Maju Bimbingan
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BAB1/bab1.tex
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%-----------------------------------------------------------------------------%
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\chapter{\babSatu}
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%-----------------------------------------------------------------------------%
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\todo{tambahkan kata-kata pengantar bab 1 disini}
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%% \todo{tambahkan kata-kata pengantar bab 1 disini}
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%-----------------------------------------------------------------------------%
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\section{Latar Belakang}
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%-----------------------------------------------------------------------------%
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\todo{tuliskan latar belakang penelitian disini}
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Multi-robot adalah sekelompok mobile robot yang bekerja sama untuk mencapai tujuan
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tertentu. Tujuan tersebut dapat menjadi sebuah topik dalam penelitian seperti
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yang dipaparkan dalam literatur oleh \kutip{Parker2003},
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yaitu mendemonstrasikan atau menerapkan tingkahlaku biologis;
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komunikasi antara robot secara langsung atau tidak langsung;
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pengembangan arsitektur kendali yang memungkinkan untuk diterapkan pada robot yang lebih
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banyak; memecahkan masalah dalam eksplorasi, pemetaan, dan lokalisasi; memecahkan
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masalah dalam transportasi obyek pada multi-robot;
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permasalahan dalam koordinasi pergerakan, seperti kendali formasi;
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dan topik yang lebih terkemuka seperti \textit{machine learning} terhadap robot.
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Pada penelitian ini akan ditujukan ke permasalah kendali formasi.
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Kendali formasi ini adalah salah satu permasalahan dalam kerjasama antar robot.
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Kendali formasi memiliki tujuan untuk mengendalikan sekelompok agen dalam mencapai formasi tertentu
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dan dapat mempertahankan formasi tersebut ketika bermanuver menuju arah yang diinginkan.
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Sehingga kemampuan ini tepat diterapkan dalam bidang militer,
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seperti patroli yang dilakukan oleh sejumlah kendaraan tanpa awak
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untuk tugas penyelamatan dan pencarian didaerah berbahaya.
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Dalam literatur yang dipaparkan oleh \kutip{Guanghua2013}, permasalahan
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kendali formasi ditujukan pada pengembangan arsitektur.
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Pengembangan dilakukan karena untuk memecahkan permasalahan dalam hal mendistribusikan tugas pada setiap robot yang terbatas dan juga berdasarkan keterbatasannya pada robot itu sendiri.
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Selain itu juga dilakukan pengembangan dalam algoritma strategi,
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contoh strategi tersebut adalah \textit{leader-follower}, struktur virtual,
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berdasarkan tingkahlaku, menggunkana teori graph, dan memanfaatkan medan potensial buatan.
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Dalam literatur oleh \kutip{OH2015424}, kendali formasi dikategorikan menjadi 3 bagian,
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yaitu berdasarkan posisi, perpindahan, dan jarak.
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Ketiga bagian tersebut tertuju pada jawaban dari pertanyaan, "variable apa yang digunakan
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sebagai sensor" dan "variable apa yang aktif dikendalikan oleh sistem multi-agent untuk
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mencapai formasi yang diinginkan".
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Untuk menetapkan variable sebagai sensor dapat dilakukan berdasarkan ketentuan kemampuan
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individu agent. Berikut adalah penjelasan singkat dari ketiga bagian tersebut:
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Pada formasi berdasarkan posisi,
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dimana agent diharuskan memiliki kemampuan untuk mengetahui koordinatnya sendiri berdasarkan koordinat global.
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Sehingga, koordinat tujuan didistribusikan kepada setiap agent dan agent bekerja untuk mencapai koordinat tersebut.
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Karena itu, kebutuhan individu untuk berinteraksi dengan individu lain sangat kecil.
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Metode formasi ini pada praktiknya, interaksi antar individu dilakukan untuk menangani masalah disturbance,
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saturasi akselerasi, dan lain-lain.
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Karena metode ini membutuhkan kemampuan untuk mengetahui koordinat global,
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dibutuhkan biaya yang lebih dibanding metode lain dalam perangkat sensor yang \textit{advance}, seperti sensor GPS;
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Pada formasi kendali berdasarkan perpindahan, secara individu agent tidak mengetahui koordinatnya berdasarkan koordinat global.
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Akan tetapi, individu agent memiliki koordinatnya sendiri terhadap individu agent tetangganya dan
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harus dilakukan penyearahan terhadap koordinat setiap robot dengan koordinat global.
