siap bimbingan artikel
|
@ -6,7 +6,13 @@
|
|||
{
|
||||
"label": "Compile thesis",
|
||||
"type": "shell",
|
||||
"command": "latexmk -pdf thesis.tex article.tex && latexmk -pdf -c thesis.tex article.tex",
|
||||
"command": "latexmk -pdf -quite thesis.tex article.tex && latexmk -pdf -quite -c thesis.tex article.tex",
|
||||
"problemMatcher": []
|
||||
},
|
||||
{
|
||||
"label": "Compile articel",
|
||||
"type": "shell",
|
||||
"command": "latexmk -pdf article.tex && latexmk -pdf -c article.tex",
|
||||
"problemMatcher": []
|
||||
}
|
||||
]
|
||||
|
|
|
@ -0,0 +1,33 @@
|
|||
\section{Pendahuluan}
|
||||
\lettrine[nindent=0em,lines=3]{K} endali formasi adalah topik penelitian kendali multi-robot untuk memecahkan permasalahan koordinasi pergerakan \kutip{Parker2003}.
|
||||
Kendali formasi bertujuan untuk mengendalikan sekelompok robot dalam mencapai formasi tertentu
|
||||
dan dapat mempertahankan formasi tersebut ketika bermanuver menuju arah yang diinginkan.
|
||||
Pengembangan kendali formasi dilakukan dari berbagai strategi \kutip{Guanghua2013}, yaitu
|
||||
\textit{leader-follower} \kutip{6889491},
|
||||
berdasarkan tingkah laku dengan \textit{Fuzzy-Logic} \kutip{ELFERIK2016117},
|
||||
struktur virtual \kutip{YOSHIOKA20085149}.
|
||||
|
||||
Dari berbagai pengembangan tersebut dapat ambil garis besar menjadi 3 bagian \kutip{OH2015424},
|
||||
yaitu berdasarkan posisi, perpindahan, dan jarak.
|
||||
Ketiga bagian tersebut tertuju pada jawaban dari pertanyaan, "variable apa yang digunakan
|
||||
sebagai sensor" dan "variable apa yang aktif dikendalikan oleh sistem multi-robot untuk
|
||||
mencapai formasi yang diinginkan".
|
||||
Dikususkan pada kendali formasi berdasarkan jarak,
|
||||
Variable yang dikendalikan pada meteode ini adalah variabel jarak antar agent yang terhubung,
|
||||
Koordinat yang digunakan tidak mengacu pada koordinat global.
|
||||
Shingga pada penerapannya, formasi berdasarkan jarak menggunakan sensor yang lebih sedikit.
|
||||
Namun salah satu permasalahan pada metode tersebut adalah penerapan model yang lebih nyata.
|
||||
|
||||
Pengembangan formasi berdasarkan jarak telah dikembangkan menggunakan teori \textit{graph}
|
||||
pada single dan double integrator \kutip{Oh2014}
|
||||
dan menerapkannya pada simpel model dengan kendali \textit{Proportional-Integral} \kutip{Rozenheck2015}.
|
||||
Akan tetapi pada penerapan kendali nya,
|
||||
pengukuran jarak antar tetangga diperoleh dari selisih koordinat global robot dan tetangganya.
|
||||
Sedangkan dalam praktiknya robot hanya bisa mengukur jarak dan tidak mengetahui koordinat
|
||||
dari robot tetangga.
|
||||
|
||||
Pada penelitian ini akan dikembangkan sebuah algoritma untuk mengetahui koordinat tetangga
|
||||
berdasarkan informasi sensor jarak sehingga hasil pencarian koordinat tersebut dapat
|
||||
digunakan pada kendali formasi berdasarkan jarak.
|
||||
Percobaan akan menggunakan model robot holonomic dengan harapan menjadi langkah awal
|
||||
mengembangkan kendali formasi berdasarkan jarak menggunakan model robot yang lebih nyata.
|
Before Width: | Height: | Size: 40 KiB After Width: | Height: | Size: 111 KiB |
Before Width: | Height: | Size: 44 KiB After Width: | Height: | Size: 239 KiB |
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After Width: | Height: | Size: 91 KiB |
|
@ -1,92 +0,0 @@
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x1,y1,x2,y2,x3,y3,dx1,dy1,dx2,dy2,dx3,dy3,xi1,xi2,xi3,xi4,xi5,xi6,xii1,xii2,xii3
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1.5,1.7,2,2.5,2.5,2.8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
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||||
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|
||||
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|
||||
3.922806241926436,2.46872119174339,3.139250756303115,2.060047276337606,3.120464713200231,2.651272129847185,0.2058392389742741,-0.2675620789404313,0.2286336679149487,0.03404798627347165,0.138335086955884,0.06635389617729015,2.422806241926439,0.7687211917433918,1.139250756303116,-0.4399527236623909,0.6204647132002306,-0.1487278701528105,1.730359546177311,0.9330582445707009,-1.178793546751582
|
||||
3.943474677112617,2.437679705470629,3.161046879651825,2.062517426839045,3.135245162871534,2.657243931305006,0.2070025507247548,-0.3511733259857545,0.2073458955106781,0.01540744612870968,0.1577438731654892,0.05242273489851117,2.443474677112621,0.7376797054706308,1.161046879651825,-0.4374825731609508,0.6352451628715332,-0.1427560686949888,1.757049669362539,0.9519620426232335,-1.193584452743808
|
||||
3.964088980018234,2.398972247792485,3.180749974628293,2.063159457978717,3.152101250469233,2.661622418112469,0.2046746775335679,-0.4202922856660727,0.1869463247268527,-0.002343301946450316,0.1797565368701295,0.03448721163074736,2.464088980018238,0.6989722477924872,1.180749974628293,-0.4368405420212793,0.6521012504692316,-0.1383775818875277,1.780997253593225,0.97343082685903,-1.207915509284057
|
||||
3.98428877563285,2.354210438442071,3.198497885568023,2.062104262690988,3.171255596029766,2.664014821819411,0.1987527348263413,-0.4717843722886824,0.1683893260687256,-0.01844952289151985,0.2035215910217364,0.01277683333065334,2.484288775632854,0.6542104384420737,1.198497885568023,-0.4378957373090087,0.6712555960297663,-0.1359851781805851,1.802426541621401,0.9976854044859635,-1.221807270249968
|
||||
4.003736946969026,2.305293360732214,3.214516460510206,2.059535745748209,3.192819557751246,2.664074471869646,0.1897953931755194,-0.5030442576160639,0.1524711722912106,-0.0325941037455514,0.2276840911771504,-0.01199950739305554,2.50373694696903,0.605293360732216,1.214516460510205,-0.4404642542517864,0.6928195577512463,-0.1359255281303501,1.821692089387695,1.024852294484122,-1.235346720415111
|
||||
4.022187184922084,2.254328207989068,3.229097441882701,2.055648478258567,3.216747791448844,2.661556236919863,0.1790353582119577,-0.5125572637583852,0.1396996303370055,-0.04485592116682949,0.2505035636484174,-0.03851561137427211,2.522187184922088,0.5543282079890698,1.229097441882699,-0.4443515217414286,0.716747791448844,-0.1384437630801341,1.839237830307045,1.054912786127268,-1.248672045357258
|
||||
4.039539058759098,2.203516926120701,3.242567180529252,2.05061802251816,3.242814466038717,2.656375359981078,0.1681106856469499,-0.4999537511916018,0.1302535637050621,-0.05550440593594896,0.2701630881122797,-0.06491268149013558,2.539539058759102,0.5035169261207024,1.242567180529251,-0.4493819774818356,0.7428144660387178,-0.1436246400189183,1.855548214714899,1.087666562036605,-1.261947522688867
|
||||
