a2nr
/
-p-formation-control
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

Update sub bab analisa

release
a2nr 2020-01-22 13:52:12 +07:00
parent 22da0c3b7a
commit da872eff02
14 changed files with 1228 additions and 802 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

3
.gitignore vendored
View File

@ -8,3 +8,6 @@ thesis.out
thesis.pdf
thesis.synctex.gz
thesis.toc
*.dia~
thesis.bbl
thesis.blg

80
BAB2/bab2.tex
View File

@ -219,71 +219,83 @@ Pembahasan kendali dari formasi multi robot menggunakan gradient control.
Apabila $n(n\geq 2)$ dimodelkan sebagai titik yang memiliki masa jenis bergerak diatas
dimensi 2(\textit{Euclidean Space}), maka pergerakan dimodelkan dengan
\begin{align}
\dot{x}_i(t) = u_i(t), \quad i = 1, \dots, n. \label{eq:modelorde1}
\begin{cases}
\dot{x}_i(t) = & v_i(t) \quad i = 1, \dots, n. \\
\dot{v}_i(t) = & u_i(t)
\end{cases}
\label{eq:modelorde2}
\end{align}
dimana $x_i(t) \in \mathbb{R}^2$ adalah posisi dari robot-$i$ dan $u_i(t)\in \mathbb{R}^2$
adalah input dari kendali. Dinotasikan $d \in \mathbb{R}^m$ adalah vector jarak dimana isi
dimana $v_i(t) \in \mathbb{R}^2$ dan $u_i(t)\in \mathbb{R}^2$adalah kecepatan dan input dari robot-$i$. Dinotasikan $d \in \mathbb{R}^m$ adalah vector jarak dimana isi
dari matrik tersebut adalah $d_k^2$ yang mempresentasikan jarak yang dinginkan antara
setiap robot $i$ dan $j$ untuk sisi $(i,j)\in \sisi$.
Lalu didefinisi persamaan potensial yang memiliki hubungan antara jarak robot yang diinginkan
dengan jarak yang sekarang
\begin{align}
\Phi(e) & = \frac{1}{2} \sum_{k=1}^{m} \big( ||e_k||^2 - d_k^2 \big)^2
\Phi(e) & = \frac{1}{2} \sum_{i \in \simpul }||v_i||^2 + \frac{1}{2} \sum_{k=1}^{m} \big( ||e_k||^2 - d_k^2 \big)^2
\end{align}
Pengamatan dilakukan agar $\Phi(e) =0$ jika dan hanya jika $||e_k||^2 = d_k^2,$ $\forall k = 1, \dots, m$.
Kendali dari setiap robot menggunakan gradien negatif dari fungsi potensial
\begin{align}
u_i(t) & = - \Big( \frac{\partial \Phi(e)}{\partial x_i} \Big)= -\sum_{j \sim i} \Big( ||e_k||^2 - d_k^2 \Big)e_k
\begin{cases}
\dot{x} & = \frac{\partial \Phi(e)}{\partial v} + Bv_{ref} \\
& = v(t) + Bv_{ref} \\
\dot{v} & = -C \Big( \frac{\partial \Phi(e)}{\partial v} + \frac{\partial \Phi(e)}{\partial v} \Big) \\
& = -C(v(t) + R(x)^T(R(x)x(t) - d )) \\
& = u(t)
\end{cases}
\label{eq:dynmState}
\end{align}
Dengan itu, dapat disubtitusi kedalam persamaan dinamika pada persamaan~\eqref{eq:modelorde1}
\begin{align}
\dot{x}(t) = -R(x)^TR(x)x(t)+ R(x)^Td \label{eq:dynmState}
\end{align}
Penambahan refresni kecepatan pada salah satu robot dapat menjadikan formasi bermanuver.
Skema kendali secara general dapat didefinisi dengan
\begin{align}
\dot{x}(t) & = u(t) + Bv_{ref} \\
u(t) & = -R(x)^TC\Big(R(x)x(t)- d\Big) \label{eq:kontrolinput}
\end{align}
dimana $B \in \mathbb{R}^{2n \times 2}$ digunakan untuk indikasi robot ke $i$ sebagai leader atau penerima kecepatan referensinya
, $v_{ref} \in \mathbb{R}^2$ sebagai kecepatan referensi,
Dimana $v \in \mathbb{R}^{2n}$ adalah vector kecepatan dari seluruh node. Penambahan refrensi kecepatan pada salah satu robot dapat menjadikan formasi bermanuver.
Dimana $B \in \mathbb{R}^{2n \times 2}$ digunakan untuk indikasi robot ke $i$ sebagai leader atau penerima kecepatan referensinya, $v_{ref} \in \mathbb{R}^2$ sebagai kecepatan referensi,
dan $C$ adalah konstanta pengendali yang akan digantikan dengan algoritma kendali.
Dengan menerapkan kendali Proportional-Integral, konstanta $C$ pada persamaan~\eqref{eq:kontrolinput}
dapat diubah dengan
\begin{align}
u(t) & = u_{k_p}(t) + u_{k_i}(t) \\
u_{k_p}(t) & = -R(x)^Tk_p\Big(R(x)x(t)- d\Big) \\
u_{k_i}(t) & = -R(x)^Tk_i\int_0^T\Big(R(x)x(\tau)- d\Big)d\tau
\begin{cases}
u_i(t) & = u_{k_{p1}}(t) + u_{k_{i1}}(t) + u_{k_{p1}}(t) + u_{k_{i1}}(t) \\
u_{k_{p1}}(t) & = -k_{p1}v_i(t) \\
u_{k_{p2}}(t) & = -R(x_1)^T k_{p2}(R(x_1)x_1(t) - d )) \\
u_{k_{i1}}(t) & = -k_{i1} \int_0^\tau x_2(\tau) d\tau \\
u_{k_{i2}}(t) & = -R(x_1)^T k_{i2} \int_0^{\tau} (R(x_1)x_1(\tau) - d )) d\tau
\end{cases}
\label{eq:kontrolinput}
\end{align}
Lalu pada bagian integrator( $k_i$ ), menghasilkan \textit{state} baru
\begin{align}
\dot{\xi}(t) & = k_i\Big(R(x)x(t)- d\Big)
\begin{cases}
\dot{\xi}_1 =& -k_{i1} v(t)\\
\dot{\xi}_2 =& -k_{i2} (R(x_1)x(t) - d
\end{cases}
\end{align}
Dengan itu dapat digabungkan menjadi persamaan \textit{state-space} menggunakan persamaan~\eqref{eq:dynmState}
\begin{align}
\begin{align*}
\begin{bmatrix}
\dot{x}(t) \\ \dot{\xi}(t)
\end{bmatrix} =
\dot{x} \\ \dot{v} \\ \dot{\xi}_1 \\ \dot{\xi}_2
\end{bmatrix} &=
\begin{bmatrix}
-k_pR(x)^TR(x) & -R(x)^T \\
k_iR(x) & 0
0 & 1 & 0 & 0\\
-k_{p2}R(x)^T R(x) & -k_{p1} & -1 & -R(x)^T \\
0 & k_{i1} & 0 & 0 \\
k_{i2}R(x) & 0 & 0 & 0 \\
\end{bmatrix}
\begin{bmatrix}
x(t) \\ \xi(t)
\end{bmatrix}+
x \\ v \\ \xi_1 \\ \xi_2
\end{bmatrix} +
\begin{bmatrix}
k_pR(x)^T \\ -k_iI
\end{bmatrix} d +
\begin{bmatrix}
B \\ 0
\end{bmatrix} v_{ref}
0 \\ k_{p2}R(x)^T \\ 0 \\ -k_{i2}
\end{bmatrix} d+Bv_{ref} \nonumber \\
\end{align*}
\begin{align}
\dot{x}_f(t) &= A_f(x)x_f(t)+B_f(x)d+Bv_{ref}
\label{eq:ss-formasi}
\end{align}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Solusi Persamaan Differensial Secara Numerik}
\label{bab:solusi_ODE}
\label{bab:dua:solusi_ODE}
Persamaan \eqref{eq:ss1} dan \eqref{eq:ss2} adalah persamaan differensial kontinu orde satu.
Dalam memecahkan persamaan differensial dapat dilakukan dalam bentuk kontinyu atau numerik.

2
BAB3/bab3.tex
View File

@ -31,7 +31,7 @@ Gagasan agent \textit{simple model} tersebut memiliki manfaat ketika menginvesti
Dengan bertambahnya kepraktisan pada metode tersebut diharapkan dapat diterapkan dalam agent secara \textit{Real}.
Pada penelitian oleh \kutip{Rozenheck2015}, kendali formasi berdasarkan jarak dikendalikan
menggunakan kendali PI dan menghasilkan pergerakan yang baik.
Dapat diperhatikan pada persamaan~\eqref{eq:modelorde1} bahwa peneliti menggunakan \textit{Simple model} untuk mengembangkan kendali multi-robotnya.
Dapat diperhatikan pada persamaan~\eqref{eq:modelorde2} bahwa peneliti menggunakan \textit{Simple model} untuk mengembangkan kendali multi-robotnya.
Maka, penelitian ini akan difokuskan pada kendali formasi berbasis jarak
kendali PI yang telah dilakukan sebelumnya dengan menggunakan model nyata.
\section{Permasalah dan Solusi}