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Koordinat relatif itulah yang menjadi variable yang dikendalikan oleh agent.
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Oleh karena itu agent diharuskan memiliki kemampuan untuk mengetahui perpindahan dari
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individu lain berdasarkan koordinat agent itu sendiri,
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dan semua agent harus menyearahkan koordinatnya berdasarkan koordinat global,
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serta dibutuhkan interaksi antara individu lain untuk mencapai formasi yang dinginkan.
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Permasalahan pada metode ini ditujukan pada kendali formasi pada agent yang bersifat heterogent,
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pemeliharaan dalam komunikasi, dan kemampuan dalam menghindari rintangan;
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Pada formasi berdasarkan jarak, dimana setiap individu agent memiliki koordinatnya masing-masing dan
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tidak perlu disearahkan dengan koordinat global.
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Variable yang dikendalikan pada meteode ini adalah variabel jarak antar agent yang terhubung,
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sehingga dibutuhkan kemampuan untuk agent saling berkomunikasi antar agent lain.
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Permasalah pada metode ini ditujukan pada analisa stabilitas secara general;
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tapi hasil penelitian untuk formasi segitiga telah dipaparkan kestabilannya.
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Permasalah pada praktik juga masih perlu untuk dilakukan investigasi pada penerapan model yang lebih nyata.
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Pemeliharaan komunikasi juga menyumbang dalam permasalahan secara praktik, dan
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kemampuan untuk menghindari rintangan juga dibutuhkan.
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Dari ketiga metode tersebut, formasi berdasarkan jarak merupakan metode yang dimungkinkan untuk diterapkan sensor lebih sedikit dari metode lainnya.
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Teknologi komunikasi sekarang pun juga sudah bisa dikatakan bisa untuk diterapkan pada metode tersebut secara praktiknya.
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Pemaparan dengan menggunakan model yang lebih real sangat dibutuhkan sebagai kontribusi dalam bidang kendali multi-robot.
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Dengan harapan penerapan real model tersebut dapat bermanfaat terhadap masyarakat luas.
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%% Penelitian oleh \kutip{Khaledyan2018} juga memaparkan formasi berdasarkan jarak, tapi
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%% ditujukan penerapan terhadap mobile-robot nonholonomic dengan memberikan kecepatan
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%% refrensi nya terhadap semua robot.
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%-----------------------------------------------------------------------------%
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\section{Permasalahan}
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\section{Identifikasi dan Perumusan Masalah}
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%-----------------------------------------------------------------------------%
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Pada bagian ini akan dijelaskan mengenai definisi permasalahan
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yang \saya~hadapi dan ingin diselesaikan serta asumsi dan batasan
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yang digunakan dalam menyelesaikannya.
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Tiga kategori metode formasi yaitu berdasarkan posisi, perpindahan, dan jarak hampir diperlukan analisa terhadap model yang nyata.
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Pada penelitian oleh \kutip{Rozenheck2015}, yang memaparkan permasalahan kendali formasi berdasarkan jarak menggunakan kendali \textit{Proportional-Integral}.
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Metode tersebut menghasilkan formasi pada multi agent tetap terjaga ketika salah satu agent diberikan kecepatan secara konstan dan memberikan respon yang baik ketika pengaturan konstanta PI dengan tepat.
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Tetapi model yang digunakan masih menggunakan model orde satu, dengan kata lain metode tersebut dimungkinkan untuk diterapkan model yang lebih komplek.
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Penelitian oleh \kutip{CORREIA20127}, memaparkan formula model orde dua \textit{holonomic mobile robot} secara detail dan komplek.
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Model tersebut dapat digunakan untuk diterapkan metode formasi berdasarkan jarak sebagai langkah awal analisa terhadap model yang nyata.
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Karena kendali formasi yang digunakan adalah kendali-PI, maka untuk kendali robot keseluruhan akan dikembangkan menggunakan
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metode \textit{self-tune control}.
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Dalam penelitian ini akan digunakan batasan-batasan permasalahan sebagai berikut :
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\begin{enumerate}
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\item Variable sensor yang digunakan adalah jarak antar individu robot.
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\item Komunikasi antar robot diasumsikan ideal, dalam artian percobaan tidak dilakukan diluar jarak jangkauan prangkat komunikasi.
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% \item Rintangan yang digunakan adalah rintangan statis.