4.055863860497521,2.155033316798471,3.255252544720628,2.044591235387763,3.270621510148392,2.648651691667202,0.1587805805521741,-0.466315101409026,0.123954296087361,-0.06482229984352994,0.2850821346934567,-0.08899220496013499,2.555863860497525,0.455033316798474,1.255252544720627,-0.4554087646122322,0.7706215101483929,-0.1513483083327932,1.871098547377143,1.122720166487966,-1.275333357556363
|
||||
4.071397419871865,2.110895723660532,3.267449978544909,2.037694071463495,3.29963673875994,2.638726152446815,0.1525059000166246,-0.4135438726808173,0.1204031949713466,-0.07291910984852541,0.2941984777052828,-0.1086054400711803,2.571397419871868,0.4108957236605344,1.267449978544908,-0.4623059285365003,0.7996367387599407,-0.1612738475531804,1.886312949384033,1.159503663286492,-1.288957079998415
|
||||
4.086499421676609,2.072875155066856,3.279407641823645,2.03005116446676,3.329252395951031,2.627139535362423,0.150257704032751,-0.3445283424043687,0.1190701136431566,-0.07970498057150149,0.2970712027603178,-0.1219671588576669,2.586499421676612,0.3728751550668586,1.279407641823644,-0.4699488355332359,0.8292523959510311,-0.1728604646375737,1.901537428214053,1.197312104145266,-1.302892506944902
|
||||
4.101594296385295,2.042429166095487,3.291322188097341,2.021805919044992,3.358847486290501,2.614579313760438,0.1523588559838559,-0.2626133169739666,0.1194756032341028,-0.08490955816383974,0.2938568942364958,-0.1279587648626034,2.601594296385298,0.3424291660954878,1.291322188097339,-0.4781940809550049,0.8588474862905007,-0.1854206862395593,1.917032080919443,1.235362328045209,-1.317149938318213
|
||||
4.11710631106508,2.020671767662394,3.30335064729729,2.013134044462466,3.387840801252116,2.601804977159216,0.1584991664568214,-0.1712930989409336,0.1213208252146422,-0.08817514515681295,0.2851645789703989,-0.1262650995084185,2.617106311065081,0.3206717676623949,1.303350647297287,-0.4868659555375323,0.8878408012521152,-0.1981950228407828,1.932982114082289,1.272854608795853,-1.331677969413676
|
||||
4.133401525605214,2.008368838378795,3.315632468468392,2.004247175947982,3.415726920263388,2.589567436791701,0.167848921833276,-0.07402595833858051,0.1245579373740443,-0.08915478567869566,0.2718718116864356,-0.1173601429031501,2.633401525605214,0.3083688383787965,1.31563246846839,-0.4957528240520148,0.9157269202633866,-0.2104325632082968,1.949523348726456,1.309030294079407,-1.346374820600433
|
||||
4.150743599368607,2.005947383400791,3.328315259103847,1.995388363976549,3.442094664719485,2.578536084566435,0.179216337585993,0.02578203259991556,0.1293933925555549,-0.08757558529719993,0.2549639229652754,-0.10237402947579,2.650743599368609,0.3059473834007921,1.328315259103845,-0.5046116360234474,0.9420946647194842,-0.2214639154335633,1.966775359592528,1.343220191057941,-1.361105933730344
|
||||
4.169265524653733,2.013503612797058,3.34157779075354,1.986823969478043,3.466632358913058,2.569242788862552,0.1912084370403243,0.124952604068948,0.1362287397081045,-0.08324219134099195,0.2354323394306954,-0.08288475284094156,2.669265524653735,0.3135036127970594,1.341577790753539,-0.5131760305219547,0.9666323589130569,-0.2307572111374465,1.984874510946584,1.374881810613992,-1.375724678258532
|
||||
4.188956905238912,2.030810473169094,3.355644461651835,1.978836791683299,3.489126088862305,2.562048145731739,0.20234751559301,0.2202875442798587,0.1455688817420957,-0.07600175618990772,0.2142498616750072,-0.06072913040223564,2.688956905238913,0.3308104731690958,1.355644461651833,-0.5211632083166975,0.9891260888623042,-0.2379518542682593,2.003999509257336,1.40362590367774,-1.39009368673493
|
||||
4.209663940165209,2.057317124933638,3.370787779278382,1.971723335617445,3.509457235967408,2.557129074630046,0.2112914003263527,0.3083625655001147,0.1578302112253925,-0.06574043030133023,0.1923422689488478,-0.03768062554410785,2.709663940165209,0.3573171249336403,1.370787779278381,-0.5282766643825514,1.009457235967408,-0.2428709253699521,2.024383333727757,1.429233233439459,-1.404104875344341
|
||||
4.231106045453381,2.092136315717746,3.387313596794037,1.965792480217263,3.527600618857807,2.554491033031606,0.2168975674109248,0.3859550208733707,0.1732180620885398,-0.05233811504505712,0.1706467500532932,-0.01533327384281924,2.731106045453382,0.3921363157177473,1.387313596794036,-0.5342075197827334,1.027600618857807,-0.2455089669683918,2.046307054485994,1.451661727338853,-1.417696460145755
|
||||
4.252906788404806,2.134046446402236,3.405529817944287,1.961362128220061,3.543624854187967,2.553998152981262,0.2183915568628345,0.4496457383434783,0.1915597709443029,-0.03573835445646562,0.1501104272630359,0.005072709654020296,2.752906788404807,0.4340464464022384,1.405529817944286,-0.5386378717799359,1.043624854187966,-0.2460018470187359,2.070073898697054,1.471043740144368,-1.43086481269621
|
||||
4.274640604429979,2.181498364333359,3.425700763039616,1.958746383975691,3.557691273828668,2.555417002732525,0.2155704875000399,0.4962736840850481,0.2121536989928651,-0.01609272504688084,0.1316378194648663,0.02282104285666631,2.774640604429979,0.4814983643333607,1.425700763039616,-0.5412536160243058,1.057691273828668,-0.2445829972674737,2.095965539196463,1.487671582448404,-1.443668775493195
|
||||
4.295893553206928,2.232650543251788,3.447993672282453,1.958227392545702,3.57004666538178,2.558467832457725,0.2089100276482159,0.5232873633527287,0.2337496813418919,0.006069818060728193,0.116003422131741,0.03772024692330385,2.795893553206928,0.5326505432517902,1.447993672282453,-0.5417726074542948,1.07004666538178,-0.2415321675422736,2.124187048892203,1.501970138680726,-1.456224322396915
|
|
|
@ -1,108 +1,184 @@
|
|||
|
||||
\section{Metode}
|
||||
|
||||
Penentuan koordinat tentangga dapat ditemukan dengang mengubah koordinat polar menjadi koordinat kartesian.
|
||||
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.
|
||||
\subsection{Kendali Robot Holonomic}
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[scale=.5]{BAB3/img/estimate_coordinate.png}
|
||||
\caption{Strategi Penentuan Koordinat}
|
||||
\label{fig:strategiPenentuanKoordinat}
|
||||
\end{figure}
|
||||
|
||||
Dapat diperhatikan pada gambar~\ref{fig:strategiPenentuanKoordinat} untuk gambaran strateginya.
|
||||
Robot $B \in \tetangga_A$, adalah tetangga dari robot $A$.
|
||||
Pertama-tama, sebelum robot $A$ bergerak, disimpan terlebih dahulu nilai $d_a$,
|
||||
atau dinotasikan dengan $d_a[k]$ sebagai jarak sebelum bergerak.
|
||||
Lalu robot $A$ berjalan secara random kesegala arah dengan jarak $l_a$.
|
||||
Disimpan kembali nilai jara $d_a$, atau dinotasikan dengan $d_a[k+1]$.
|
||||
Setalah itu dapat ditentukan sudut $\alpha[k+1]$
|
||||
Berikut adalah model dari robot holonomic dalam bentuk \textit{state-space} \kutip{CORREIA20127}.
|
||||
Dimana robot menggunakan tiga buah motor yang dihubungkan pada \textit{omniwheel} sehingga robot
|
||||
dapat bergerak kesegala arah.