220
BAB4/bab4.tex
View File

@ -1,10 +1,58 @@
\chapter{\babEmpat}
\section{Perangkat Percobaan}
Sub bab ini akan dibahas mengenai prangkat penunjang sebagai pembatu dalam menyelesaikan penelitian.
Sebagai langkah awal pengembangan, metode yang digunakan adalah \textit{Hardware-In Loop}.
\begin{figure}
\centering
\includegraphics[scale=.5]{BAB3/img/hil_graph.png}
\caption{Hardware-in-the-loop (\kutip{Jim1999}). }
\label{fig:hil_graph}
\end{figure}
\textit{Hardware-in-the-loop} (HIL) adalah metode untuk pengembangan prangkat kendali dengan memanfaatkan model sebagai objek kendalinya. Seperti pada gambar~\ref{fig:hil_graph},
bahwa HIL terdiri dari dua prangkat, yaitu prangkat untuk menjalankan objek kendali atau dapat
disebut sebagai model/plant dan prangkat sistem kontrolnya, dalam kasus ini sistem kontrol menggunakan sistem tertanam (\textit{embedded system}).
Metode HIL, banyak digunakan oleh peneliti dalam proses pengembangan dengan pertimbangan efisiensi terhadap berbagai hal.
Seperti yang digunakan oleh~\kutip{Irwanto2018}, mengembangkan kendali UAV menggunakan HIL;
dan \kutip{QUESADA2019275}, mengembangkan prangkat pankreas buatan yang digunakan untuk mengendalikan kadar gula pada pengidap diabetes.
\begin{figure}
\centering
\input{BAB4/img/Diagram_hil_controller.tex}
\caption{HIL Kendali Multi-Robot.}
\label{fig:hil_graph_1}
\end{figure}
Pada penelitian ini akan digunakan \textit{microcontroller}(MCU) STM32F466 sebagai prangkat kendalinya.
MCU tersebut ber-arsitektur ARM Cortex-M4 dengan clock 180MHz, menampung ukuran program sampai 256K didalam memori Flash, serta fitur komunikasi standart MCU dengan lengkap.
\textit{Platform Library} yang digunakan dalam pembuatan aplikasi didalamnya adalah \textit{Mbed},
yang menyediakan berbagai banyak fungsi yang lengkap dan mudah untuk berinteraksi dengan fitur-fitur MCU. \textit{Mbed} juga menyediakan fungsi untuk mengaplikasikan RTOS (Real-time Operating System) dengan mudah dan terdokumentasi secara jelas didalam lamannya.
Pada prangkat PC akan dikembangkan program berbasis \textit{Python} yang akan
menjalankan simulasi model dan berkomunikasi dengan MCU secara \textit{real-time}.
Program \textit{Python} akan menjalankan model pada persamaan~\eqref{eq:ss1}-\eqref{eq:ss2}
dengan metode yang dijabarkan pada sub bab~\ref{bab:dua:solusi_ODE}.
Dalam penerapan multi-robot, digunakan 3 perangkat sistem tertanam untuk mempresentasikan kendali 3 robot (Gambar.~\ref{fig:hil_graph_1}).
Setiap prangkat pengendali akan saling terhubung satu sama lain dan semua prangkat pengendali terhubung dengan prangkat PC.
Komunikasi antar prangkat pengendali akan digunakan untuk pertukaran informasi.
Sedangkan komunikasi dengan PC akan mempresentasikan aktuator dan sensor untuk setiap prangkat
kendali. PC akan merekam setiap keluaran dari model dan masukan dari setiap prangkat kendali
sebagai tampilan pergerakan robotnya.
\todo{
Tambahkan subsection mengenai
\begin{itemize}
%% \item pengembangan data/akuisisi data ?
% \item skenario pengujian/simulasi? (lebih ke teknis seperti lapangan environtment dll)
% \item skenario Analisa hasil
\item jadwal penelitian
\end{itemize}
}
\section{Strategi Kendali Multi Robot}
Analisa akan dilakukan dalam beberapa bagian agar mudah dipahami dan diterapkan.
Analisa tersebut adalah mengenai kendali dari model dinamika robot dan kendali formasi,
dan mengenai metode percobaan akan dibahas secara matematis, simulasi, dan HIL.\
Pembahasan strategi akan dibagi menjadi dua bagian, yaitu kendali tingkat bawah dan kendali tingkat atas.
Kendali tingkat bawah akan membahas mengenai kendali robot secara individu, sedangkan kendali tingkat atas akan dibahas mengenai penggabungan antara kendali tingkat bawah dan atas.
\subsection{Kendali Robot}
Pada kendali robot akan dibahas mengenai analisis kendali robot menggunakan
@ -56,7 +104,6 @@ kendalinya dibutuhkan Observer. Dimana tugasnya adalah mengestimasi state pada
sistem dengan membandingkan keluaran dan masukan. Syarat untuk dapat diterap-
kan state feedback, sistem harus observable dan controlable. Berikut adalah rumus
untuk menguji apakah sistem bersifat controlable atau tidak (Dorf, dkk (2010)).
\begin{align*} P_c = \begin{bmatrix} B & AB & A^2B & \dots & A^{n-1}B \end{bmatrix}\end{align*}
\begin{align} rank[P_c] = n \end{align}
Apabila hasil dari $rank(P_c ) \neq n$ maka sistem tidak \textit{fully controlable}. Sedangkan untuk
@ -64,12 +111,39 @@ menguji observabilitas dapat menggunakan rumus berikut.
\begin{align*} P_o = \begin{bmatrix} C \\ CA \\ CA^2 \\ \vdots \\ CA^{n-1} \end{bmatrix}\end{align*}
\begin{align} rank[P_o] = n \end{align}
Apabila sistem observable, rank dari matriks Observablity $P_o$ sama dengan besar orde sistem.
Menggunakan parameter robot oleh~\kutip{CORREIA20127} yang diterapkan pada per-
samaan~\eqref{eq:ss1}-\eqref{eq:ss2}, hasil pengujian controlable $rank[P_c] = 6$, maka dapat disim-
pulkan sistem robot controlable. Hasil pengujian observable $rank[P o] = 6$, maka
sistem robot juga observable. Karena pengukuran pada setiap \textit{state} dapat dilakukan,
Menggunakan parameter robot pada Tabel~\ref{tab:param_model} untuk diimplementasi pada persamaan~\eqref{eq:ss1}-\eqref{eq:ss2} akan menghasilkan $rank[P_c]=6$ dan $rank[P o] = 6$ .
Maka dari itu dapat disimpulkan sistem robot adalah controlable dan observable.
Karena pengukuran pada setiap \textit{state} dapat dilakukan,
maka \textit{observer} tidak dibutuhkan dalam desain kendali robot.
\begin{table}
\caption{Parameter model oleh~\kutip{CORREIA20127}}
\label{table:parameter_model}
\begin{center}
\begin{tabular}{| c | c | c |}
\hline
Simbol & Deskripsi & Nilai\\ \hline
$B_v (N/m/s)$ & viscous friction coefficient related to v & 0.94 \\
$B_{vn} (N/m/s)$ & viscous friction coefficient related to vn & 0.96 \\
$B_\omega (N/rad/s)$ &viscous friction coefficient related to $\omega$ & 0.01 \\
$C_v (N )$ & coulomb friction coefficient related to v & 2.2 \\
$C_{vn} (N )$ & coulomb friction coefficient related to vn & 1.5 \\
$C_\omega (N.m)$ & coulomb friction coefficient related to $\omega$ & 0.099 \\
$b(m)$ & radius of the robot & 0.1 \\
$M (kg)$ & mass of the robot & 1.5 \\
$In(kg.m^2 )$ & inertia moment of the robot & 0.025 \\
$\delta$ & angle & $30^\circ$ \\
$r_1 , r_2 , r_3 (m)$ &radius of the wheels & 0.035 \\
$l_1, l_2, l_3$ & reduction of the motors & 19:1 \\
$L_{a1...3} (H)$ & motor’s armature inductance & 0.00011 \\
$R_{a1...3} (\Omega)$ & motor’s armature resistance & 1.69 \\
$K_v (V olts/rad/$s) & motor’s emf constant & 0.0059 \\
$K_{t1...3}$ (N.m/A) & motor’s torque constant & 0.0059\\
\hline
\end{tabular}
\end{center}
\label{tab:param_model}
\end{table}
\subsubsection{Desain Kendali}
Berdasarkan \kutip{Richard2010}, bahwa kendali optimal berdasarkan indeks kinerja sistem. Indeks tersebut adalah hasil dari meminimalisasi pada integral kuadrat error atau \textit{integration square error} (ISE).
@ -134,8 +208,11 @@ Berikut adalah persamaan \textit{input refrence} sebagai penambah dari \textit{s
\end{align}
Sehingga persamaan \textit{state space} menjadi berikut.
\begin{align}
\dot{x} & = (A-BK_s)x + BNr \\
y & = Cx
\begin{cases}
\dot{x} & = (A-BK_s)x + BNr \\
y & = Cx
\end{cases}
\label{eq:ss-control-robot}
\end{align}
Untuk mendapatkan nilai $N$ maka dapat diasumsikan bahwa sistem dalam keadaan \textit{steady state}, yaitu $\dot{x} = 0$, sehingga persamaan state space menjadi berikut.
\begin{align}
@ -213,10 +290,13 @@ Apabila hanya variable jarak tersebut sebagai acuan kendali, maka robot tidak me
harusnya robot itu bergerak untuk meminimalisasi error jaraknya.
\subsubsection{Strategi Penentuan Koordinat Tetangga}
\label{bab:empat:Strategi_koordinat_tetangga}
Penentuan koordinat tentangga dapat ditemukan dengang mengubah koordinat polar menjadi koordinat kartesian.
Koordinat polar membutuhkan panjang, $d_a$, dan sudut, $\alpha$.
Variable $d_a$ dapat diperoleh dari sensor, akan tetapi sudu $\alpha$ tidak bisa dideteksi secara langsung oleh sensor.
Dengan menggunakan \textit{cosinus} pada segitiga dimungkinkan untuk mendapatkan sudut tersebut.
Koordinat polar membutuhkan panjang $d_a$, dan sudut $\alpha$.
Panjang $d_a$ adalah variable yang didapat dari sensor yang memberikan nilai jarak dari robot $A$ ke robot $B$,
akan tetapi untuk mendapatkan koordinat polar, pengukuran sudu $\alpha$ tidak tersedia.
Algoritama yang ditawarkan memanfaatkan hukum \textit{cosinus} pada segitiga untuk mendapatkan sudut tersebut.
\begin{figure}
\centering
@ -245,8 +325,8 @@ Sehingga diperlukan sedikit algoritma
\end{cases}.\label{eq:init_relatif_koordinat}
\end{align}