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\end{enumerate}
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Berikut adalah beberapa point permasalahan yang ditujukan pada penelitian ini, yaitu:
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\begin{enumerate}
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\item Bagaimanakan strategi untuk kendali formasi apabila variable yang dikendalikan adalah jarak antar robot?.
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\item Bagaimanakah kestabilan kendali formasi berdasarkan jarak apabila model yang digunakan adalah holonomic mobile robot ?.
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\end{enumerate}
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%-----------------------------------------------------------------------------%
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\subsection{Definisi Permasalahan}
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\section{Tujuan dan Manfaat}
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%-----------------------------------------------------------------------------%
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\todo{Tuliskan permasalahan yang ingin diselesaikan. Bisa juga
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berbentuk pertanyaan}
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%% \todo{tulis tujuan sebagai jawaban pertanyaan permasalahan}
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Tujuan dari penelitian ini adalah
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\begin{enumerate}
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\item Mengetahui strategi untuk kendali formasi apabila variable yang dikendalikan adalah jarak antar robot.
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\item Mengetahui kestabilan kendali formasi berdasarkan jarak apabila model yang digunakan adalah holonomic mobile robot.
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\end{enumerate}
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Manfaat dari penelitian ini adalah
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\begin{enumerate}
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\item Memberikan refrensi untuk permasalahan kendali multi-robot, kususnya pada permasalhaan kendali formasi, terhadap model yang lebih nyata.
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\item Membuka peluang penelitian dibidang kendali mengenai kendali formasi pada kendali multi-robot dilingkungan Fakultas Teknik Elektro, Universitas Brawijaya.
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\end{enumerate}
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%% %-----------------------------------------------------------------------------%
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%% \section{Posisi Penelitian}
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%% %-----------------------------------------------------------------------------%
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%% \todo{Posisi penelitian Anda jika dilihat secara bersamaan dengan
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%% peneliti-peneliti lainnya. Akan lebih baik lagi jika ikut menyertakan
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%% diagram yang menjelaskan hubungan dan keterkaitan antar
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%% penelitian-penelitian sebelumnya}
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%-----------------------------------------------------------------------------%
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\subsection{Batasan Permasalahan}
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%-----------------------------------------------------------------------------%
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\todo{Umumnya ada asumsi atau batasan yang digunakan untuk
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menjawab pertanyaan-pertanyaan penelitian diatas.}
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%% %-----------------------------------------------------------------------------%
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%% \section{Metodologi Penelitian}
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%% %-----------------------------------------------------------------------------%
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%% \todo{Tuliskan metodologi penelitian yang digunakan.}
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%-----------------------------------------------------------------------------%
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\section{Tujuan}
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%-----------------------------------------------------------------------------%
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\todo{Tuliskan tujuan penelitian.}
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%% %-----------------------------------------------------------------------------%
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%% \section{Sistematika Penulisan}
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%% %-----------------------------------------------------------------------------%
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%% Sistematika penulisan laporan adalah sebagai berikut:
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%% \begin{itemize}
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%% \item Bab 1 \babSatu \\
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%% \item Bab 2 \babDua \\
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%% \item Bab 3 \babTiga \\
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%% \item Bab 4 \babEmpat \\
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%% \item Bab 5 \babLima \\
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%% \item Bab 6 \babEnam \\
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%% \item Bab 7 \kesimpulan \\
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%% \end{itemize}
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%-----------------------------------------------------------------------------%
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\section{Posisi Penelitian}
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%-----------------------------------------------------------------------------%
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\todo{Posisi penelitian Anda jika dilihat secara bersamaan dengan
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peneliti-peneliti lainnya. Akan lebih baik lagi jika ikut menyertakan
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diagram yang menjelaskan hubungan dan keterkaitan antar
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penelitian-penelitian sebelumnya}
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%-----------------------------------------------------------------------------%
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\section{Metodologi Penelitian}
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%-----------------------------------------------------------------------------%
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\todo{Tuliskan metodologi penelitian yang digunakan.}
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%-----------------------------------------------------------------------------%
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\section{Sistematika Penulisan}
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%-----------------------------------------------------------------------------%
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Sistematika penulisan laporan adalah sebagai berikut:
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\begin{itemize}
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\item Bab 1 \babSatu \\
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\item Bab 2 \babDua \\
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\item Bab 3 \babTiga \\
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\item Bab 4 \babEmpat \\