|
||||
\begin{align}
|
||||
d_a[k]^2 & = d_a[k+1]^2 + l_a^2 + 2 d_a[k+1] l_a \cos{(\alpha[k+1])} \\
|
||||
\alpha[k+1] & = cos^{-1}\Bigg( \frac{l_a^2 + d_a[k+1]^2 -d_a[k]^2}{2d_a[k+1]l_a} \Bigg)
|
||||
\dot{x}(t) & = A_r x(t) + B_r u(t) + K_rsgn(x(t)) \label{eq:ss1} \\
|
||||
y(t) & = Cx(t) \label{eq:ss2}
|
||||
\end{align}
|
||||
Vector
|
||||
$u(t) = \begin{bmatrix}
|
||||
u_1(t) & u_1(t) & u(2)(t)
|
||||
\end{bmatrix}^T$
|
||||
adalah masukan model bersatuan $volt$ dengan batasan $-6 \leq u_i(t) \leq 6$ pada tegangan motor robot.
|
||||
Vector $y(t) = x(t) = \begin{bmatrix}
|
||||
v(t) & v_n(t) & w(t)
|
||||
\end{bmatrix}^T$
|
||||
adalah kecepatan robot yang akan diperoleh dari sensor percepatan,
|
||||
dimana $v(t)$ adalah kecepatan pada sumbu $x$,
|
||||
$v_n(t)$ adalah kecepatan pada sumbu $y$, dan
|
||||
$w(t)$ adalah kecepatan rotasi dari frame robot.
|
||||
Matrix $A_r \in \mathbb{R}^{3\times 3}$ dan $B_r \in \mathbb{R}^{3 \times 3}$ adalah parameter fisik robot berdasarkan
|
||||
yang diperoleh dari identifikasi secara persamaan fisika.
|
||||
Matrix $K_r \in \mathbb{R}^{3 \times 3}$ adalah parameter \textit{friction} dari robot yang diestimasi dari
|
||||
hasil percobaan.
|
||||
|
||||
Kendali dari robot akan menggunakan dua mode \textit{state-feedback}.
|
||||
\textbf{Mode satu}, bertujuan untuk mencapai kecepatan robot yang diinginkan.
|
||||
Untuk mencapai tujuan tersebut akan menggunakan persamaan kendali sebagai berikut
|
||||
\begin{equation}
|
||||
\begin{split}
|
||||
u_{c1}(t) &= -K^c_1 x(t) + N^c_1 r^c_1 \\
|
||||
r^c_1 &= \begin{bmatrix}
|
||||
v^*(t) & v_n^*(t) & w^*(t)
|
||||
\end{bmatrix}^T
|
||||
\end{split}
|
||||
\label{eq:kendali_kecepatan}
|
||||
\end{equation}
|
||||
Dimana $r^c_1$ , $K^c_1 \in \mathbb{R} ^ {3 \times 3}$ dan $N^c_1 \in \mathbb{R} ^ {3 \times 3}$
|
||||
adalah setpoint kendali mode satu, konstanta yang diperoleh dari optimasi
|
||||
persamaan \textit{Riccati} terhadap matrix $A_r$ dan $B_r$,
|
||||
dan kostanta yang diperoleh dari \textit{inverse state-space} pada keadaan \textit{steady state}.
|
||||
\begin{equation*}
|
||||
N^c_1 = -[ C(A_r - B_rK^c_1)^{-1}B_r ] ^{-1}
|
||||
\end{equation*}
|
||||
Dengan menggabungkan persamaan~\eqref{eq:ss1} dengan persamaan~\eqref{eq:kendali_kecepatan}
|
||||
akan mendapatkan persamaan \textit{state-space} robot yang baru
|
||||
\begin{align}
|
||||
\begin{split}
|
||||
\dot{x}(t) & = (A_r - B_r K^c_1) x(t)+B_r N^c_1 r^c_1 + K_r sgn(x(t)) \\
|
||||
& = A_c x(t) + B_c r^c_1 + K_r sgn(x(t))
|
||||
\end{split}
|
||||
\label{eq:ss_kendali_kecepatan}
|
||||
\end{align}
|
||||
\textbf{Mode dua}, bertujuan untuk mencapai titik koordinat tertentu
|
||||
berdasarkan koordinat frame robot. Untuk mencapai tujuan tersebut
|
||||
akan dimodifikasi persamaan~\eqref{eq:ss1} dengan menambah state koordinat frame robot
|
||||
menjadi $y_{c2}(t) = x_{c2}(t) = \begin{bmatrix}
|
||||
x_r(t) & y_r(t) & \theta_r(t) & v(t) & v_n(t) & w(t)
|
||||
\end{bmatrix}^T$, $
|
||||
A_{c2} = \begin{bmatrix}
|
||||
0 & I \\
|
||||
0 & A_r \\
|
||||
\end{bmatrix} \in \mathbb{R}^{6 \times 6}
|
||||
$,
|
||||
$B_{c2} = \begin{bmatrix}
|
||||
0 \\ B_r
|
||||
\end{bmatrix} \in \mathbb{R} ^ {6 \times 3} $,
|
||||
$K_{c2}(x) = \begin{bmatrix}
|
||||
0 & 0 \\
|
||||
0 & K_rsgn(x) \\
|
||||
\end{bmatrix} \in \mathbb{R} ^ {6 \times 3} $.
|
||||
Berikut adalah state space model untuk kendali mode satu.
|
||||
\begin{equation*}
|
||||
\begin{split}
|
||||
\dot{x}_{c2}(t) & = A_{c2} x_{c2}(t) + B_{c2} u_{c2}(t) + K_{c2}(x_{c2}(t)) \\
|
||||
y_{c2}(t) & = C_{c2} x_{c2}(t) \\
|
||||
\end{split}
|
||||
\end{equation*}
|
||||
Dimana $u_{c2}(t)$ adalah persamaan kendali mode dua.
|
||||
\begin{equation}
|
||||
\begin{split}
|
||||
u_{c2} (t) &= -K^c_2 x_{c2}(t) + N^c_2 r^c_2 \\
|
||||
r^c_2 &= \begin{bmatrix}
|
||||
x_r^*(t) & y_r^*(t) & \theta_r^*(t) & v^*(t) & v_n^*(t) & w^*(t)
|
||||
\end{bmatrix}^T
|
||||
\end{split}
|
||||
\end{equation}
|
||||
Dimana $r^c_2$, $K^c_2 \in \mathbb{R} ^ {3 \times 6}$ dan $N^c_2 \in \mathbb{R} ^ {3 \times 6}$
|
||||
adalah setpoint kendali mode dua dan kostanta yang diperoleh dari cara yang sama pada mode satu
|
||||
menggunakan matrix model yang dimodifikasi.
|
||||
|
||||
\subsection{Kendali Formasi Berdasarkan Jarak}
|
||||
Dinotasikan $n \triangleq | \simpul |$ sebagai jumlah dari node
|
||||
dan $m \triangleq | \sisi |$ sebagai jumlah dari sisinya.
|
||||
Dinotasikan $p = \begin{bmatrix} x_1^T & \dots & x_n^T \end{bmatrix}^T \in \mathbb{R}^{3n}$,
|
||||
dimana $x_i \in \mathbb{R}^3$ dan $x_i \neq x_j$ untuk semua $i \neq j$.
|
||||
Dinotasikan vektor posisi relatif $ e_k \triangleq x_j - x_i$ dan semua vector sisi
|
||||
$e=\begin{bmatrix}e_1^t & \dots & e_m^T\end{bmatrix} \in \mathbb{R}^{3m}$.
|
||||
didefinisikan fungsi \textit{Jacobian} sisi \kutip{Rozenheck2015}),
|
||||
\begin{align}
|
||||
R(p) & \triangleq diag(e_i^T)(E^T \otimes I_2) \in \mathbb{R}^{m\times 3n} \nonumber \\
|
||||
\end{align}
|
||||
Dimana $E \in \mathbb{R}^{n\times m}$, adalah matrik \textit{incidence} $\{0,\pm 1\}$ dimana
|
||||
baris matrik mengindikasikan simpulnya dan kolomnya sebagai sisinya dan
|
||||
$diag(A_i) \triangleq blkdiag\{A_1, \dots, A_n\} \in \mathbb{R}^{np \times nq}$
|
||||
Orde kendali formasi yang digunakan adalah orde dua
|
||||
Mengadopsi persamaan potensial, didefinisi persamaan \kutip{Oh2014}.