Strategi pada gambar~\ref{fig:strategiPenentuanKoordinat} hanya berlaku apabila target ukur berhenti. Apabila dinotasikan koordinat $x_B^A$ adalah koordinat relatif robot $B$ terhadap $A$,
maka $\dot{x}_B^A$ adalah notasi kecepatan koordinat dari robot B.
Strategi pada gambar~\ref{fig:strategiPenentuanKoordinat} hanya berlaku apabila target ukur berhenti. Apabila dinotasikan koordinat $(x_B^A, y_B^A)$ adalah koordinat relatif robot $B$ terhadap $A$,
maka $(\dot{x}_B^A, \dot{y}_B^A)$ adalah notasi kecepatan koordinat dari robot B.
Dengan menggunakan persamaan~\eqref{eq:kinematika_robot} untuk menyelesaikan koordinat dalam
keadaan robot $B$ bergerak, yaitu mengirimkan informasi kecepatan koordinatnya
ke robot $A$. Lalu robot $A$ dapat mengkalkulasi koordinat relatif dengan persamaan berikut
@ -267,57 +347,71 @@ berada pada sudut $90^\circ$.
Akan tetapi, \kutip{Cao2007} sudah menjelaskan mengenai kriteria posisi agent ketika dalam kondisi inisial.
Yaitu semua agent tidak berada pada kondisi sejajar secara koordinat global pada kondisi inisial.
\section{Kestabilan Perangkat Percobaan}
Sub bab ini akan dibahas mengenai prangkat penunjang sebagai pembatu dalam menyelesaikan penelitian.
Sebagai langkah awal pengembangan, metode yang digunakan adalah \textit{Hardware-In Loop}.
\todo{ buat psudo code dari algoritma ini, sehingga dapat di ambil referensi ke bab lain}
\begin{algorithm}
\DontPrintSemicolon
TODO: make your algo here !
\label{algo:solution_purpose}
\end{algorithm}
\subsubsection{Implementasi Kendali Formasi Dengan Kendali Robot}
Implementasi kendali formasi pada kendali robot akan menggabungkan persamaan state space pada~\eqref{eq:ss-formasi} dengan persamaan~\eqref{eq:ss-control-robot}.
Implementasi ini akan menjadikan persamaan~\eqref{eq:ss-formasi} sebagai kendali utama sedangkan pada persamaan~\eqref{eq:ss-control-robot} adalah kendali tingkat bawah.
Kendali utama akan diberikan input berupa jarak, $d$, sebagai tujuan pengendali. Sedangkan keluaran dari kendali tersebut adalah koordinat yang perlu dicapai oleh kendali tingkat bawah.
Pembahasan akan diambil dari sudut pandang robot secara individual.
Dengan menulis ulang persamaan~\eqref{eq:ss-control-robot} dengan notasi baru akan lebih mudah dalam penjelasaan lebih lanjut.
\begin{align}
\begin{cases}
\dot{x_r} & = (A_r-B_rK_s)x_r + B_rN_rr \\
y_r & = C_rx_r
\end{cases}
\label{eq:ss-control-robot-implement}
\end{align}
Apabila diasumsikan state pada persamaan~\eqref{eq:ss-formasi} sebagai berikut
\begin{align*}
x(t) &= \begin{bmatrix}
y_r^T & y_{rj1}^T & y_{rj2}^T & \dots & y_{rjn}^T
\end{bmatrix}^T , \quad (i,jn) \in \sisi
\end{align*}
maka $y_{rjn}$ adalah koordinat yang didapat dari algoritma atau hasil pengiriman data dari robot tetangga.
Sedangkan $r$ pada persamaan~\eqref{eq:ss-control-robot-implement} adalah koordinat refrensi yang dihasilkan dari persamaan~\eqref{eq:ss-formasi}, $r = C_fx(t)$. Untuk lebih mudah dalam memahami dapat diperhatikan diagram pada gambar~\ref{fig:all-control}
\begin{figure}
\centering
\begin{subfigure}[t]{.4\textwidth}
\includegraphics[scale=.5]{BAB3/img/hil_graph.png}
\caption{}
\label{fig:hil_graph}
\end{subfigure}
\begin{subfigure}[t]{.4\textwidth}
\includegraphics[scale=.5]{BAB3/img/hil_graph_1.png}
\caption{}
\label{fig:hil_graph_1}
\end{subfigure}
\caption{(a)Grafik Hardware-in-the-loop (\kutip{Jim1999}). (b) HIL Kendali Multi-Robot. }
\input{BAB4/img/implement-control.tex}
\caption{Kendali keseluruhan}
\label{fig:all-control}
\end{figure}
\textit{Hardware-in-the-loop} (HIL) adalah metode untuk pengembangan prangkat kendali dengan memanfaatkan model sebagai objek kendalinya. Seperti pada gambar~\ref{fig:hil_graph},
bahwa HIL terdiri dari dua prangkat, yaitu prangkat untuk menjalankan objek kendali atau dapat
disebut sebagai model/plant dan prangkat sistem kontrolnya, dalam kasus ini sistem kontrol menggunakan sistem tertanam (\textit{embedded system}).
Metode HIL, banyak digunakan oleh peneliti dalam proses pengembangan dengan pertimbangan efisiensi terhadap berbagai hal.
Seperti yang digunakan oleh~\kutip{Irwanto2018}, mengembangkan kendali UAV menggunakan HIL;
dan \kutip{QUESADA2019275}, mengembangkan prangkat pankreas buatan yang digunakan untuk mengendalikan kadar gula pada pengidap diabetes.
Pada penelitian ini akan digunakan \textit{microcontroller}(MCU) STM32F466 sebagai prangkat kendalinya.
MCU tersebut ber-arsitektur ARM Cortex-M4 dengan clock 180MHz, menampung ukuran program sampai 256K didalam memori Flash, serta fitur komunikasi standart MCU dengan lengkap.
\textit{Platform Library} yang digunakan dalam pembuatan aplikasi didalamnya adalah \textit{Mbed},
yang menyediakan berbagai banyak fungsi yang lengkap dan mudah untuk berinteraksi dengan fitur-fitur MCU. \textit{Mbed} juga menyediakan fungsi untuk mengaplikasikan RTOS (Real-time Operating System) dengan mudah dan terdokumentasi secara jelas didalam lamannya.
Pada prangkat PC akan dikembangkan program berbasis \textit{Python} yang akan
menjalankan simulasi model dan berkomunikasi dengan MCU secara \textit{real-time}.
Program \textit{Python} akan menjalankan model pada persamaan~\eqref{eq:ss1}-\eqref{eq:ss2}
dengan metode yang dijabarkan pada sub bab~\ref{bab:solusi_ODE}.
Dapat diperhatikan pada gambar~\ref{fig:hil_graph_1}, pada HIL untuk kendali multi robot akan
menggunakan tiga kendali untuk mempresentasikan tiga robot.
Setiap prangkat pengendali akan saling terhubung satu sama lain dan semua prangkat pengendali terhubung dengan prangkat PC.
Komunikasi antar prangkat pengendali akan digunakan untuk pertukaran informasi.
Sedangkan komunikasi dengan PC akan mempresentasikan aktuator dan sensor untuk setiap prangkat
kendali. PC akan merekam setiap keluaran dari model dan masukan dari setiap prangkat kendali
sebagai tampilan pergerakan robotnya.
\section{Strategi Uji Coba}
Strategi ujicoba akan diawali dengan menghitung kesetabilan menggunakan teori Euler pada Bab \ref{bab:dua:solusi_ODE}.
Langkah selanjutnya adalah percobaan terhadap Algoritma~\ref{algo:solution_purpose} dengan kondisi robot tetangga dalam keadaan statis.
Percobaan tersebut bermaksut untuk menguji apakah algoritma berjalan dengan benar.
Langkah terakhir adalah percobaan keseluruhan robot menggunakan Algoritma yang dikembangkan
dengan skenario percobaan yang sama dengan penelitian sebelumnya oleh \kutip{Rozenheck2015}.
\todo{
Tambahkan subsection mengenai
\begin{itemize}
\item pengembangan data/akuisisi data ?
\item skenario pengujian/simulasi? (lebih ke teknis seperti lapangan environtment dll)
\item skenario Analisa hasil
\item jadwal penelitian
\end{itemize}
}
\subsection{Rencana Hardware-in-Loop}
\todo{kutip hasil HIL yang sudah ada lalu gabungkan model dan kendali jadi satu secara sederhana}
\subsection{Rencana Uji Lapangan}
\todo{Membahas mengenai cara pengambilan data penerapan pada robot aslinya}
\subsection{Analisa Kesetabilan Model}
Perhitungan kesetabilan akan menggunakan parameter model dari penelitian sebelumnya, dapat diperhatikan di Tabel \ref{tab:param_model}.
Parameter tersebut akan diimplementasi di persamaan~\eqref{eq:ss1}-\eqref{eq:ss2}.
Lalu ditentukan waktu sample dan diubah menjadi persamaan diskrit meggunakan persamaan~\eqref{eq:disstab}.
Setelah itu akan diuji menggunakan diagram Gambar.\ref{fig:explicit_euler} untuk mengetahui kesetabilan model.
Dari hasil analisa ini akan menghasilkan parameter waktu sampling ($h$) untuk menjalankan Algoritma~\ref{algo:eEuler}.
Pembuktian secara grafik sangat dibutuhkan untuk mengetahui respon model.
\subsection{Analisa Algoritama Dengan Tetangga Statis}
Telah dijelaskan pada Bab \ref{bab:empat:Strategi_koordinat_tetangga} bahwa robot bergerak kearah yang random dengan jarak tertentu untuk mengetahui koordinat tetangga.
Analisa akan dilakukan dengan membandingkan berbagai jarak dari tinggat rendah, sedang, dan tinggi untuk mengetahui respon algoritma yang sesuai dan optimal untuk mendapatkan koordinat tetangga.
Dari hasil analisa ini akan menghasilkan jarak terbaik untuk algoritma menentukan koordinat tetangga. Pembuktian akan dilakukan secara menampilkan grafik respon.
\subsection{Analisa Percobaan Keseluruhan}
Percobaan keseluruhan akan menjalankan Algoritma \ref{algo:solution_purpose} yang diterapkan pada seluruh robot. Lalu, seperti skenario penelitian sebelumnya salah satu robot diberikan kecepatan refrensi untuk bergerak ke arah tertentu.
Dari hasil percobaan ini akan menghasilkan grafik respon dari keseluruhan robot terhadap perubahan error yang terjadi.
Dengan hipotesis, keseluruhan robot akan menjaga jarak formasi dengan baik.
%% \subsection{