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\item Bab 5 \babLima \\
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\item Bab 6 \babEnam \\
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\item Bab 7 \kesimpulan \\
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\end{itemize}
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\todo{Tambahkan penjelasan singkat mengenai isi masing-masing bab.}
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%% \todo{Tambahkan penjelasan singkat mengenai isi masing-masing bab.}
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523
BAB2/bab2.tex
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BAB2/bab2.tex
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@ -1,206 +1,339 @@
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%-----------------------------------------------------------------------------%
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\chapter{\babDua}
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%-----------------------------------------------------------------------------%
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\todo{tambahkan kata-kata pengantar bab 2 disini}
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%-----------------------------------------------------------------------------%
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\section{\latex~Secara Singkat}
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%-----------------------------------------------------------------------------%
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Berdasarkan \cite{latex.intro}: \\
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\begin{tabular}{| p{13cm} |}
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\hline
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\\
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LaTeX is a family of programs designed to produce publication-quality
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typeset documents. It is particularly strong when working with
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mathematical symbols. \\
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The history of LaTeX begins with a program called TEX. In 1978, a
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computer scientist by the name of Donald Knuth grew frustrated with the
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mistakes that his publishers made in typesetting his work. He decided
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to create a typesetting program that everyone could easily use to
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typeset documents, particularly those that include formulae, and made
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it freely available. The result is TEX. \\
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Knuth's product is an immensely powerful program, but one that does
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focus very much on small details. A mathematician and computer
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scientist by the name of Leslie Lamport wrote a variant of TEX called
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LaTeX that focuses on document structure rather than such details. \\
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\\
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\hline
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\end{tabular}
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\vspace*{0.8cm}
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Dokumen \latex~sangat mudah, seperti halnya membuat dokumen teks biasa. Ada
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beberapa perintah yang diawali dengan tanda '\bslash'.
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Seperti perintah \bslash\bslash~yang digunakan untuk memberi baris baru.
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Perintah tersebut juga sama dengan perintah \bslash newline.
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Pada bagian ini akan sedikit dijelaskan cara manipulasi teks dan
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perintah-perintah \latex~yang mungkin akan sering digunakan.
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Jika ingin belajar hal-hal dasar mengenai \latex, silahkan kunjungi:
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\begin{itemize}
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\item \url{http://frodo.elon.edu/tutorial/tutorial/}, atau
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\item \url{http://www.maths.tcd.ie/~dwilkins/LaTeXPrimer/}
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\end{itemize}
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%-----------------------------------------------------------------------------%
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\section{\latex~Kompiler dan IDE}
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%-----------------------------------------------------------------------------%
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Agar dapat menggunakan \latex~(pada konteks hanya sebagai pengguna), Anda
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tidak perlu banyak tahu mengenai hal-hal didalamnya.
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Seperti halnya pembuatan dokumen secara visual (contohnya Open Office (OO)
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Writer), Anda dapat menggunakan \latex~dengan cara yang sama.
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Orang-orang yang menggunakan \latex~relatif lebih teliti dan terstruktur
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mengenai cara penulisan yang dia gunakan, \latex~memaksa Anda untuk seperti
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itu.
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Kembali pada bahasan utama, untuk mencoba \latex~Anda cukup mendownload
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kompiler dan IDE. Saya menyarankan menggunakan Texlive dan Texmaker.
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Texlive dapat didownload dari \url{http://www.tug.org/texlive/}.
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Sedangkan Texmaker dapat didownload dari
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\url{http://www.xm1math.net/texmaker/}.
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Untuk pertama kali, coba buka berkas thesis.tex dalam template yang Anda miliki
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pada Texmaker.
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Dokumen ini adalah dokumen utama.
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Tekan F6 (PDFLaTeX) dan Texmaker akan mengkompilasi berkas tersebut menjadi
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berkas PDF.
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Jika tidak bisa, pastikan Anda sudah menginstall Texlive.
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Buka berkas tersebut dengan menekan F7.
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Hasilnya adalah sebuah dokumen yang sama seperti dokumen yang Anda baca saat
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ini.
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%-----------------------------------------------------------------------------%
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\section{Bold, Italic, dan Underline}
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%-----------------------------------------------------------------------------%
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Hal pertama yang mungkin ditanyakan adalah bagaimana membuat huruf tercetak
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tebal, miring, atau memiliki garis bawah.
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Pada Texmaker, Anda bisa melakukan hal ini seperti halnya saat mengubah dokumen
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dengan OO Writer.