|
||||
\begin{align}
|
||||
\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}
|
||||
Lalu kendali formasi menggunakan persamaan~\eqref{eq:ss_kendali_kecepatan} sebagai modelnya
|
||||
diberikan \textit{negative gradient} dari fungsi potensial dan
|
||||
konstanta \textit{proportional} \kutip{Rozenheck2015}
|
||||
\begin{equation}
|
||||
\begin{split}
|
||||
\dot{p} & = A_f p(t) + B_f\frac{\partial \Phi(e)}{\partial v} \\
|
||||
& = A_f p(t) + B_fv(t) \\
|
||||
\dot{v} & = -C \Big( \frac{\partial \Phi(e)}{\partial v} + \frac{\partial \Phi(e)}{\partial p} \Big) \\
|
||||
& = -k_{p1}v(t) + R(p(t))^Tk_{p2}(R(p(t))p(t) - d )) \\
|
||||
\end{split}
|
||||
\label{eq:dynmState}
|
||||
\end{equation}
|
||||
Dimana $A_f \in \mathbb{R}^{3n \times 3n}$ dan $B_f \in \mathbb{R}^{3n \times 3n}$ adalah
|
||||
matrix diagonal dari $A_c$ dan $B_c$.
|
||||
|
||||
\subsection{Algoritma Cosinus}
|
||||
Robot $B_i \in \tetangga_A$, adalah tetangga dari robot $A$ .
|
||||
$d_i[k]$ adalah jarak yang diperoleh dari sensor.
|
||||
Dalam strategi (Gambar~\ref{fig:strategiPenentuanKoordinat}) ini diperlukan perpindahan robot $A$ ke $ A' = (0, l_a)$.
|
||||
Perpindahan tersebut akan menghasilkan jarak $d_i[k+1]$.
|
||||
Dari perbedaan tersebut akan didapatkan sudut $\alpha_i^\circ$.
|
||||
\begin{align}
|
||||
\alpha_i^\circ & = 180^\circ \pm cos^{-1}\Bigg( \frac{l_a^2 + d_i[k+1]^2 -d_i[k]^2}{2 d_i[k+1] l_a} \Bigg).\nonumber \\
|
||||
& = 180^\circ \pm \zeta_i^a
|
||||
\label{eq:algo_getAngle}
|
||||
\end{align}
|
||||
Sebelum $\alpha[k+1]$ digunakan, jarak $d_a[k+1]$ dan $d_a[k]$ berpengaruh dalam penentuan koordinat.
|
||||
Sehingga diperlukan sedikit algoritma
|
||||
Dari persamaan~\eqref{eq:algo_getAngle} akan didapat koordinat tetangga.
|
||||
\begin{align}
|
||||
\alpha_i=
|
||||
\begin{cases}
|
||||
\alpha[k+1] & ,d_a[k+1] > d_a[k] \\
|
||||
180-\alpha[k+1] & ,d_a[k+1] < d_a[k]
|
||||
\end{cases}.\label{eq:init_relatif_koordinat}
|
||||
\end{align}
|
||||
|
||||
Strategi pada gambar~\ref{fig:strategiPenentuanKoordinat} hanya berlaku apabila target ukur berhenti. Apabila dinotasikan koordinat $(x_B^A, y_B^A)$ 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
|
||||
\begin{align}
|
||||
\alpha[k+1] & = \alpha[k]+tan^{-1} \Big[ \frac{\dot{x}_B^A}{\dot{y}_B^A} \Big]
|
||||
\end{align}
|
||||
dimana kondisi inisial adalah $\alpha[k] = \alpha_i$ diperoleh dari hasil strategi pada persamaan~\eqref{eq:init_relatif_koordinat}.
|
||||
Dengan memanfaatkan kedua strategi tersebut dapat digunakan untuk
|
||||
mengkalkulasi koordinat robot $B$ relatif terhadap robot $A$
|
||||
\begin{align}
|
||||
x_B^A = \begin{bmatrix}
|
||||
x_B = d_a[k]\cos \alpha[k] \\
|
||||
y_B = d_a[k]\sin \alpha[k]
|
||||
x_{B_i}^A = \begin{bmatrix}
|
||||
x_{B_i} = d_i[k+1]\cos \alpha_i^\circ \\
|
||||
y_{B_i} = d_i[k+1]\sin \alpha_i^\circ
|
||||
\end{bmatrix}
|
||||
\label{eq:algo_koordinat_tetangga}
|
||||
\end{align}
|
||||
Dalam strategi ini akan terjadi ketidak akuratan dalam pengukuran apabila target ukur
|
||||
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.
|
||||
Untuk memvalidasi apakah koordinat telah sesuai dapat menggunakan nilai jarak pada sensor
|
||||
dibandingkan dengan jarak dari hasil koordinat persamaan~\eqref{eq:algo_koordinat_tetangga}.
|
||||
Akan tetapi hasil validasi tersebut akan mengalami bias dikarenakan
|
||||
sudut $\zeta_i^a$ adalah sudut segitiga $\angle{AA'B_1}$ atau $\angle{AA'B_2}$.
|
||||
Oleh karena itu pada persamaan~\eqref{eq:algo_getAngle} terdapat operasi $\pm$
|
||||
dimana operasi tersebut akan dilakukan berdasarkan letak kuadran $B_i$.
|
||||
\begin{align}
|
||||
\alpha_i^\circ & =
|
||||
\begin{cases}
|
||||
180^\circ - \zeta_i^a, & \text{Kuadran \RN{1},\RN{2}} \\
|
||||
180^\circ + \zeta_i^a, & \text{Kuadran \RN{3},\RN{4}} \\
|
||||
\end{cases}.
|
||||
\label{eq:algo_getAngle2}
|
||||
\end{align}
|
||||
Diperlukan satu langkah lagi untuk menentukan kejadian pada
|
||||
persamaan~\eqref{eq:algo_getAngle2}(Gambar~\ref{fig:strategiPenentuanKoordinat2}).
|
||||
Langkah 2 adalah langkah pengujian dari hasil koordinat yang telah dikalkulasi
|
||||
dan membandingkannya dengan nilai yang didapat dari sensor.
|
||||
Apabila terdapat perbedaan maka kejadian pada persamaan~\eqref{eq:algo_getAngle2}
|
||||
diubah ke kejadian selanjutnya.