BIN
BAB4/img/Diagram_hil_controller.dia Normal file
View File

Binary file not shown.

215
BAB4/img/Diagram_hil_controller.tex Normal file
View File

@ -0,0 +1,215 @@
% Graphic for TeX using PGF
% Title: /home/adnr/Disk/Opo/PASCASARJANA/RESEARCH/[T01][FormationControl]/[DOC]/-p-formation-control/BAB4/img/Diagram_hil_controller.dia
% Creator: Dia v0.97.3
% CreationDate: Mon Dec 16 14:12:45 2019
% For: adnr
% \usepackage{tikz}
% The following commands are not supported in PSTricks at present
% We define them conditionally, so when they are implemented,
% this pgf file will use them.
\ifx\du\undefined
\newlength{\du}
\fi
\setlength{\du}{15\unitlength}
\begin{tikzpicture}
\pgftransformxscale{1.000000}
\pgftransformyscale{-1.000000}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (13.904617\du,3.268831\du)--(13.904617\du,8.035651\du)--(30.596370\du,8.035651\du)--(30.596370\du,3.268831\du)--cycle;
\pgfsetlinewidth{0.050000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (13.904617\du,3.268831\du)--(13.904617\du,8.035651\du)--(30.596370\du,8.035651\du)--(30.596370\du,3.268831\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (22.250493\du,5.769741\du){};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (14.769125\du,4.521642\du)--(14.769125\du,6.421642\du)--(19.286625\du,6.421642\du)--(19.286625\du,4.521642\du)--cycle;
\pgfsetlinewidth{0.050000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (14.769125\du,4.521642\du)--(14.769125\du,6.421642\du)--(19.286625\du,6.421642\du)--(19.286625\du,4.521642\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (17.027875\du,5.666642\du){$Model_1$};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (20.042584\du,4.524796\du)--(20.042584\du,6.424796\du)--(24.560084\du,6.424796\du)--(24.560084\du,4.524796\du)--cycle;
\pgfsetlinewidth{0.050000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (20.042584\du,4.524796\du)--(20.042584\du,6.424796\du)--(24.560084\du,6.424796\du)--(24.560084\du,4.524796\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (22.301334\du,5.669796\du){$Model_2$};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (25.231953\du,4.485904\du)--(25.231953\du,6.385904\du)--(29.749453\du,6.385904\du)--(29.749453\du,4.485904\du)--cycle;
\pgfsetlinewidth{0.050000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (25.231953\du,4.485904\du)--(25.231953\du,6.385904\du)--(29.749453\du,6.385904\du)--(29.749453\du,4.485904\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (27.490703\du,5.630904\du){$Model_3$};
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (29.082760\du,7.578415\du){PC};
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (20.371542\du,12.191246\du){};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (14.376710\du,9.025804\du)--(14.376710\du,10.925804\du)--(19.446710\du,10.925804\du)--(19.446710\du,9.025804\du)--cycle;
\pgfsetlinewidth{0.050000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (14.376710\du,9.025804\du)--(14.376710\du,10.925804\du)--(19.446710\du,10.925804\du)--(19.446710\du,9.025804\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (16.911710\du,10.093304\du){$Controller_1$};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (19.764724\du,13.065250\du)--(19.764724\du,14.965250\du)--(24.834724\du,14.965250\du)--(24.834724\du,13.065250\du)--cycle;
\pgfsetlinewidth{0.050000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (19.764724\du,13.065250\du)--(19.764724\du,14.965250\du)--(24.834724\du,14.965250\du)--(24.834724\du,13.065250\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (22.299724\du,14.132750\du){$Controller_2$};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (24.976692\du,8.990066\du)--(24.976692\du,10.890066\du)--(30.046692\du,10.890066\du)--(30.046692\du,8.990066\du)--cycle;
\pgfsetlinewidth{0.050000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (24.976692\du,8.990066\du)--(24.976692\du,10.890066\du)--(30.046692\du,10.890066\du)--(30.046692\du,8.990066\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (27.511692\du,10.057566\du){$Controller_3$};
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{{\pgflinewidth}{0.200000\du}}{0cm}
\pgfsetdash{{\pgflinewidth}{0.200000\du}}{0cm}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsstart{stealth}
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (16.936852\du,9.000965\du)--(17.002733\du,6.446481\du);
}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{{\pgflinewidth}{0.200000\du}}{0cm}
\pgfsetdash{{\pgflinewidth}{0.200000\du}}{0cm}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsstart{stealth}
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (27.507150\du,8.965227\du)--(27.495246\du,6.410743\du);
}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{{\pgflinewidth}{0.200000\du}}{0cm}
\pgfsetdash{{\pgflinewidth}{0.200000\du}}{0cm}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsstart{stealth}
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (22.299907\du,13.043607\du)--(22.301151\du,6.446439\du);
}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsstart{stealth}
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (18.212016\du,10.950656\du)--(20.999418\du,13.040399\du);
}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsstart{stealth}
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (26.267233\du,10.913096\du)--(23.544183\du,13.042220\du);
}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsstart{stealth}
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (19.471777\du,9.967173\du)--(24.951626\du,9.948697\du);
}
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (22.301334\du,5.474796\du){};
\end{tikzpicture}

BIN
BAB4/img/implement-control.dia Normal file
View File

Binary file not shown.

