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\begin{figure*}
\centering
\subfloat[]{
\begin{minipage}[b][][t]{.3\textwidth} % [b] bottom [t] top
\centering
\includegraphics[width=\linewidth]{fig_sim_singleIntegrator_noIntegralStationary_traj}
\includegraphics[width=\linewidth]{fig_sim_singleIntegrator_noIntegralStationary_bearingerror}
\end{minipage}}%
\subfloat[]{
\begin{minipage}[b][][t]{.3\textwidth} % [b] bottom [t] top
\centering
\includegraphics[width=\linewidth]{fig_sim_singleIntegrator_noIntegralMoving_traj}
\includegraphics[width=\linewidth]{fig_sim_singleIntegrator_noIntegralMoving_bearingerror}
\end{minipage}}%
\subfloat[]{
\begin{minipage}[b][][t]{.3\textwidth} % [b] bottom [t] top
\centering
\includegraphics[width=\linewidth]{fig_sim_singleIntegrator_PIMoving_traj}
\includegraphics[width=\linewidth]{fig_sim_singleIntegrator_PIMoving_bearingerror}
\end{minipage}}%
\caption{The bearing error is $\sum_{(i,j)\in\E}\|g_{ij}-g_{ij}^*\|$.}
\label{fig_sim_PI_noIntegral}
\end{figure*}
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Keywords: unicycle, single integrator, double integrator, feedback linearization

There are two types of feedback linearization of unicycle models. The first is to obtain a single-integrator model. The second is to obtain a double-integrator model (reference for the double integrator model: Automatica “Distributed formation control of nonholonomic mobile robots without global position measurements”).

my memo: unicycle linearization

Matlab function:

function rho=fcn_EulerFromRotation(R)
% R is the rotation from body to world frame

% assume -pi/2<tht<pi/2

%R31=-sin(tht)
tht=-asin(R(3,1));

%R32=sin(phi)*cos(tht), R33=cos(phi)*cos(tht)
phi=atan2(R(3,2),R(3,3));

%R21=cos(tht)*sin(psi), R11=cos(tht)*cos(psi)
psi=atan2(R(2,1),R(1,1));

rho=[phi,tht,psi]';

use the following command before the rand function, you will get the same random number everytime you run the m file.

rand(‘seed’, 0);

rand

The command is:

\renewcommand*\rmdefault{ptm} %ppl

if you want to understand the three letter word: ptm or ppl. Read the table III of this document: http://tug.ctan.org/macros/latex/required/psnfss/psnfss2e.pdf

Here is a good introduction:

https://www.tug.org/pracjourn/2006-1/schmidt/schmidt.pdf

Theorem -> Thm.
Corollary -> Cor.
See https://en.wikipedia.org/wiki/List_of_mathematical_abbreviations

Chapter -> Chap.

Keywords: youtube, video, PPT, powerpoint, starting time

• First, go to youtube and find the video. Then click Share->Embed. You will get a code as below:

• Second, paste the code to word and modify it. Specify the starting and ending times as shown below.

• Third, go to PPT and click Insert->Video->Online Video->From a Video Embed Code (not the Youtube one). Copy and paste and nail it.