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Namun jika tetap masih tertarik dengan cara lain, ini dia:
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\begin{itemize}
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\item \bo{Bold} \\
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Gunakan perintah \bslash textbf$\lbrace\rbrace$ atau
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\bslash bo$\lbrace\rbrace$.
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\item \f{Italic} \\
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Gunakan perintah \bslash textit$\lbrace\rbrace$ atau
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\bslash f$\lbrace\rbrace$.
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\item \underline{Underline} \\
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Gunakan perintah \bslash underline$\lbrace\rbrace$.
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\item $\overline{Overline}$ \\
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Gunakan perintah \bslash overline.
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\item $^{superscript}$ \\
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Gunakan perintah \bslash $\lbrace\rbrace$.
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\item $_{subscript}$ \\
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Gunakan perintah \bslash \_$\lbrace\rbrace$.
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\end{itemize}
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Perintah \bslash f dan \bslash bo hanya dapat digunakan jika package
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uithesis digunakan.
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%-----------------------------------------------------------------------------%
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\section{Memasukan Gambar}
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%-----------------------------------------------------------------------------%
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Setiap gambar dapat diberikan caption dan diberikan label. Label dapat
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digunakan untuk menunjuk gambar tertentu.
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Jika posisi gambar berubah, maka nomor gambar juga akan diubah secara
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otomatis.
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Begitu juga dengan seluruh referensi yang menunjuk pada gambar tersebut.
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Contoh sederhana adalah \pic~\ref{fig:testGambar}.
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Silahkan lihat code \latex~dengan nama bab2.tex untuk melihat kode lengkapnya.
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Harap diingat bahwa caption untuk gambar selalu terletak dibawah gambar.
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\label{bab:dua}
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\section{Pemodelan Robot}
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Robot menggunakan 3 aktuator penggerak dengan roda \textit{omniwheel}, sehingga robot dapat bergerak kesegala arah.
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Pemasangan roda \textit{omniwheel} memiliki sudut $120^\circ$ terhadap roda lainnya.
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Sehingga setiap roda memilki gaya dengan arah $90^\circ$ dari sudut pemasangannya.
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Agar robot bergerak kesegala arah, ketiga aktuator harus dikendalikan untuk menghasilkan resultan gaya dengan arah yang diinginkan.
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\begin{figure}
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\centering
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\includegraphics[width=0.50\textwidth]
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{OTHER/img/creative_common.png}
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\caption{\license.}
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\label{fig:testGambar}
|
||||
\centering
|
||||
\begin{subfigure}[t]{.4\textwidth}
|
||||
%[hbt!]
|
||||
\centering
|
||||
\includegraphics[scale=.4]{BAB2/img/MDC_fig1.png}
|
||||
%% \caption{Geometri Robot (\kutip{CORREIA20127})}
|
||||
\caption{}
|
||||
% \label{fig:1}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.4\textwidth}
|
||||
\centering
|
||||
\includegraphics[scale=.5]{BAB2/img/ADNR_fig1.png}
|
||||
%% \caption{Grafik Gaya Robot}
|
||||
\caption{}
|
||||
% \label{fig:adnr1}
|
||||
\end{subfigure}
|
||||
\caption{(a) Geometri Robot (\kutip{CORREIA20127}) (b) Grafik Gaya Robot}
|
||||
\end{figure}
|
||||
|
||||
Kinematika robot dapat dirumuskan menjadi
|
||||
\begin{align}
|
||||
\dot{\textbf{x}}_p & = R^T(\theta).\dot{\textbf{x}}_r, \label{eq:kinematika_robot}
|
||||
\end{align}
|
||||
dimana $R(\theta)$ adalah matrik rotasi ortogonal
|
||||
\begin{align*}
|
||||
R(\theta) =
|
||||
\begin{bmatrix}
|
||||
\cos(\theta) & \sin(\theta) & 0 \\
|
||||
-\sin(\theta) & \cos(\theta) & 0 \\
|
||||
0 & 0 & 1 \\
|
||||
\end{bmatrix}.
|
||||
\end{align*}
|
||||
Koordinat robot dideskripsikan menggunakan vector $\textbf{x}_p = \begin{bmatrix} x_p & y_p & \theta \end{bmatrix}^T$,
|
||||
dimana $x_p$ dan $y_p$ adalah titik pusat, $P$, pada frame robot dan $\theta_p$ adalah selisih sudut antara \textit{angular} frame global dengan robot.