725
BAB4/img/implement-control.tex Normal file
View File

@ -0,0 +1,725 @@
% Graphic for TeX using PGF
% Title: /home/adnr/Disk/Opo/PASCASARJANA/RESEARCH/[T01][FormationControl]/[DOC]/-p-formation-control/BAB4/img/implement-control.dia
% Creator: Dia v0.97.3
% CreationDate: Fri Dec 20 17:01:35 2019
% For: adnr
% \usepackage{tikz}
% The following commands are not supported in PSTricks at present
% We define them conditionally, so when they are implemented,
% this pgf file will use them.
\ifx\du\undefined
\newlength{\du}
\fi
\setlength{\du}{15\unitlength}
\begin{tikzpicture}
\pgftransformxscale{1.000000}
\pgftransformyscale{-1.000000}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (25.926400\du,13.079600\du)--(25.926400\du,14.979600\du)--(27.941400\du,14.979600\du)--(27.941400\du,13.079600\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (25.926400\du,13.079600\du)--(25.926400\du,14.979600\du)--(27.941400\du,14.979600\du)--(27.941400\du,13.079600\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (26.933900\du,14.147100\du){$B_r$};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (32.286250\du,15.980900\du)--(32.286250\du,17.880900\du)--(34.328750\du,17.880900\du)--(34.328750\du,15.980900\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (32.286250\du,15.980900\du)--(32.286250\du,17.880900\du)--(34.328750\du,17.880900\du)--(34.328750\du,15.980900\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (33.307500\du,17.048400\du){$A_r$};
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (33.684400\du,14.049100\du){};
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (33.684400\du,14.049100\du){};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (25.886300\du,17.308503\du)--(25.886300\du,19.208503\du)--(28.161300\du,19.208503\du)--(28.161300\du,17.308503\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (25.886300\du,17.308503\du)--(25.886300\du,19.208503\du)--(28.161300\du,19.208503\du)--(28.161300\du,17.308503\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (27.023800\du,18.376003\du){$-K_s$};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (19.855000\du,13.092600\du)--(19.855000\du,14.992600\du)--(21.855000\du,14.992600\du)--(21.855000\du,13.092600\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (19.855000\du,13.092600\du)--(19.855000\du,14.992600\du)--(21.855000\du,14.992600\du)--(21.855000\du,13.092600\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (20.855000\du,14.160100\du){N};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (38.930901\du,13.167200\du)--(38.930901\du,15.067200\du)--(40.955901\du,15.067200\du)--(40.955901\du,13.167200\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (38.930901\du,13.167200\du)--(38.930901\du,15.067200\du)--(40.955901\du,15.067200\du)--(40.955901\du,13.167200\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (39.943401\du,14.234700\du){$C_r$};
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (36.098189\du,14.046817\du)--(38.880665\du,14.097748\du);
}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
\pgfsetmiterjoin
\pgfsetlinewidth{0.100000\du}
\pgfsetbuttcap
\pgfsetmiterjoin
\pgfsetdash{}{0pt}
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\pgfpathellipse{\pgfpoint{30.746915\du}{14.018715\du}}{\pgfpoint{0.481715\du}{0\du}}{\pgfpoint{0\du}{0.481715\du}}
\pgfusepath{fill}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\pgfpathellipse{\pgfpoint{30.746915\du}{14.018715\du}}{\pgfpoint{0.481715\du}{0\du}}{\pgfpoint{0\du}{0.481715\du}}
\pgfusepath{stroke}
\pgfsetbuttcap
\pgfsetmiterjoin
\pgfsetdash{}{0pt}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (30.406291\du,13.678091\du)--(30.746915\du,14.018715\du)--(30.406291\du,14.359341\du);
\pgfsetlinewidth{0.000100\du}
\pgfsetbuttcap
\pgfsetmiterjoin
\pgfsetdash{}{0pt}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
\pgfpathmoveto{\pgfpoint{31.087541\du}{13.678091\du}}
\pgfpathcurveto{\pgfpoint{31.087541\du}{13.678091\du}}{\pgfpoint{31.228630\du}{13.802896\du}}{\pgfpoint{31.228630\du}{14.018715\du}}
\pgfpathcurveto{\pgfpoint{31.228630\du}{14.234533\du}}{\pgfpoint{31.087541\du}{14.359341\du}}{\pgfpoint{31.087541\du}{14.359341\du}}
\pgfpathlineto{\pgfpoint{30.746915\du}{14.018715\du}}
\pgfpathlineto{\pgfpoint{31.087541\du}{13.678091\du}}
\pgfusepath{fill}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\pgfpathmoveto{\pgfpoint{31.087541\du}{13.678091\du}}
\pgfpathcurveto{\pgfpoint{31.087541\du}{13.678091\du}}{\pgfpoint{31.228630\du}{13.802896\du}}{\pgfpoint{31.228630\du}{14.018715\du}}
\pgfpathcurveto{\pgfpoint{31.228630\du}{14.234533\du}}{\pgfpoint{31.087541\du}{14.359341\du}}{\pgfpoint{31.087541\du}{14.359341\du}}
\pgfpathlineto{\pgfpoint{30.746915\du}{14.018715\du}}
\pgfpathlineto{\pgfpoint{31.087541\du}{13.678091\du}}
\pgfusepath{stroke}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
{\pgfsetcornersarced{\pgfpoint{0.000000\du}{0.000000\du}}\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (32.240420\du,16.930983\du)--(30.742500\du,16.931100\du)--(30.746099\du,14.549132\du);
}}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (27.983969\du,14.026602\du)--(30.216295\du,14.020230\du);
}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (30.789233\du,11.923482\du)--(30.757167\du,13.511146\du);
}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (31.278812\du,14.019814\du)--(34.002358\du,14.025440\du);
}
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (35.530900\du,9.989040\du)--(35.530900\du,11.889040\du)--(38.145900\du,11.889040\du)--(38.145900\du,9.989040\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (35.530900\du,9.989040\du)--(35.530900\du,11.889040\du)--(38.145900\du,11.889040\du)--(38.145900\du,9.989040\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (36.838400\du,11.056540\du){sgn};
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
{\pgfsetcornersarced{\pgfpoint{0.000000\du}{0.000000\du}}\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (37.025681\du,14.063794\du)--(37.017827\du,16.967433\du)--(34.379062\du,16.941481\du);
}}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
\pgfsetmiterjoin
\pgfsetlinewidth{0.100000\du}
\pgfsetbuttcap
\pgfsetmiterjoin
\pgfsetdash{}{0pt}
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\pgfpathellipse{\pgfpoint{23.937515\du}{14.059215\du}}{\pgfpoint{0.481715\du}{0\du}}{\pgfpoint{0\du}{0.481715\du}}
\pgfusepath{fill}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\pgfpathellipse{\pgfpoint{23.937515\du}{14.059215\du}}{\pgfpoint{0.481715\du}{0\du}}{\pgfpoint{0\du}{0.481715\du}}
\pgfusepath{stroke}
\pgfsetbuttcap
\pgfsetmiterjoin
\pgfsetdash{}{0pt}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (23.596891\du,13.718591\du)--(23.937515\du,14.059215\du)--(23.596891\du,14.399841\du);
\pgfsetlinewidth{0.000100\du}
\pgfsetbuttcap
\pgfsetmiterjoin
\pgfsetdash{}{0pt}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
\pgfpathmoveto{\pgfpoint{24.278141\du}{13.718591\du}}
\pgfpathcurveto{\pgfpoint{24.278141\du}{13.718591\du}}{\pgfpoint{24.419230\du}{13.843396\du}}{\pgfpoint{24.419230\du}{14.059215\du}}
\pgfpathcurveto{\pgfpoint{24.419230\du}{14.275033\du}}{\pgfpoint{24.278141\du}{14.399841\du}}{\pgfpoint{24.278141\du}{14.399841\du}}
\pgfpathlineto{\pgfpoint{23.937515\du}{14.059215\du}}
\pgfpathlineto{\pgfpoint{24.278141\du}{13.718591\du}}
\pgfusepath{fill}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\pgfpathmoveto{\pgfpoint{24.278141\du}{13.718591\du}}
\pgfpathcurveto{\pgfpoint{24.278141\du}{13.718591\du}}{\pgfpoint{24.419230\du}{13.843396\du}}{\pgfpoint{24.419230\du}{14.059215\du}}
\pgfpathcurveto{\pgfpoint{24.419230\du}{14.275033\du}}{\pgfpoint{24.278141\du}{14.399841\du}}{\pgfpoint{24.278141\du}{14.399841\du}}
\pgfpathlineto{\pgfpoint{23.937515\du}{14.059215\du}}
\pgfpathlineto{\pgfpoint{24.278141\du}{13.718591\du}}
\pgfusepath{stroke}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (24.419200\du,14.059200\du)--(25.876695\du,14.042044\du);
}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (21.904590\du,14.049299\du)--(23.455800\du,14.059200\du);
}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
{\pgfsetcornersarced{\pgfpoint{0.000000\du}{0.000000\du}}\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (25.839033\du,18.252271\du)--(23.967878\du,18.242428\du)--(23.941360\du,14.590785\du);
}}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
{\pgfsetcornersarced{\pgfpoint{0.000000\du}{0.000000\du}}\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (37.025681\du,14.063794\du)--(37.017827\du,18.267428\du)--(28.210835\du,18.259563\du);
}}
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (29.809400\du,9.974960\du)--(29.809400\du,11.874960\du)--(31.809400\du,11.874960\du)--(31.809400\du,9.974960\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (29.809400\du,9.974960\du)--(29.809400\du,11.874960\du)--(31.809400\du,11.874960\du)--(31.809400\du,9.974960\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (30.809400\du,11.042460\du){K};
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (35.480918\du,10.935870\du)--(31.858882\du,10.927411\du);
}
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (24.698400\du,13.515600\du){u};
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (29.042800\du,13.272400\du){};
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (25.646800\du,13.976000\du){};
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (36.896700\du,13.603100\du){$x_r$};
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (40.292814\du,15.717428\du){$y_r$};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (34.048300\du,13.077600\du)--(34.048300\du,14.977600\du)--(36.048300\du,14.977600\du)--(36.048300\du,13.077600\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (34.048300\du,13.077600\du)--(34.048300\du,14.977600\du)--(36.048300\du,14.977600\du)--(36.048300\du,13.077600\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (35.048300\du,14.145100\du){$\int$};
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (31.923600\du,13.615500\du){$\dot{x}_r$};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (25.949852\du,25.438042\du)--(25.949852\du,27.338042\du)--(27.952352\du,27.338042\du)--(27.952352\du,25.438042\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (25.949852\du,25.438042\du)--(25.949852\du,27.338042\du)--(27.952352\du,27.338042\du)--(27.952352\du,25.438042\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (26.951102\du,26.505542\du){$A_f$};
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (27.328002\du,23.506242\du){};
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (27.328002\du,23.506242\du){};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (31.262009\du,22.449342\du)--(31.262009\du,24.349342\du)--(33.262009\du,24.349342\du)--(33.262009\du,22.449342\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (31.262009\du,22.449342\du)--(31.262009\du,24.349342\du)--(33.262009\du,24.349342\du)--(33.262009\du,22.449342\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (32.262009\du,23.516842\du){$C_f$};
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (29.741754\du,23.459628\du)--(31.212157\du,23.424455\du);
}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
\pgfsetmiterjoin
\pgfsetlinewidth{0.100000\du}
\pgfsetbuttcap
\pgfsetmiterjoin
\pgfsetdash{}{0pt}
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\pgfpathellipse{\pgfpoint{24.390517\du}{23.475857\du}}{\pgfpoint{0.481715\du}{0\du}}{\pgfpoint{0\du}{0.481715\du}}
\pgfusepath{fill}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\pgfpathellipse{\pgfpoint{24.390517\du}{23.475857\du}}{\pgfpoint{0.481715\du}{0\du}}{\pgfpoint{0\du}{0.481715\du}}
\pgfusepath{stroke}
\pgfsetbuttcap
\pgfsetmiterjoin
\pgfsetdash{}{0pt}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (24.049893\du,23.135233\du)--(24.390517\du,23.475857\du)--(24.049893\du,23.816482\du);
\pgfsetlinewidth{0.000100\du}
\pgfsetbuttcap
\pgfsetmiterjoin
\pgfsetdash{}{0pt}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
\pgfpathmoveto{\pgfpoint{24.731143\du}{23.135233\du}}
\pgfpathcurveto{\pgfpoint{24.731143\du}{23.135233\du}}{\pgfpoint{24.872232\du}{23.260037\du}}{\pgfpoint{24.872232\du}{23.475857\du}}
\pgfpathcurveto{\pgfpoint{24.872232\du}{23.691675\du}}{\pgfpoint{24.731143\du}{23.816482\du}}{\pgfpoint{24.731143\du}{23.816482\du}}
\pgfpathlineto{\pgfpoint{24.390517\du}{23.475857\du}}
\pgfpathlineto{\pgfpoint{24.731143\du}{23.135233\du}}
\pgfusepath{fill}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\pgfpathmoveto{\pgfpoint{24.731143\du}{23.135233\du}}
\pgfpathcurveto{\pgfpoint{24.731143\du}{23.135233\du}}{\pgfpoint{24.872232\du}{23.260037\du}}{\pgfpoint{24.872232\du}{23.475857\du}}
\pgfpathcurveto{\pgfpoint{24.872232\du}{23.691675\du}}{\pgfpoint{24.731143\du}{23.816482\du}}{\pgfpoint{24.731143\du}{23.816482\du}}
\pgfpathlineto{\pgfpoint{24.390517\du}{23.475857\du}}
\pgfpathlineto{\pgfpoint{24.731143\du}{23.135233\du}}
\pgfusepath{stroke}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
{\pgfsetcornersarced{\pgfpoint{0.000000\du}{0.000000\du}}\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (25.904061\du,26.388123\du)--(24.386102\du,26.388242\du)--(24.389713\du,24.006286\du);
}}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (21.979918\du,23.467570\du)--(23.908802\du,23.475857\du);
}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (24.922415\du,23.476955\du)--(27.645960\du,23.482581\du);
}
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (37.967823\du,26.142397\du){x};
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (31.717848\du,21.917414\du){y};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (27.691902\du,22.534742\du)--(27.691902\du,24.434742\du)--(29.691902\du,24.434742\du)--(29.691902\du,22.534742\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (27.691902\du,22.534742\du)--(27.691902\du,24.434742\du)--(29.691902\du,24.434742\du)--(29.691902\du,22.534742\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (28.691902\du,23.602242\du){$\int$};
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (25.567202\du,23.072642\du){$\dot{x}$};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (19.915395\du,22.513030\du)--(19.915395\du,24.413030\du)--(21.930395\du,24.413030\du)--(21.930395\du,22.513030\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (19.915395\du,22.513030\du)--(19.915395\du,24.413030\du)--(21.930395\du,24.413030\du)--(21.930395\du,22.513030\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (20.922895\du,23.580530\du){$B_f$};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (38.702810\du,25.442382\du)--(38.702810\du,27.342382\du)--(41.217810\du,27.342382\du)--(41.217810\du,25.442382\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (38.702810\du,25.442382\du)--(38.702810\du,27.342382\du)--(41.217810\du,27.342382\du)--(41.217810\du,25.442382\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (39.960310\du,26.587382\du){Algo};
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (39.542817\du,15.842438\du){};
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
{\pgfsetcornersarced{\pgfpoint{0.000000\du}{0.000000\du}}\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (32.263491\du,22.413699\du)--(32.267846\du,19.517423\du)--(20.892891\du,19.517423\du)--(20.861922\du,15.042731\du);
}}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
{\pgfsetcornersarced{\pgfpoint{0.000000\du}{0.000000\du}}\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (38.652958\du,26.391946\du)--(28.000795\du,26.388392\du);
}}
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (34.300331\du,20.292418\du)--(34.300331\du,22.192418\du)--(37.810331\du,22.192418\du)--(37.810331\du,20.292418\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (34.300331\du,20.292418\du)--(34.300331\du,22.192418\du)--(37.810331\du,22.192418\du)--(37.810331\du,20.292418\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (36.055331\du,21.437418\du){Sensor};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (33.824083\du,19.881170\du)--(33.824083\du,21.781170\du)--(37.334083\du,21.781170\du)--(37.334083\du,19.881170\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (33.824083\du,19.881170\du)--(33.824083\du,21.781170\du)--(37.334083\du,21.781170\du)--(37.334083\du,19.881170\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (35.579083\du,21.026170\du){Sensor};
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
{\pgfsetcornersarced{\pgfpoint{0.000000\du}{0.000000\du}}\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (39.944776\du,15.115158\du)--(39.958936\du,25.394424\du);
}}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (36.812302\du,22.240727\du)--(39.203339\du,25.394074\du);
}
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (36.592829\du,23.467408\du){};
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (37.940323\du,23.062411\du){$y_{rji}$};
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
\pgfsetfillcolor{dialinecolor}
\fill (23.390381\du,20.019922\du)--(23.390381\du,21.919922\du)--(25.405381\du,21.919922\du)--(25.405381\du,20.019922\du)--cycle;
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (23.390381\du,20.019922\du)--(23.390381\du,21.919922\du)--(25.405381\du,21.919922\du)--(25.405381\du,20.019922\du)--cycle;
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node at (24.397881\du,21.087422\du){B};
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
{\pgfsetcornersarced{\pgfpoint{0.000000\du}{0.000000\du}}\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (24.394943\du,21.969604\du)--(24.392080\du,22.944202\du);
}}
\pgfsetlinewidth{0.100000\du}
\pgfsetdash{}{0pt}
\pgfsetdash{}{0pt}
\pgfsetmiterjoin
\pgfsetbuttcap
{
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetfillcolor{dialinecolor}
% was here!!!
\pgfsetarrowsend{stealth}
{\pgfsetcornersarced{\pgfpoint{0.000000\du}{0.000000\du}}\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\draw (21.517888\du,20.992417\du)--(23.340032\du,20.978184\du);
}}
% setfont left to latex
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
\pgfsetstrokecolor{dialinecolor}
\node[anchor=west] at (19.865395\du,21.112419\du){$v_{ref}$};
\end{tikzpicture}