|
||||
|
||||
\begin{algorithm}
|
||||
\DontPrintSemicolon
|
||||
\KwInput{
|
||||
Integer $l_a>0$,
|
||||
$\tetangga_i=getConnectionRobot()$, }
|
||||
\KwOutput{$x_i^j$}
|
||||
|
||||
\If{isInisilised() == false}{
|
||||
\tcc{inisialisasi}
|
||||
\tcc{getRandomDirection() akan mengembalikan sudur random antara 0 - 360}
|
||||
$dir = getRandomDirection()$\;
|
||||
$d_{before} = getDistanceFromSensor(\tetangga_i)$\;
|
||||
$r = \begin{bmatrix}
|
||||
l_a \cos(dir) \\
|
||||
l_a \sin(dir)
|
||||
\end{bmatrix}$\;
|
||||
|
||||
\tcc{Menjalankan robot hingga mencapai setpoint}
|
||||
\While{isSetpointReached()}{
|
||||
$runRobotToSetpoint(r)$\;
|
||||
}
|
||||
|
||||
\tcc{Mengambil jarak setelah robot mencapai setpoint}
|
||||
$d_{after} = getDistanceFromSensor(\tetangga_i)$\;
|
||||
|
||||
\tcc{Mengkalkulasi sudut}
|
||||
$ang = cos^{-1}\Bigg[ \frac{l_a^2 + d_{after}^2 -d_{before}^2}{2d_{before}l_a} \Bigg]$\;
|
||||
}
|
||||
\Else{
|
||||
\tcc{mendapatkan infromasi state dari tetangga}
|
||||
$\begin{bmatrix}
|
||||
\dot{x}_B^A \\ \dot{y}_B^A
|
||||
\end{bmatrix} = getState()$ \;
|
||||
$ang = \alpha[k]+tan^{-1} \Big[ \frac{\dot{x}_B^A}{\dot{y}_B^A} \Big]$ \;
|
||||
}
|
||||
|
||||
\If{$d_{before}<d_{after}$}
|
||||
{
|
||||
$ang = 180-ang$\;
|
||||
}
|
||||
\tcc{Menjadikan koordinat kartesian}
|
||||
\Return $x_i^j = \begin{bmatrix}
|
||||
d_{after} \cos(ang) \\
|
||||
d_{after} \sin(ang)
|
||||
\end{bmatrix}$\;
|
||||
|
||||
\caption{\textit{Algoritma Cosinus}}
|
||||
\label{algo:algoritma_cosinus}
|
||||
\end{algorithm}
|
||||
\begin{figure}[ht]
|
||||
\begin{subfigure}[t]{.5\textwidth}
|
||||
\centering
|
||||
\includegraphics[scale=.2]{BAB3/img/estimate_coordinate.png}
|
||||
\caption{}
|
||||
\label{fig:strategiPenentuanKoordinat}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.5\textwidth}
|
||||
\centering
|
||||
\includegraphics[scale=.2]{BAB3/img/estimate_coordinate2.png}
|
||||
\caption{}
|
||||
\label{fig:strategiPenentuanKoordinat2}
|
||||
\end{subfigure}
|
||||
\caption{Strategi penentuan koordinat (a) langkah 1 dan (b) Langkah 2}
|
||||
\end{figure}
|
|
@ -0,0 +1 @@
|
|||
\section{Diskusi}
|
|
@ -0,0 +1,40 @@
|
|||
\section{Hasil}
|
||||
Berikut pada gambar~\ref{fig:hasil} adalah hasil dari algoritma cosinus.
|
||||
Parameter $l_a = 1$ pada persamaan~\eqref{eq:algo_getAngle} dan $(x_a*,y_a*) = (1,1)$.
|
||||
Pada gambar~(\ref{fig:sensor_jarak},\ref{fig:motion_robot})
|
||||
dan gambar~(\ref{fig:sensor_jarak_algo},\ref{fig:motion_robot_algo}) menunjukkan bahwa
|
||||
algoritma tidak mempengaruhi kendali formasi.
|
||||
|
||||
\begin{figure}[ht]
|
||||
\begin{subfigure}[t]{.5\textwidth}
|
||||
\centering
|
||||
\includegraphics[scale=.2]{BAB5/img/distance.png}
|
||||
% \caption[.]{Sensor jarak robot menggunakan algoritma}
|
||||
\caption{}
|
||||
\label{fig:sensor_jarak_algo}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.5\textwidth}
|
||||
\centering
|
||||
\includegraphics[scale=.2]{BAB5/img/motion.png}
|
||||
% \caption[.]{Pergerakan robot}
|
||||
\caption{}
|
||||
\label{fig:motion_robot_algo}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.5\textwidth}
|
||||
\centering
|
||||
\includegraphics[scale=.2]{BAB5/img/distance ori.png}
|
||||
% \caption[.]{Sensor jarak robot}
|
||||
\caption{}
|
||||
\label{fig:sensor_jarak}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.5\textwidth}
|
||||
\centering
|
||||
\includegraphics[scale=.2]{BAB5/img/motion ori.png}
|
||||
% \caption[.]{Pergerakan robot}
|
||||
\caption{}
|
||||
\label{fig:motion_robot}
|
||||
\end{subfigure}
|
||||
\caption{Plot menggunakan algoritma (a. Sensor Jarak dan b. Pergerakan robot)
|
||||
dan tidak menggunakan algoritma (c. Sensor Jarak dan d. Pergerakan Robot)}
|
||||
\label{fig:hasil}
|
||||
\end{figure}
|
After Width: | Height: | Size: 34 KiB |
After Width: | Height: | Size: 48 KiB |
After Width: | Height: | Size: 56 KiB |
After Width: | Height: | Size: 52 KiB |
|
@ -7,5 +7,5 @@
|
|||
% required.
|
||||
|
||||
@Control{biblatex-control,
|
||||
options = {3.7:0:0:1:0:1:1:0:0:1:0:2:3:1:3:1:0:0:3:1:79:+:+:nyt},
|
||||
options = {3.7:0:0:1:0:1:1:0:0:0:0:1:3:1:3:1:0:0:3:1:79:+:+:nty},
|
||||
}
|
||||
|
|
477
article.bbl
|
@ -16,75 +16,444 @@
|
|||
{}
|
||||
\endgroup
|
||||
|
||||
\datalist[entry]{nyt/global//global/global}
|
||||
\entry{Cao2007}{inproceedings}{}
|
||||
\name{author}{5}{}{%
|
||||
{{hash=CM}{%
|
||||
family={{Cao}},
|
||||
\datalist[entry]{nty/global//global/global}
|
||||
\entry{CORREIA20127}{article}{}
|
||||
\name{author}{3}{}{%
|
||||
{{hash=CMD}{%
|
||||
family={Correia},
|
||||
familyi={C\bibinitperiod},
|
||||
given={M.},
|
||||
giveni={M\bibinitperiod},
|
||||
given={Mariane\bibnamedelima Dourado},
|
||||
giveni={M\bibinitperiod\bibinitdelim D\bibinitperiod},
|
||||
}}%
|
||||
{{hash=MAS}{%
|
||||
family={{Morse}},
|
||||
familyi={M\bibinitperiod},
|
||||
given={A.\bibnamedelima S.},
|
||||
giveni={A\bibinitperiod\bibinitdelim S\bibinitperiod},
|
||||
{{hash=GA}{%
|
||||
family={Gustavo},
|
||||
familyi={G\bibinitperiod},
|
||||
given={André},
|
||||
giveni={A\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.},
|
||||
{{hash=CS}{%
|
||||
family={Conceição},
|
||||
familyi={C\bibinitperiod},
|
||||
given={Scolari},
|
||||
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}
|
||||
\keyw{Models, Friction, Parameter estimation, Autonomous mobile robots}
|
||||
\strng{namehash}{CMDGACS1}
|
||||
\strng{fullhash}{CMDGACS1}
|
||||
\field{labelnamesource}{author}
|
||||
\field{labeltitlesource}{title}
|
||||
\field{labelyear}{2007}
|
||||
\field{labeldatesource}{}
|
||||
\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.%
|
||||
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.%
|
||||
}
|
||||
\field{booktitle}{2007 46th IEEE Conference on Decision and Control}
|
||||
\verb{doi}
|
||||
\verb 10.1109/CDC.2007.4434757
|
||||
\verb https://doi.org/10.3182/20120905-3-HR-2030.00002
|
||||
\endverb
|
||||
\field{issn}{0191-2216}
|
||||
\field{pages}{3603\bibrangedash 3608}
|
||||
\field{title}{Controlling a triangular formation of mobile autonomous
|
||||
agents}
|
||||
\field{year}{2007}
|
||||
\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{ELFERIK2016117}{article}{}
|
||||
\name{author}{3}{}{%
|
||||
{{hash=FSE}{%
|
||||
family={Ferik},
|
||||
familyi={F\bibinitperiod},
|
||||
given={Sami\bibnamedelima El},
|
||||
giveni={S\bibinitperiod\bibinitdelim E\bibinitperiod},
|
||||
}}%
|
||||
{{hash=NMT}{%
|
||||
family={Nasir},
|
||||
familyi={N\bibinitperiod},
|
||||
given={Mohammad\bibnamedelima Tariq},
|
||||
giveni={M\bibinitperiod\bibinitdelim T\bibinitperiod},
|
||||
}}%
|
||||
{{hash=BU}{%
|
||||
family={Baroudi},
|
||||
familyi={B\bibinitperiod},
|
||||
given={Uthman},
|
||||
giveni={U\bibinitperiod},
|
||||
}}%
|
||||
}
|
||||
\keyw{Cluster space, Behavioral control, Fuzzy adaptive, Multi-robots}
|
||||
\strng{namehash}{FSENMTBU1}
|
||||
\strng{fullhash}{FSENMTBU1}
|
||||
\field{labelnamesource}{author}
|
||||
\field{labeltitlesource}{title}
|
||||
\field{sortinit}{F}
|
||||
\field{sortinithash}{F}
|
||||
\field{abstract}{%
|
||||
Cooperation between autonomous robot vehicles holds several promising
|
||||
advantages like robustness, adaptability, configurability, and scalability.
