label{ssec:interface}
+
+\paragraph{Speech State Machine}
+
+Based on NAOqi API and NAO built-in voice recognition
+
+\begin{table}
+\caption{Commands of the speech recognition module}
+\begin{center}
+\begin{tabular}{|c|c|c|}
+\hline
+\textbf{Command}&\textbf{Action}&\textbf{Available in state} \\
+\hline
+``Go'' & Wake Up & Sleep \\
+\hline
+``Kill'' & Go to sleep & Idle, Imitation \\
+\hline
+``Arms'' & Start imitation & Idle \\
+\hline
+``Stop'' & Stop imitation & Imitation \\
+\hline
+``Open'' & Open hands & Idle, Imitation \\
+\hline
+``Close'' & Close hands & Idle, Imitation \\
+\hline
+\end{tabular}
+\label{tab_speech_states}
+\end{center}
+\end{table}
+
+\paragraph{Teleoperation Interface}
+
+In order to make it possible to operate
+the NAO without visual contact, a teleoperation interface was developed. This
+interface allows the operator to receive visual feedback on the NAO as well as
+additional information regarding his own position.
+
+The NAO-part contains video streams of the top and bottom cameras on the robots
+head. These were created by subscribing to their respective topics (FIND NAME)
+using the \textit{rqt\_gui} package. Moreover, it also consists of a rviz
+window which gives a visual representation of the NAO. For this, the robot's
+joint positions are displayed by subscribing to the topic tf where the
+coordinates and the different coordinate frames are published. We further used
+the \textit{NAO-meshes} package to create the 3D model of the NAO.
+
+\begin{figure}
+  \centering
+  %\hfill
+  \begin{subfigure}[b]{0.4\linewidth}
+    \includegraphics[width=\linewidth]{figures/rviz_human.png}
+    \caption{}
+    %{{\small $i = 1 \mu m$}}
+    \label{fig_human_model}
+  \end{subfigure}
+  \begin{subfigure}[b]{0.4\linewidth}
+    \includegraphics[width=\linewidth]{figures/interface_nao.png}
+    \caption{}
+    %{{\small $i = -1 \mu A$}}
+    \label{fig_nao_model}
+  \end{subfigure}
+  \caption{Operator and NAO in rviz.}
+  \label{fig_interface}
+\end{figure}
+
+
+\subsection{Navigation}\label{ssec:navigation}
+
+- Human Joystick (3dof)
+
+One of the two main feature in our robot is an intuitive navigation tool, which
+allows the robot to navigate the environment by tracking the user movements.
+
+By fixing an ArUco marker on the user's chest, we can continuously track its
+position and orientation in a three dimensional space and so capture its
+motion.
+
+In order to simplify the task we define a buffer zone where the robot can only
+track the orientation of the user then depending on which direction the user
+will exit the zone the robot will either go forward, backward, left or right.
+Also the covered distance will influence the speed of the robot, the further
+the user is from the center of the buffer zone the faster the movement of the
+robot will be. The extent of the movement and buffer zone are determined
+automatically through calibration.
+
+\begin{figure}
+  \centering
+  \includegraphics[width=0.8\linewidth]{figures/usr_pt.png}
+  \caption{User position tracking model}
+  \label{fig_user_tracking}
+\end{figure}
+
+\subsection{Imitation}\label{ssec:imitation}
+
+One of the main objectives of our project was the imitation of the operator
+arm motions by the NAO. In order to perform this, first the appropriate mapping
+between the relative locations of the detected ArUco markers and the desired
+hand positions of the robot needs to be calculated. Then, based on the
+target coordinates, the robot joint rotations need to be calculated.
+
+\paragraph{Posture retargeting}
+
+First, let us define the notation of the coordinates that we will use to
+describe the posture retargeting procedure. Let $r$ denote the 3D $(x, y, z)$
+coordinates, then the subscript defines the object which has these coordinates,
+and the superscript defines the coordinate frame in which these coordinates are
+taken. So, for example, $r_{NAO hand}^{NAO torso}$ gives the coordinate of the
+hand of the NAO robot in the frame of the robot's torso.
+
+After the ArUco markers are detected and published on ROS TF, as was described
+in \ref{ssec:vision}, we have the three vectors $r_{aruco,chest}^{webcam}$,
+$r_{aruco,lefthand}^{webcam}$ and $r_{aruco,righthand}^{webcam}$. We describe
+the retargeting for one hand, since it is symmetrical for the other hand. We
+also assume that all coordinate systems have the same orientation, with the
+z-axis pointing upwards, the x-axis pointing straight into webcam and the
+y-axis to the left of the webcam. Therefore, we can directly calculate the hand
+position in the user chest frame by the means of the following equation:
+
+$$r_{hand,user}^{chest,user} = r_{aruco,hand}^{webcam} -
+r_{aruco,chest}^{webcam}$$.