132
BAB5/bab5.tex
View File

@ -1,80 +1,80 @@
%-----------------------------------------------------------------------------%
\chapter{\babLima}
%-----------------------------------------------------------------------------%
\todo{Tambahkan kata-kata pengantar bab 5 disini.}
% %-----------------------------------------------------------------------------%
% \chapter{\babLima}
% %-----------------------------------------------------------------------------%
% \todo{Tambahkan kata-kata pengantar bab 5 disini.}
%-----------------------------------------------------------------------------%
\section{Mengubah Tampilan Teks}
%-----------------------------------------------------------------------------%
Beberapa perintah yang dapat digunakan untuk mengubah tampilan adalah:
\begin{itemize}
\item \bslash f \\
Merupakan alias untuk perintah \bslash textit, contoh
\f{contoh hasil tulisan}.
\item \bslash bi \\
\bi{Contoh hasil tulisan}.
\item \bslash bo \\
\bo{Contoh hasil tulisan}.
\item \bslash m \\
\m{Contoh hasil tulisan}.
\item \bslash mc \\
\mc{Contoh hasil tulisan}.
\item \bslash code \\
\code{Contoh hasil tulisan}.
\end{itemize}
% %-----------------------------------------------------------------------------%
% \section{Mengubah Tampilan Teks}
% %-----------------------------------------------------------------------------%
% Beberapa perintah yang dapat digunakan untuk mengubah tampilan adalah:
% \begin{itemize}
% \item \bslash f \\
% Merupakan alias untuk perintah \bslash textit, contoh
% \f{contoh hasil tulisan}.
% \item \bslash bi \\
% \bi{Contoh hasil tulisan}.
% \item \bslash bo \\
% \bo{Contoh hasil tulisan}.
% \item \bslash m \\
% \m{Contoh hasil tulisan}.
% \item \bslash mc \\
% \mc{Contoh hasil tulisan}.
% \item \bslash code \\
% \code{Contoh hasil tulisan}.
% \end{itemize}
%-----------------------------------------------------------------------------%
\section{Memberikan Catatan}
%-----------------------------------------------------------------------------%
Ada dua perintah untuk memberikan catatan penulisan dalam dokumen yang Anda
kerjakan, yaitu:
\begin{itemize}
\item \bslash todo \\
Contoh: \\ \todo{Contoh bentuk todo.}
\item \bslash todoCite \\
Contoh: \todoCite
\end{itemize}
% %-----------------------------------------------------------------------------%
% \section{Memberikan Catatan}
% %-----------------------------------------------------------------------------%
% Ada dua perintah untuk memberikan catatan penulisan dalam dokumen yang Anda
% kerjakan, yaitu:
% \begin{itemize}
% \item \bslash todo \\
% Contoh: \\ \todo{Contoh bentuk todo.}
% \item \bslash todoCite \\
% Contoh: \todoCite
% \end{itemize}
%-----------------------------------------------------------------------------%
\section{Menambah Isi Daftar Isi}
%-----------------------------------------------------------------------------%
Terkadang ada kebutuhan untuk memasukan kata-kata tertentu kedalam Daftar Isi.
Perintah \bslash addChapter dapat digunakan untuk judul bab dalam Daftar isi.
Contohnya dapat dilihat pada berkas thesis.tex.
% %-----------------------------------------------------------------------------%
% \section{Menambah Isi Daftar Isi}
% %-----------------------------------------------------------------------------%
% Terkadang ada kebutuhan untuk memasukan kata-kata tertentu kedalam Daftar Isi.
% Perintah \bslash addChapter dapat digunakan untuk judul bab dalam Daftar isi.
% Contohnya dapat dilihat pada berkas thesis.tex.
%-----------------------------------------------------------------------------%
\section{Memasukan PDF}
%-----------------------------------------------------------------------------%
Untuk memasukan PDF dapat menggunakan perintah \bslash inpdf yang menerima satu
buah argumen. Argumen ini berisi nama berkas yang akan digabungkan dalam
laporan. PDF yang dimasukan degnan cara ini akan memiliki header dan footer
seperti pada halaman lainnya.
% %-----------------------------------------------------------------------------%
% \section{Memasukan PDF}
% %-----------------------------------------------------------------------------%
% Untuk memasukan PDF dapat menggunakan perintah \bslash inpdf yang menerima satu
% buah argumen. Argumen ini berisi nama berkas yang akan digabungkan dalam
% laporan. PDF yang dimasukan degnan cara ini akan memiliki header dan footer
% seperti pada halaman lainnya.
\inpdf{OTHER/include}
% \inpdf{OTHER/include}
Cara lain untuk memasukan PDF adalah dengan menggunakan perintah \bslash putpdf
dengan satu argumen yang berisi nama berkas pdf. Berbeda dengan perintah
sebelumnya, PDF yang dimasukan dengan cara ini tidak akan memiliki footer atau
header seperti pada halaman lainnya.
% Cara lain untuk memasukan PDF adalah dengan menggunakan perintah \bslash putpdf
% dengan satu argumen yang berisi nama berkas pdf. Berbeda dengan perintah
% sebelumnya, PDF yang dimasukan dengan cara ini tidak akan memiliki footer atau
% header seperti pada halaman lainnya.
\putpdf{OTHER/include}
% \putpdf{OTHER/include}
%-----------------------------------------------------------------------------%
\section{Membuat Perintah Baru}
%-----------------------------------------------------------------------------%
Ada dua perintah yang dapat digunakan untuk membuat perintah baru, yaitu:
\begin{itemize}
\item \bslash Var \\
Digunakan untuk membuat perintah baru, namun setiap kata yang diberikan
akan diproses dahulu menjadi huruf kapital.
Contoh jika perintahnya adalah \bslash Var\{adalah\} makan ketika
perintah \bslash Var dipanggil, yang akan muncul adalah ADALAH.
\item \bslash var \\
Digunakan untuk membuat perintah atau baru.
\end{itemize}
% %-----------------------------------------------------------------------------%
% \section{Membuat Perintah Baru}
% %-----------------------------------------------------------------------------%
% Ada dua perintah yang dapat digunakan untuk membuat perintah baru, yaitu:
% \begin{itemize}
% \item \bslash Var \\
% Digunakan untuk membuat perintah baru, namun setiap kata yang diberikan
% akan diproses dahulu menjadi huruf kapital.
% Contoh jika perintahnya adalah \bslash Var\{adalah\} makan ketika
% perintah \bslash Var dipanggil, yang akan muncul adalah ADALAH.
% \item \bslash var \\
% Digunakan untuk membuat perintah atau baru.
% \end{itemize}

BIN
OTHER/CITESRC/07074770.pdf Normal file
View File

Binary file not shown.

BIN
OTHER/CITESRC/Oh_et_al-2014-International_Journal_of_Robust_and_Nonlinear_Control.pdf Normal file
View File

Binary file not shown.

15
OTHER/references.bib
View File

@ -185,4 +185,19 @@ doi={10.1109/CDC.2007.4434757},
ISSN={0191-2216},
month={Dec},}
@article{Oh2014,
author = {Oh, Kwang-Kyo and Ahn, Hyo-Sung},
title = {Distance-based undirected formations of single-integrator and double-integrator modeled agents in n-dimensional space},
journal = {International Journal of Robust and Nonlinear Control},
volume = {24},
number = {12},
pages = {1809-1820},
keywords = {formation control, distance-based control, graph rigidity, Hamiltonian systems, gradient systems},
doi = {10.1002/rnc.2967},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/rnc.2967},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/rnc.2967},
abstract = {SUMMARYWe study the local asymptotic stability of undirected formations of single-integrator and double-integrator modeled agents based on interagent distance control. First, we show that n-dimensional undirected formations of single-integrator modeled agents are locally asymptotically stable under a gradient control law. The stability analysis in this paper reveals that the local asymptotic stability does not require the infinitesimal rigidity of the formations. Second, on the basis of the topological equivalence of a dissipative Hamiltonian system and a gradient system, we show that the local asymptotic stability of undirected formations of double-integrator modeled agents in n-dimensional space is achieved under a gradient-like control law. Simulation results support the validity of the stability analysis. Copyright © 2013 John Wiley \& Sons, Ltd.},
year = {2014}
}