|
||||
Coordination between the different robots and the individual relative motion
|
||||
represent both the main challenges especially when dealing with formation
|
||||
control and maintenance. Cluster space control provides a simple concept for
|
||||
controlling multi-agent formation. In the classical approach, formation
|
||||
control is the unique task for the multi-agent system. In this paper, the
|
||||
development and application of a novel Behavioral Adaptive Fuzzy-based
|
||||
Cluster Space Control (BAFC) to non-holonomic robots is presented. By
|
||||
applying a fuzzy priority control approach, BAFC deals with two conflicting
|
||||
tasks: formation maintenance and target following. Using priority rules, the
|
||||
fuzzy approach is used to adapt the controller and therefore the behavior of
|
||||
the system, taking into accounts the errors in the formation states and the
|
||||
target following states. The control approach is easy to implement and has
|
||||
been implemented in this paper using SIMULINK real-time platform. The
|
||||
communication between the different agents and the controller is established
|
||||
through Wi-Fi link. Both simulation and experimental results demonstrate the
|
||||
behavioral response where the robot performs the higher priority tasks first.
|
||||
This new approach shows a great performance with a lower control signal when
|
||||
benchmarked with previously known results in the literature.%
|
||||
}
|
||||
\verb{doi}
|
||||
\verb https://doi.org/10.1016/j.asoc.2016.03.018
|
||||
\endverb
|
||||
\field{issn}{1568-4946}
|
||||
\field{pages}{117 \bibrangedash 127}
|
||||
\field{title}{A Behavioral Adaptive Fuzzy controller of multi robots in a
|
||||
cluster space}
|
||||
\verb{url}
|
||||
\verb http://www.sciencedirect.com/science/article/pii/S1568494616301272
|
||||
\endverb
|
||||
\field{volume}{44}
|
||||
\field{journaltitle}{Applied Soft Computing}
|
||||
\field{year}{2016}
|
||||
\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{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{Oh2014}{article}{}
|
||||
\name{author}{2}{}{%
|
||||
{{hash=OKK}{%
|
||||
family={Oh},
|
||||
familyi={O\bibinitperiod},
|
||||
given={Kwang-Kyo},
|
||||
giveni={K\bibinithyphendelim K\bibinitperiod},
|
||||
}}%
|
||||
{{hash=AHS}{%
|
||||
family={Ahn},
|
||||
familyi={A\bibinitperiod},
|
||||
given={Hyo-Sung},
|
||||
giveni={H\bibinithyphendelim S\bibinitperiod},
|
||||
}}%
|
||||
}
|
||||
\keyw{formation control, distance-based control, graph rigidity,
|
||||
Hamiltonian systems, gradient systems}
|
||||
\strng{namehash}{OKKAHS1}
|
||||
\strng{fullhash}{OKKAHS1}
|
||||
\field{labelnamesource}{author}
|
||||
\field{labeltitlesource}{title}
|
||||
\field{sortinit}{O}
|
||||
\field{sortinithash}{O}
|
||||
\field{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.%
|
||||
}
|
||||
\verb{doi}
|
||||
\verb 10.1002/rnc.2967
|
||||
\endverb
|
||||
\verb{eprint}
|
||||
\verb https://onlinelibrary.wiley.com/doi/pdf/10.1002/rnc.2967
|
||||
\endverb
|
||||
\field{number}{12}
|
||||
\field{pages}{1809\bibrangedash 1820}
|
||||
\field{title}{Distance-based undirected formations of single-integrator and
|
||||
double-integrator modeled agents in n-dimensional space}
|
||||
\verb{url}
|
||||
\verb https://onlinelibrary.wiley.com/doi/abs/10.1002/rnc.2967
|
||||
\endverb
|
||||
\field{volume}{24}
|
||||
\field{journaltitle}{International Journal of Robust and Nonlinear Control}
|
||||
\field{year}{2014}
|
||||
\endentry
|
||||
|
||||
\entry{OH2015424}{article}{}
|
||||
\name{author}{3}{}{%
|
||||
{{hash=OKK}{%
|
||||
family={Oh},
|
||||
familyi={O\bibinitperiod},
|
||||
given={Kwang-Kyo},
|
||||
giveni={K\bibinithyphendelim K\bibinitperiod},
|
||||
}}%
|
||||
{{hash=PMC}{%
|
||||
family={Park},
|
||||
familyi={P\bibinitperiod},
|
||||
given={Myoung-Chul},
|
||||
giveni={M\bibinithyphendelim C\bibinitperiod},
|
||||
}}%
|
||||
{{hash=AHS}{%
|
||||
family={Ahn},
|
||||
familyi={A\bibinitperiod},
|
||||
given={Hyo-Sung},
|
||||
giveni={H\bibinithyphendelim 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{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{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{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{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
|
||||
|
||||
\entry{6889491}{inproceedings}{}
|
||||
\name{author}{3}{}{%
|
||||
{{hash=WX}{%
|
||||
family={{Wang}},
|
||||
familyi={W\bibinitperiod},
|
||||
given={X.},
|
||||
giveni={X\bibinitperiod},
|
||||
}}%
|
||||
{{hash=YZ}{%
|
||||
family={{Yan}},
|
||||
familyi={Y\bibinitperiod},
|
||||
given={Z.},
|
||||
giveni={Z\bibinitperiod},
|
||||
}}%
|
||||
{{hash=WJ}{%
|
||||
family={{Wang}},
|
||||
familyi={W\bibinitperiod},
|
||||
given={J.},
|
||||
giveni={J\bibinitperiod},
|
||||
}}%
|
||||
}
|
||||
\keyw{dynamic programming;mobile robots;multi-robot
|
||||
systems;neurocontrollers;optimal control;predictive control;quadratic
|
||||
programming;recurrent neural nets;torque control;trajectory control;model
|
||||
predictive control approach;multirobot formation control problem;simplified
|
||||
dual neural network;leader-follower scheme;desired trajectory
|
||||
tracking;dynamic quadratic optimization problem;one-layer recurrent neural
|
||||
network;optimal control input;Vectors;Lead;Wheels;Neural networks;Robot
|
||||
kinematics;Mathematical model}
|
||||
\strng{namehash}{WXYZWJ1}
|
||||
\strng{fullhash}{WXYZWJ1}
|
||||
\field{labelnamesource}{author}
|
||||
\field{labeltitlesource}{title}
|
||||
\field{sortinit}{W}
|
||||
\field{sortinithash}{W}
|
||||
\field{booktitle}{2014 International Joint Conference on Neural Networks
|
||||
(IJCNN)}
|
||||
\verb{doi}
|
||||
\verb 10.1109/IJCNN.2014.6889491
|
||||
\endverb
|
||||
\field{issn}{2161-4393}
|
||||
\field{pages}{3161\bibrangedash 3166}
|
||||
\field{title}{Model predictive control of multi-robot formation based on
|
||||
the simplified dual neural network}
|
||||
\field{year}{2014}
|
||||
\warn{\item Invalid format of field 'month'}
|
||||
\endentry
|
||||
|
||||
\entry{YOSHIOKA20085149}{article}{}
|
||||
\name{author}{2}{}{%
|
||||
{{hash=YC}{%
|
||||
family={Yoshioka},
|
||||
familyi={Y\bibinitperiod},
|
||||
given={Chika},
|
||||
giveni={C\bibinitperiod},
|
||||
}}%
|
||||
{{hash=NT}{%
|
||||
family={Namerikawa},
|
||||
familyi={N\bibinitperiod},