+
+Next, we remap the hand coordinates in the chest frame into the user shoulder
+frame, using the following relation:
+
+$$r_{hand,user}^{shoulder,user} = r_{hand,user}^{chest,user} - r_{shoulder,user}^{chest,user}$$
+
+We know the coordinates of the user's shoulder in the user's chest frame from
+the calibration procedure, described in \ref{ssec:interface}.
+
+Now, we perform the retargeting of the user's hand coordinates to the desired
+NAO's hand coordinates in the NAO's shoulder frame with the following formula:
+
+$$r_{hand,NAO}^{shoulder,NAO} =
+\frac{L_{arm,NAO}}{L_{arm,user}} r_{hand,user}^{shoulder,user}$$
+
+As before, we know the length of the user's arm through calibration and the
+length of the NAO's arm through the specification provided by the manufacturer.
+
+A final step of the posture retargeting is to obtain the coordinates of the
+end effector in the torso frame. This can be done through the following relation:
+
+$$r_{hand,NAO}^{torso,NAO} =
+r_{hand,NAO}^{shoulder,NAO} + r_{shoulder,NAO}^{torso,NAO}$$
+
+The coordinates of the NAO's shoulder in the NAO's torso frame can be obtained
+through a call to the NAOqi API.
+
+Now that the desired position of the NAO's hands are known, the appropriate
+joint motions need to be calculated by the means of Cartesian control.
+
+\paragraph{Cartesian control}
+
+For this a singular robust cartesian controller was build.
+
+The output of our cartesian controller are the 4 angles of the rotational
+joints for the shoulder and the elbow part of each arm of the NAO robot, which
+is described by the inverse kinematic formula
+
+$$\Delta\theta = J^{-1,robust}\Delta r$$
+
+To build the cartesian controller first the Jacobian matrix is needed. The
+content of the Jacobian matrix describes an approximation for the movement of
+each joint of the robot. There are 2 main ways to determine the Jacobian
+matrix. The first way is the numerical method, where this approximation is done
+by checking how the end effector moves with small angles for rotational joints.
+For this we can approximate each column of the Jacobian Matrix as followed:
+
+$$\frac{\partial r}{\partial\theta} \sim \frac{\Delta r}{\Delta\theta} =
+\left(
+    \begin{array}{ccc}
+      \frac{\Delta r_x}{\Delta\theta} &
+      \frac{\Delta r}{\Delta\theta} &
+      \frac{\Delta r}{\Delta\theta}
+    \end{array}
+  \right)^{T}$$
+
+The other method is the analytical method, which was used in this project.
+Since only rotational joints were available, the approximation for the
+Jacobian matrix, which is the tangent in rotational joints, can be calculated
+using the cross product between the rotational axis $e$ and the rotational
+vector \\ $r_{end}-r_{joint}$.
+
+$$
+\frac{\partial r_{end}}{\partial\theta _{joint}} =
+(e \times (r_{end}-r_{joint}))
+$$
+
+which gives us one column of the Jacobian matrix. This can be repeated for
+each rotational joint until the whole matrix is filled.
+
+The next step for the cartesian controller is to determine the inverse Jacobian
+matrix for the inverse kinematic. For this singular value decomposition is
+used. - Cartesian Controller
+
+\section{System Integration}
+
+
+\section{Drawbacks and conclusions}
+
+% \begin{table}[htbp]
+% \caption{Table Type Styles}
+% \begin{center}
+% \begin{tabular}{|c|c|c|c|}
+% \hline
+% \textbf{Table}&\multicolumn{3}{|c|}{\textbf{Table Column Head}} \\
+% \cline{2-4}
+% \textbf{Head} & \textbf{\textit{Table column subhead}}& \textbf{\textit{Subhead}}& \textbf{\textit{Subhead}} \\
+% \hline
+% copy& More table copy$^{\mathrm{a}}$& &  \\
+% \hline
+% \multicolumn{4}{l}{$^{\mathrm{a}}$Sample of a Table footnote.}
+% \end{tabular}
+% \label{tab_sample}
+% \end{center}
+% \end{table}
+
+% \begin{thebibliography}{00}
+
+% \bibitem{b1}
+
+% G. Eason, B. Noble, and I. N. Sneddon,
+% ``On certain integrals of Lipschitz-Hankel type involving
+% products of Bessel functions,''
+% Phil. Trans. Roy. Soc. London, vol. A247, pp. 529--551, April 1955.
+
+% \end{thebibliography}
+
+\end{document}