553
thesis.bbl
View File

@ -1,553 +0,0 @@
% $ biblatex auxiliary file $
% $ biblatex bbl format version 2.9 $
% Do not modify the above lines!
%
% This is an auxiliary file used by the 'biblatex' package.
% This file may safely be deleted. It will be recreated as
% required.
%
\begingroup
\makeatletter
\@ifundefined{ver@biblatex.sty}
{\@latex@error
{Missing 'biblatex' package}
{The bibliography requires the 'biblatex' package.}
\aftergroup\endinput}
{}
\endgroup
\datalist[entry]{nyt/global//global/global}
\entry{Cao2007}{inproceedings}{}
\name{author}{5}{}{%
{{hash=CM}{%
family={{Cao}},
familyi={C\bibinitperiod},
given={M.},
giveni={M\bibinitperiod},
}}%
{{hash=MAS}{%
family={{Morse}},
familyi={M\bibinitperiod},
given={A.\bibnamedelima S.},
giveni={A\bibinitperiod\bibinitdelim S\bibinitperiod},
}}%
{{hash=YC}{%
family={{Yu}},
familyi={Y\bibinitperiod},
given={C.},
giveni={C\bibinitperiod},
}}%
{{hash=ABDO}{%
family={{Anderson}},
familyi={A\bibinitperiod},
given={B.\bibnamedelima D.\bibnamedelima O.},
giveni={B\bibinitperiod\bibinitdelim D\bibinitperiod\bibinitdelim
O\bibinitperiod},
}}%
{{hash=DS}{%
family={{Dasguvta}},
familyi={D\bibinitperiod},
given={S.},
giveni={S\bibinitperiod},
}}%
}
\keyw{distributed control;mobile robots;multi-robot systems;spatial
variables control;triangular formation;mobile autonomous agents;collinear
formations;distributed control law;Autonomous agents;USA Councils;Distributed
control;H infinity control;Differential equations;Information
technology;Art;Australia Council}
\strng{namehash}{CM+1}
\strng{fullhash}{CMMASYCABDODS1}
\field{labelnamesource}{author}
\field{labeltitlesource}{title}
\field{labelyear}{2007}
\field{labeldatesource}{year}
\field{sortinit}{C}
\field{sortinithash}{C}
\field{abstract}{%
This paper proposes a distributed control law for maintaining a triangular
formation in the plane consisting of three mobile autonomous agents. It is
shown that the control law can cause any initially non-collinear,
positively-oriented {resp. negatively-oriented} triangular formation to
converge exponentially fast to a desired positively-oriented {resp.
negatively- oriented} triangular formation. It is also shown that there is a
thin set of initially collinear formations which remain collinear and may
drift off to infinity as t rarr infin. These findings complement and extend
earlier findings cited below.%
}
\field{booktitle}{2007 46th IEEE Conference on Decision and Control}
\verb{doi}
\verb 10.1109/CDC.2007.4434757
\endverb
\field{issn}{0191-2216}
\field{pages}{3603\bibrangedash 3608}
\field{title}{Controlling a triangular formation of mobile autonomous
agents}
\field{year}{2007}
\warn{\item Invalid format of field 'month'}
\endentry
\entry{CORREIA20127}{article}{}
\name{author}{3}{}{%
{{hash=CMD}{%
family={Correia},
familyi={C\bibinitperiod},
given={Mariane\bibnamedelima Dourado},
giveni={M\bibinitperiod\bibinitdelim D\bibinitperiod},
}}%
{{hash=GA}{%
family={Gustavo},
familyi={G\bibinitperiod},
given={André},
giveni={A\bibinitperiod},
}}%
{{hash=CS}{%
family={Conceição},
familyi={C\bibinitperiod},
given={Scolari},
giveni={S\bibinitperiod},
}}%
}
\keyw{Models, Friction, Parameter estimation, Autonomous mobile robots}
\strng{namehash}{CMDGACS1}
\strng{fullhash}{CMDGACS1}
\field{labelnamesource}{author}
\field{labeltitlesource}{title}
\field{labelyear}{2012}
\field{labeldatesource}{year}
\field{sortinit}{C}
\field{sortinithash}{C}
\field{abstract}{%
This paper presents a model of a three-wheeled omnidirectional robot
including a static friction model. Besides the modeling is presented a
practical approach in order to estimate the coefficients of coulomb and
viscous friction, which used sensory information about force and velocity of
the robot's center of mass. The proposed model model has the voltages of the
motors as inputs and the linear and angular velocities of the robot as
outputs. Actual results and simulation with the estimated model are compared
to demonstrate the performance of the proposed modeling.%
}
\verb{doi}
\verb https://doi.org/10.3182/20120905-3-HR-2030.00002
\endverb
\field{issn}{1474-6670}
\field{note}{10th IFAC Symposium on Robot Control}
\field{number}{22}
\field{pages}{7 \bibrangedash 12}
\field{title}{Modeling of a Three Wheeled Omnidirectional Robot Including
Friction Models}
\verb{url}
\verb http://www.sciencedirect.com/science/article/pii/S1474667016335807
\endverb
\field{volume}{45}
\field{journaltitle}{IFAC Proceedings Volumes}
\field{year}{2012}
\endentry
\entry{Richard2010}{book}{}
\name{author}{2}{}{%
{{hash=DR}{%
family={Dorf},
familyi={D\bibinitperiod},
given={Richard},
giveni={R\bibinitperiod},
}}%
{{hash=BR}{%
family={Bishop},
familyi={B\bibinitperiod},
given={Robert},
giveni={R\bibinitperiod},
}}%
}
\strng{namehash}{DRBR1}
\strng{fullhash}{DRBR1}
\field{labelnamesource}{author}
\field{labeltitlesource}{title}
\field{labelyear}{2010}
\field{labeldatesource}{year}
\field{sortinit}{D}
\field{sortinithash}{D}
\field{isbn}{ISBN-10: 0136024580; ISBN-13: 978-0136024583}
\field{title}{Modern Control Systems, 12th Edition}
\field{month}{07}
\field{year}{2010}
\endentry
\entry{Fabien2009}{inbook}{}
\name{author}{1}{}{%
{{hash=FB}{%
family={Fabien},
familyi={F\bibinitperiod},
given={Brian},
giveni={B\bibinitperiod},
}}%
}
\list{publisher}{1}{%
{Springer US}%
}
\strng{namehash}{FB1}
\strng{fullhash}{FB1}
\field{labelnamesource}{author}
\field{labeltitlesource}{title}
\field{labelyear}{2009}
\field{labeldatesource}{year}
\field{sortinit}{F}
\field{sortinithash}{F}
\field{booktitle}{Analytical System Dynamics: Modeling and Simulation}
\verb{doi}
\verb 10.1007/978-0-387-85605-6_5
\endverb
\field{isbn}{978-0-387-85605-6}
\field{pages}{1\bibrangedash 59}
\field{title}{Numerical Solution of ODEs and DAEs}
\verb{url}
\verb https://doi.org/10.1007/978-0-387-85605-6_5
\endverb
\list{location}{1}{%
{Boston, MA}%
}
\field{year}{2009}
\endentry
\entry{Guanghua2013}{inproceedings}{}
\name{author}{4}{}{%
{{hash=GW}{%
family={Guanghua},
familyi={G\bibinitperiod},
given={Wang},
giveni={W\bibinitperiod},
}}%
{{hash=DL}{%
family={Deyi},
familyi={D\bibinitperiod},
given={Li},
giveni={L\bibinitperiod},
}}%
{{hash=WG}{%
family={Wenyan},
familyi={W\bibinitperiod},
given={Gan},
giveni={G\bibinitperiod},
}}%
{{hash=PJ}{%
family={Peng},
familyi={P\bibinitperiod},
given={Jia},
giveni={J\bibinitperiod},
}}%
}
\strng{namehash}{GW+1}
\strng{fullhash}{GWDLWGPJ1}
\field{labelnamesource}{author}
\field{labeltitlesource}{title}
\field{labelyear}{2013}
\field{labeldatesource}{year}
\field{sortinit}{G}
\field{sortinithash}{G}
\verb{doi}
\verb 10.1109/ISDEA.2012.316
\endverb
\field{isbn}{978-1-4673-4893-5}
\field{pages}{1335\bibrangedash 1339}
\field{title}{Study on Formation Control of Multi-Robot Systems}
\field{month}{01}
\field{year}{2013}
\endentry
\entry{Hacene2019}{article}{}
\name{author}{2}{}{%
{{hash=HN}{%
family={Hacene},
familyi={H\bibinitperiod},
given={Nacer},
giveni={N\bibinitperiod},
}}%
{{hash=MB}{%
family={Mendil},
familyi={M\bibinitperiod},
given={Boubekeur},
giveni={B\bibinitperiod},
}}%
}
\strng{namehash}{HNMB1}
\strng{fullhash}{HNMB1}
\field{labelnamesource}{author}
\field{labeltitlesource}{title}
\field{labelyear}{2019}
\field{labeldatesource}{year}
\field{sortinit}{H}
\field{sortinithash}{H}
\field{abstract}{%
In this paper, a fuzzy behavior-based approach for a three wheeled
omnidirectional mobile robot (TWOMR) navigation has been proposed. The robot
has to track either static or dynamic target while avoiding either static or
dynamic obstacles along its path. A simple controller design is adopted, and
to do so, two fuzzy behaviors ``Track the Target'' and ``Avoid Obstacles and
Wall Following'' are considered based on reduced rule bases (six and five
rules respectively). This strategy employs a system of five ultrasonic
sensors which provide the necessary information about obstacles in the
environment. Simulation platform was designed to demonstrate the
effectiveness of the proposed approach.%
}
\verb{doi}
\verb 10.1007/s11633-018-1135-x
\endverb
\field{issn}{1751-8520}
\field{number}{2}
\field{pages}{163\bibrangedash 185}
\field{title}{Fuzzy Behavior-based Control of Three Wheeled Omnidirectional
Mobile Robot}
\verb{url}
\verb https://doi.org/10.1007/s11633-018-1135-x
\endverb
\field{volume}{16}
\field{journaltitle}{International Journal of Automation and Computing}
\field{month}{04}
\field{year}{2019}
\endentry
\entry{Irwanto2018}{misc}{}
\name{author}{1}{}{%
{{hash=IHY}{%
family={Irwanto},
familyi={I\bibinitperiod},
given={Herma\bibnamedelima Yudhi},
giveni={H\bibinitperiod\bibinitdelim Y\bibinitperiod},
}}%
}
\strng{namehash}{IHY1}
\strng{fullhash}{IHY1}
\field{labelnamesource}{author}
\field{labeltitlesource}{title}
\field{labelyear}{2018}
\field{labeldatesource}{year}
\field{sortinit}{I}
\field{sortinithash}{I}
\field{number}{1}
\field{title}{Development of Mobile Ground Control System and GPS Base Auto
Tracking Antenna}
\field{volume}{16}
\field{journaltitle}{Jurnal Teknologi Dirgantara}
\field{year}{2018}
\warn{\item Invalid format of field 'month'}
\endentry
\entry{Jim1999}{inbook}{}
\name{author}{1}{}{%
{{hash=LJA}{%
family={Ledin},
familyi={L\bibinitperiod},
given={Jim\bibnamedelima A.},
giveni={J\bibinitperiod\bibinitdelim A\bibinitperiod},
}}%
}
\strng{namehash}{LJA1}
\strng{fullhash}{LJA1}
\field{labelnamesource}{author}
\field{labeltitlesource}{title}
\field{labelyear}{1999}
\field{labeldatesource}{year}
\field{sortinit}{L}
\field{sortinithash}{L}
\field{booktitle}{Embedded Systems Programming}
\field{title}{Hardware-in-the-Loop Simulation}
\field{year}{1999}
\warn{\item Invalid format of field 'month'}
\endentry
\entry{OH2015424}{article}{}
\name{author}{3}{}{%
{{hash=OKK}{%
family={Oh},
familyi={O\bibinitperiod},
given={Kwang-Kyo},
giveni={K\bibinitperiod-K\bibinitperiod},
}}%
{{hash=PMC}{%
family={Park},
familyi={P\bibinitperiod},
given={Myoung-Chul},
giveni={M\bibinitperiod-C\bibinitperiod},
}}%
{{hash=AHS}{%
family={Ahn},
familyi={A\bibinitperiod},
given={Hyo-Sung},
giveni={H\bibinitperiod-S\bibinitperiod},
}}%
}
\keyw{Formation control, Position-based control, Displacement-based
control, Distance-based control}
\strng{namehash}{OKKPMCAHS1}
\strng{fullhash}{OKKPMCAHS1}
\field{labelnamesource}{author}
\field{labeltitlesource}{title}
\field{labelyear}{2015}
\field{labeldatesource}{year}
\field{sortinit}{O}
\field{sortinithash}{O}
\field{abstract}{%
We present a survey of formation control of multi-agent systems. Focusing
on the sensing capability and the interaction topology of agents, we
categorize the existing results into position-, displacement-, and
distance-based control. We then summarize problem formulations, discuss
distinctions, and review recent results of the formation control schemes.
Further we review some other results that do not fit into the
categorization.%
}
\verb{doi}
\verb https://doi.org/10.1016/j.automatica.2014.10.022
\endverb
\field{issn}{0005-1098}
\field{pages}{424 \bibrangedash 440}
\field{title}{A survey of multi-agent formation control}
\verb{url}
\verb http://www.sciencedirect.com/science/article/pii/S0005109814004038
\endverb
\field{volume}{53}
\field{journaltitle}{Automatica}
\field{year}{2015}
\endentry
\entry{Parker2003}{article}{}
\name{author}{1}{}{%
{{hash=PL}{%
family={Parker},
familyi={P\bibinitperiod},
given={Lynne},
giveni={L\bibinitperiod},
}}%
}
\strng{namehash}{PL1}
\strng{fullhash}{PL1}
\field{labelnamesource}{author}
\field{labeltitlesource}{title}
\field{labelyear}{2003}
\field{labeldatesource}{year}
\field{sortinit}{P}
\field{sortinithash}{P}
\verb{doi}
\verb 10.1007/BF02480877
\endverb
\field{pages}{1\bibrangedash 5}
\field{title}{Current research in multirobot systems}
\field{volume}{7}
\field{journaltitle}{Artificial Life and Robotics}
\field{month}{03}
\field{year}{2003}
\endentry
\entry{QUESADA2019275}{article}{}
\name{author}{4}{}{%
{{hash=QLF}{%
family={Quesada},
familyi={Q\bibinitperiod},
given={Luisa\bibnamedelima Fernanda},
giveni={L\bibinitperiod\bibinitdelim F\bibinitperiod},
}}%
{{hash=RJD}{%
family={Rojas},
familyi={R\bibinitperiod},
given={José\bibnamedelima David},
giveni={J\bibinitperiod\bibinitdelim D\bibinitperiod},
}}%
{{hash=AO}{%
family={Arrieta},
familyi={A\bibinitperiod},
given={Orlando},
giveni={O\bibinitperiod},
}}%
{{hash=VR}{%
family={Vilanova},
familyi={V\bibinitperiod},
given={Ramon},
giveni={R\bibinitperiod},
}}%
}
\keyw{Controlled system, insulin control, Hardware in the loop, PID
control, Optimal control}
\strng{namehash}{QLF+1}
\strng{fullhash}{QLFRJDAOVR1}
\field{labelnamesource}{author}
\field{labeltitlesource}{title}
\field{labelyear}{2019}
\field{labeldatesource}{year}
\field{sortinit}{Q}
\field{sortinithash}{Q}
\field{abstract}{%
Artificial pancreas control is an important research area in the biomedical
field. However, it is dangerous to test new control algorithms on humans in
order to improve the performance of the control system. This paper presents
the results of using an open-source low-cost hardware in the loop platform to
test different control strategies for artificial pancreas research. An
Arduino platform was selected as the main device to implement the real time
differential equations solver needed for the HIL simulation. The platform was
successfully tested with both a PID controller and an LQR controller. The
code and schematics of the platform are available upon request.%
}
\verb{doi}
\verb https://doi.org/10.1016/j.ifacol.2019.06.074
\endverb
\field{issn}{2405-8963}
\field{note}{12th IFAC Symposium on Dynamics and Control of Process
Systems, including Biosystems DYCOPS 2019}
\field{number}{1}
\field{pages}{275 \bibrangedash 280}
\field{title}{Open-source low-cost Hardware-in-the-loop simulation platform
for testing control strategies for artificial pancreas research}
\verb{url}
\verb http://www.sciencedirect.com/science/article/pii/S2405896319301594
\endverb
\field{volume}{52}
\field{journaltitle}{IFAC-PapersOnLine}
\field{year}{2019}
\endentry
\entry{Rozenheck2015}{inproceedings}{}
\name{author}{3}{}{%
{{hash=RO}{%
family={{Rozenheck}},
familyi={R\bibinitperiod},
given={O.},
giveni={O\bibinitperiod},
}}%
{{hash=ZS}{%
family={{Zhao}},
familyi={Z\bibinitperiod},
given={S.},
giveni={S\bibinitperiod},
}}%
{{hash=ZD}{%
family={{Zelazo}},
familyi={Z\bibinitperiod},
given={D.},
giveni={D\bibinitperiod},
}}%
}
\keyw{gradient methods;multi-agent systems;PI control;velocity
control;proportional-integral controller;distance-based formation
tracking;multiagent formation control problem;additional velocity reference
command;interagent distance constraints;gradient formation
controller;formation error dynamics;steady-state formation error;Stability
analysis;Steady-state;Symmetric matrices;Aerodynamics;Jacobian
matrices;Numerical stability;Asymptotic stability}
\strng{namehash}{ROZSZD1}
\strng{fullhash}{ROZSZD1}
\field{labelnamesource}{author}
\field{labeltitlesource}{title}
\field{labelyear}{2015}
\field{labeldatesource}{year}
\field{sortinit}{R}
\field{sortinithash}{R}
\field{booktitle}{2015 European Control Conference (ECC)}
\verb{doi}
\verb 10.1109/ECC.2015.7330781
\endverb
\field{pages}{1693\bibrangedash 1698}
\field{title}{A proportional-integral controller for distance-based
formation tracking}
\field{year}{2015}
\warn{\item Invalid format of field 'month'}
\endentry
\enddatalist
\endinput