|
||||
given={Toru},
|
||||
giveni={T\bibinitperiod},
|
||||
}}%
|
||||
}
|
||||
\strng{namehash}{YCNT1}
|
||||
\strng{fullhash}{YCNT1}
|
||||
\field{labelnamesource}{author}
|
||||
\field{labeltitlesource}{title}
|
||||
\field{sortinit}{Y}
|
||||
\field{sortinithash}{Y}
|
||||
\field{abstract}{%
|
||||
This paper deals with formation control strategies based on Virtual
|
||||
Structure (VS) for multi-vehicle systems. We propose several control laws for
|
||||
networked multi-nonholonomic vehicle systems in order to achieve VS
|
||||
consensus, VS Flocking and VS Flocking with collision-avoidance. First,
|
||||
Virtual Vehicle for the feedback linearization is considered, and we propose
|
||||
VS consensus and Flocking control laws based on a virtual structure and
|
||||
consensus algorithms. Then, VS Flocking control law considering collision
|
||||
avoidance is proposed and its asymptotical stability is proven. Finally,
|
||||
simulation and experimental results show effectiveness of our proposed
|
||||
approaches.%
|
||||
}
|
||||
\verb{doi}
|
||||
\verb https://doi.org/10.3182/20080706-5-KR-1001.00865
|
||||
\endverb
|
||||
\field{issn}{1474-6670}
|
||||
\field{note}{17th IFAC World Congress}
|
||||
\field{number}{2}
|
||||
\field{pages}{5149 \bibrangedash 5154}
|
||||
\field{title}{Formation Control of Nonholonomic Multi-Vehicle Systems based
|
||||
on Virtual Structure}
|
||||
\verb{url}
|
||||
\verb http://www.sciencedirect.com/science/article/pii/S1474667016397609
|
||||
\endverb
|
||||
\field{volume}{41}
|
||||
\field{journaltitle}{IFAC Proceedings Volumes}
|
||||
\field{year}{2008}
|
||||
\endentry
|
||||
\enddatalist
|
||||
\endinput
|
||||
|
|
BIN
article.pdf
|
@ -56,9 +56,8 @@
|
|||
<file>blx-bibtex.def</file>
|
||||
<file>biblatex.def</file>
|
||||
<file>standard.bbx</file>
|
||||
<file>authoryear.bbx</file>
|
||||
<file>authoryear-icomp.bbx</file>
|
||||
<file>authoryear-icomp.cbx</file>
|
||||
<file>numeric.bbx</file>
|
||||
<file>numeric.cbx</file>
|
||||
<file>biblatex.cfg</file>
|
||||
<file>english.lbx</file>
|
||||
</requires>
|
||||
|
|
95
article.tex
|
@ -35,11 +35,12 @@
|
|||
|
||||
\pretitle{\begin{center}\Huge\bfseries} % Article title formatting
|
||||
\posttitle{\end{center}} % Article title closing formatting
|
||||
\title{Article Title} % Article title
|
||||
\title{\Large\Judul} % Article title
|
||||
\author{%
|
||||
\textsc{John Smith}\thanks{A thank you or further information} \\[1ex] % Your name
|
||||
\normalsize University of California \\ % Your institution
|
||||
\normalsize \href{mailto:john@smith.com}{john@smith.com} % Your email address
|
||||
\textsc{\Penulis} \\[1ex] % Your name
|
||||
%\thanks{A thank you or further information} \\[1ex] % Your name
|
||||
\normalsize \NamaUni \\ % Your institution
|
||||
% \normalsize \href{mailto:john@smith.com}{john@smith.com} % Your email address
|
||||
%\and % Uncomment if 2 authors are required, duplicate these 4 lines if more
|
||||
%\textsc{Jane Smith}\thanks{Corresponding author} \\[1ex] % Second author's name
|
||||
%\normalsize University of Utah \\ % Second author's institution
|
||||
|
@ -48,7 +49,16 @@
|
|||
\date{\today} % Leave empty to omit a date
|
||||
\renewcommand{\maketitlehookd}{%
|
||||
\begin{abstract}
|
||||
\noindent \blindtext % Dummy abstract text - replace \blindtext with your abstract text
|
||||
% \noindent \blindtext % Dummy abstract text - replace \blindtext with your abstract text
|
||||
Penelitian ini ditujukan untuk mengembangkan algoritma kendali formasi berdasarkan jarak
|
||||
pada multi mobile robot dimana setiap robot hanya bisa mendeteksi tetangganya saja.
|
||||
Kendali formasi berdasarkan jarak diterapkan pada model holonomic mobile robot
|
||||
menggunakan \textit{omniwheel}.
|
||||
Algoritma \textit{cosinus} digunakan untuk menemukan koordinat tetangga
|
||||
pada kondisi awal.
|
||||
Hasil percobaan dibuktikan secara grafik dari perbandingan menggunakan algoritma dan tidak, bahwa
|
||||
penerapan algoritma dapat mendeteksi koordinat tetangga pada kondisi awal
|
||||
dan tidak mempengaruhi kendali formasi.
|
||||
\end{abstract}
|
||||
}
|
||||
|
||||
|
@ -62,82 +72,17 @@
|
|||
%----------------------------------------------------------------------------------------
|
||||
% ARTICLE CONTENTS
|
||||
%----------------------------------------------------------------------------------------
|
||||
|
||||
\section{Pendahuluan}
|
||||
|
||||
\lettrine[nindent=0em,lines=3]{L} orem ipsum dolor sit amet, consectetur adipiscing elit.
|
||||
\include{BAB1/art_pendahuluan}
|
||||
% \blindtext % Dummy text
|
||||
% \blindtext % Dummy text
|
||||
|
||||
%------------------------------------------------
|
||||
|
||||
\section{Metode}
|
||||
\include{BAB4/art_metode}
|
||||
% Maecenas sed ultricies felis. Sed imperdiet dictum arcu a egestas.
|
||||
% \begin{itemize}
|
||||
% \item Donec dolor arcu, rutrum id molestie in, viverra sed diam
|
||||
% \item Curabitur feugiat
|
||||
% \item turpis sed auctor facilisis
|
||||
% \item arcu eros accumsan lorem, at posuere mi diam sit amet tortor
|
||||
% \item Fusce fermentum, mi sit amet euismod rutrum
|
||||
% \item sem lorem molestie diam, iaculis aliquet sapien tortor non nisi
|
||||
% \item Pellentesque bibendum pretium aliquet
|
||||
% \end{itemize}
|
||||
% \blindtext % Dummy text
|
||||
|
||||
% Text requiring further explanation\footnote{Example footnote}.
|
||||
|
||||
%------------------------------------------------
|
||||
|
||||
\section{Hasil}
|
||||
\include{BAB5/art_hasil}
|
||||
|
||||
% \begin{table}
|
||||
% \caption{Example table}
|
||||
% \centering
|
||||
% \begin{tabular}{llr}
|
||||
% \toprule
|
||||
% \multicolumn{2}{c}{Name} \\
|
||||
% \cmidrule(r){1-2}
|
||||
% First name & Last Name & Grade \\
|
||||
% \midrule
|
||||
% John & Doe & $7.5$ \\
|
||||
% Richard & Miles & $2$ \\
|
||||
% \bottomrule
|
||||
% \end{tabular}
|
||||
% \end{table}
|
||||
|
||||
% \blindtext % Dummy text
|
||||
|
||||
% \begin{equation}
|
||||
% \label{eq:emc}
|
||||
% e = mc^2
|
||||
% \end{equation}
|
||||
|
||||
% \blindtext % Dummy text
|
||||
|
||||
%------------------------------------------------
|
||||
|
||||
\section{Diskusi}
|
||||
\include{BAB5/art_diskusi}
|
||||
|
||||
% \subsection{Subsection One}
|
||||
|
||||
% A statement requiring citation \cite{Figueredo:2009dg}.