85
thesis.blg
View File

@ -1,85 +0,0 @@
This is BibTeX, Version 0.99d (TeX Live 2018)
Capacity: max_strings=100000, hash_size=100000, hash_prime=85009
The top-level auxiliary file: thesis.aux
The style file: biblatex.bst
A level-1 auxiliary file: OTHER/sampul_Unibraw.aux
A level-1 auxiliary file: OTHER/judul_dalam.aux
A level-1 auxiliary file: OTHER/pengesahan.aux
A level-1 auxiliary file: OTHER/orisinal.aux
A level-1 auxiliary file: OTHER/pengesahan_sidang.aux
A level-1 auxiliary file: OTHER/pengantar.aux
A level-1 auxiliary file: OTHER/persetujuan_publikasi.aux
A level-1 auxiliary file: OTHER/abstrak.aux
A level-1 auxiliary file: OTHER/abstract.aux
A level-1 auxiliary file: BAB1/bab1.aux
A level-1 auxiliary file: BAB2/bab2.aux
A level-1 auxiliary file: BAB3/bab3.aux
A level-1 auxiliary file: BAB4/bab4.aux
A level-1 auxiliary file: BAB5/bab5.aux
A level-1 auxiliary file: BAB6/bab6.aux
A level-1 auxiliary file: OTHER/kesimpulan.aux
A level-1 auxiliary file: OTHER/markLampiran.aux
A level-1 auxiliary file: OTHER/lampiran.aux
Reallocated glb_str_ptr (elt_size=4) to 20 items from 10.
Reallocated global_strs (elt_size=20001) to 20 items from 10.
Reallocated glb_str_end (elt_size=4) to 20 items from 10.
Reallocated singl_function (elt_size=4) to 100 items from 50.
Reallocated singl_function (elt_size=4) to 100 items from 50.
Reallocated singl_function (elt_size=4) to 100 items from 50.
Reallocated wiz_functions (elt_size=4) to 6000 items from 3000.
Reallocated singl_function (elt_size=4) to 100 items from 50.
Reallocated singl_function (elt_size=4) to 100 items from 50.
Reallocated singl_function (elt_size=4) to 100 items from 50.
Reallocated singl_function (elt_size=4) to 100 items from 50.
Reallocated singl_function (elt_size=4) to 100 items from 50.
Reallocated singl_function (elt_size=4) to 100 items from 50.
Reallocated singl_function (elt_size=4) to 100 items from 50.
Database file #1: thesis-blx.bib
Database file #2: OTHER/references.bib
Warning--entry type for "Irwanto2018" isn't style-file defined
--line 10 of file OTHER/references.bib
Biblatex version: 3.8
Reallocated wiz_functions (elt_size=4) to 9000 items from 6000.
Reallocated singl_function (elt_size=4) to 100 items from 50.
You've used 13 entries,
6268 wiz_defined-function locations,
1317 strings with 15640 characters,
and the built_in function-call counts, 69429 in all, are:
= -- 4412
> -- 1394
< -- 367
+ -- 1634
- -- 548
* -- 5614
:= -- 6933
add.period$ -- 0
call.type$ -- 13
change.case$ -- 148
chr.to.int$ -- 58
cite$ -- 24
duplicate$ -- 7545
empty$ -- 6627
format.name$ -- 836
if$ -- 14218
int.to.chr$ -- 0
int.to.str$ -- 26
missing$ -- 0
newline$ -- 495
num.names$ -- 518
pop$ -- 4138
preamble$ -- 1
purify$ -- 216
quote$ -- 0
skip$ -- 2079
stack$ -- 0
substring$ -- 7256
swap$ -- 2143
text.length$ -- 366
text.prefix$ -- 12
top$ -- 1
type$ -- 429
warning$ -- 0
while$ -- 895
width$ -- 0
write$ -- 483
(There was 1 warning)