|
||||
% \blindtext % Dummy text
|
||||
|
||||
% \subsection{Subsection Two}
|
||||
|
||||
% \blindtext % Dummy text
|
||||
\input{BAB1/art_pendahuluan}
|
||||
\input{BAB4/art_metode}
|
||||
\input{BAB5/art_hasil}
|
||||
% \input{BAB5/art_diskusi}
|
||||
|
||||
%----------------------------------------------------------------------------------------
|
||||
% REFERENCE LIST
|
||||
%----------------------------------------------------------------------------------------
|
||||
|
||||
\renewcommand{\bibname}{\mybibname}
|
||||
\section{\bibname}
|
||||
\printbibliography[title=\bibname]
|
||||
\printbibliography[heading=none]
|
||||
|
||||
%----------------------------------------------------------------------------------------
|
||||
|
||||
|
|
|
@ -0,0 +1,25 @@
|
|||
INFO: latexindent version 3.8.1, 2020-05-05, a script to indent .tex files
|
||||
latexindent lives here: /usr/share/texlive/texmf-dist/scripts/latexindent/
|
||||
Wed Mar 17 13:44:15 2021
|
||||
Filename: /home/a2nr/Documents/-p-formation-control/BAB5/__latexindent_temp.tex
|
||||
INFO: Processing switches:
|
||||
-y|--yaml: YAML settings specified via command line
|
||||
-c|--cruft: cruft directory
|
||||
INFO: Directory for backup files and /home/a2nr/Documents/-p-formation-control//indent.log: /home/a2nr/Documents/-p-formation-control/
|
||||
INFO: YAML settings read: defaultSettings.yaml
|
||||
Reading defaultSettings.yaml from /usr/share/texlive/texmf-dist/scripts/latexindent/defaultSettings.yaml
|
||||
INFO: YAML settings read: indentconfig.yaml or .indentconfig.yaml
|
||||
Home directory is /home/a2nr (didn't find either indentconfig.yaml or .indentconfig.yaml)
|
||||
To specify user settings you would put indentconfig.yaml here: /home/a2nr/indentconfig.yaml
|
||||
Alternatively, you can use the hidden file .indentconfig.yaml as: /home/a2nr/.indentconfig.yaml
|
||||
INFO: YAML settings read: -y switch
|
||||
Updating masterSettings with defaultIndent:
|
||||
INFO: Phase 1: searching for objects
|
||||
INFO: Phase 2: finding surrounding indentation
|
||||
INFO: Phase 3: indenting objects
|
||||
INFO: Phase 4: final indentation check
|
||||
INFO: Output routine:
|
||||
Not outputting to file; see -w and -o switches for more options.
|
||||
--------------
|
||||
INFO: Please direct all communication/issues to:
|
||||
https://github.com/cmhughes/latexindent.pl
|
65
uithesis.sty
|
@ -36,10 +36,8 @@
|
|||
\linespread{1.05} % Line spacing - Palatino needs more space between lines
|
||||
\usepackage{microtype} % Slightly tweak font spacing for aesthetics
|
||||
|
||||
\usepackage[english]{babel} % Language hyphenation and typographical rules
|
||||
|
||||
\usepackage[hmarginratio=1:1,top=32mm,columnsep=20pt]{geometry} % Document margins
|
||||
\usepackage[hang, small,labelfont=bf,up,textfont=it,up]{caption} % Custom captions under/above floats in tables or figures
|
||||
\usepackage{booktabs} % Horizontal rules in tables
|
||||
|
||||
\usepackage{lettrine} % The lettrine is the first enlarged letter at the beginning of the text
|
||||
|
@ -67,6 +65,8 @@
|
|||
\usepackage{titling} % Customizing the title section
|
||||
|
||||
% \usepackage{hyperref} % For hyperlinks in the PDF
|
||||
\usepackage{multicol}
|
||||
|
||||
|
||||
}
|
||||
{
|
||||
|
@ -218,7 +218,20 @@
|
|||
%
|
||||
% Menggunakan biblatex untuk referensi
|
||||
%
|
||||
\usepackage[backend=bibtex, style=authoryear-icomp,autocite=inline]{biblatex}
|
||||
\@ifclassloaded{article}
|
||||
{
|
||||
\usepackage[backend=bibtex,autocite=inline]{biblatex}
|
||||
}
|
||||
{
|
||||
|
||||
}
|
||||
\@ifclassloaded{report}
|
||||
{
|
||||
\usepackage[backend=bibtex, style=authoryear-icomp,autocite=inline]{biblatex}
|
||||
}
|
||||
{
|
||||
|
||||
}
|
||||
%
|
||||
% Digunakan untuk menghasilkan tabel pseudocode
|
||||
%
|
||||
|
@ -254,10 +267,6 @@
|
|||
round-mode = places,
|
||||
round-precision = 2,
|
||||
}
|
||||
%
|
||||
% Digunakan untuk penulisan formula pada caption gambar
|
||||
%
|
||||
\usepackage{caption}
|
||||
|
||||
\usepackage{gantt}
|
||||
%-----------------------------------------------------------------------------%
|
||||
|
@ -354,7 +363,8 @@
|
|||
\pagestyle{fancy} % All pages have headers and footers
|
||||
\fancyhead{} % Blank out the default header
|
||||
\fancyfoot{} % Blank out the default footer
|
||||
\fancyhead[C]{Running title $\bullet$ May 2016 $\bullet$ Vol. XXI, No. 1} % Custom header text
|
||||
% \fancyhead[C]{Running title $\bullet$ May 2016 $\bullet$ Vol. XXI, No. 1} % Custom header text
|
||||
\fancyhead{}
|
||||
\fancyfoot[RO,LE]{\thepage} % Custom footer tex
|
||||
}
|
||||
{
|
||||
|
@ -396,6 +406,28 @@
|
|||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
}
|
||||
% Parameter : 1 -> no marks / only marks
|
||||
% 2 -> label untuk sumbu x
|
||||
% 3 -> label untuk sumbu y
|
||||
% 4 -> lagend entries = {plota , plotb, plot c}
|
||||
% 5 -> \addplot
|
||||
% table[x=<var in tabel x>,y=<var in tabel y,col sep=comma]{<path tabel>};
|
||||
\newcommand{\dataMultiGraph}[5][no marks]{
|
||||
\begin{tikzpicture}
|
||||
%%https://www.latex-tutorial.com/tutorials/pgfplots/
|
||||
\begin{axis}[
|
||||
width=\linewidth, % Scale the plot to \linewidth
|
||||
grid=major, % Display a grid
|
||||
grid style={dashed,gray!30}, % Set the style
|
||||
xlabel=#2, % Set the labels
|
||||
ylabel=#3,
|
||||
#1,
|
||||
legend entries = {#4}
|
||||
]
|
||||
#5
|
||||
\end{axis}
|
||||
\end{tikzpicture}
|
||||
}
|
||||
|
||||
%
|
||||
% Mengganti .et.al pada sitasi dengan dkk
|
||||
|
@ -474,7 +506,22 @@
|
|||
\newcommand{\daftaIsi}{\phantomsection \tableofcontents}
|
||||
\newcommand{\daftarGambar}{\phantomsection \listoffigures}
|
||||
\newcommand{\daftarTabel}{\phantomsection \listoftables}
|
||||
\newcommand{\kutip}[1]{\citeauthor*{#1}\space(\citeyear{#1})}
|
||||
\@ifclassloaded{report}
|
||||
{
|
||||
\newcommand{\kutip}[1]{\citeauthor*{#1}\space(\citeyear{#1})}
|
||||
}
|
||||
{
|
||||
|
||||
}
|
||||
|
||||
\@ifclassloaded{article}
|
||||
{
|
||||
\newcommand{\kutip}[1]{\cite{#1}}
|
||||
}
|
||||
{
|
||||
|
||||
}
|
||||
|
||||
\newcommand{\kutipLs}[1]{\citeauthor*{#1},\citeyear{#1}}
|
||||
\newcommand{\kutipLsHal}[2]{\citeauthor*{#1}, \citeyear{#1}, #2}
|
||||
|
||||
|
|