|
||||
Vector $\dot{\textbf{x}}_r = \begin{bmatrix} \dot{x}_r & \dot{y}_r & \dot{\theta}_r \end{bmatrix}^T$ mendeskripsikan variable kecepatan terhadap titik pusat, $P$,dimana $w$ sebagai kecepatan angular robot terhadap frame global.
|
||||
Karena robot memiliki aktuator, maka kecepatan roda memiliki hubungan terhadap kecepatan robot, dengan kata lain
|
||||
kecepatan pada titik pusat adalah sebuah fungsi dengan kecepatan roda sebagai parameternya.
|
||||
Untuk mendapatkan persamaan tersebut, maka dapat dianalisis dengan hukum \textit{Power}.
|
||||
Apabila didefinisi hubungan antara gaya resultan robot dengan gaya yang dihasilkan roda
|
||||
\begin{align*}
|
||||
F_{\dot{x}_r} & = \cos{90^\circ}.F_{w1}(t) + \cos{30^\circ}.F_{w2}(t) + (-\cos{30^\circ}).F_{w3}(t) \\
|
||||
F_{\dot{y}_r} & = (-1).F_{w1}(t) + \cos{60^\circ}.F_{w2}(t) + \cos{60^{\circ}}.F_{w3}(t) \\
|
||||
\Gamma & = d.F_{w1}(t) + d.F_{w2}(t) + d.F_{w3}(t)
|
||||
\end{align*}
|
||||
dimana $d$ adalah jarak dari titik $P$ ke lokasi roda, maka akan didapat matriks geometri
|
||||
antara $F_R = \begin{bmatrix} F_{\dot{x}_r} & F_{\dot{y}_r} & \Gamma \end{bmatrix}^T$ dengan
|
||||
$F_w = \begin{bmatrix} F_{w1} & F_{w2} & F_{w3} \end{bmatrix}^T$
|
||||
\begin{align}
|
||||
F_R & = \begin{bmatrix}
|
||||
0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2} \\
|
||||
-1 & \frac{1}{2} & \frac{1}{2} \\
|
||||
l & l & l
|
||||
\end{bmatrix}.F_W \nonumber \\
|
||||
F_R & = A.F_w. \label{eq:gaya_robot}
|
||||
\end{align}
|
||||
Dalam kasus robot, \textit{power} yang dihasilkan oleh setiap roda sama dengan \textit{power} dari robot itu sendiri
|
||||
(\kutip{Hacene2019}).
|
||||
Dengan menggunakan persamaan~\eqref{eq:gaya_robot} akan menghasilkan persamaan kinematika robot menggunakan 3 roda
|
||||
\textit{omniwheel} \begin{align}
|
||||
P_{w} & = P_{R} \nonumber \\
|
||||
F_w^T.\dot{x}_w & = F_R^T.\dot{\textbf{x}}_r \nonumber \\
|
||||
F_w^T.\dot{x}_w & = {(A.F_w)}^T.\dot{\textbf{x}}_r \nonumber \\
|
||||
\dot{x}_w & = A^T.\dot{\textbf{x}}_r \nonumber \\
|
||||
\dot{\textbf{x}}_r & = {(A^T)}^{-1}.\dot{x}_w.\label{eq:kecepatan_robot}
|
||||
\end{align}
|
||||
dengan mensubtitusi persamaan~\eqref{eq:kecepatan_robot} pada~\eqref{eq:kinematika_robot}
|
||||
\begin{align}
|
||||
\dot{\textbf{x}}_p & = R^T{(\theta)}.{(A^T)}^{-1}.\dot{x}_w
|
||||
\end{align}
|
||||
|
||||
%-----------------------------------------------------------------------------%
|
||||
\section{Membuat Tabel}
|
||||
%-----------------------------------------------------------------------------%
|
||||
Seperti pada gambar, tabel juga dapat diberi label dan caption.
|
||||
Caption pada tabel terletak pada bagian atas tabel.
|
||||
Contoh tabel sederhana dapat dilihat pada \tab~\ref{tab:tab1}.
|
||||
Pergerakan robot juga dideskripsikan secara dinamika menggunakan hukum pergerakan dari \textit{Newton}.
|
||||
\begin{align}
|
||||
F_{\dot{x}_r}(t) - B_{\dot{x}_r}.\dot{x}_r(t) - C_{\dot{x}_r}.sgn(\dot{x}_r(t)) & = M.\ddot{x}_r(t) \\
|
||||
F_{\dot{y}_r}(t) - B_{\dot{y}_r}.\dot{y}_r(t) - C_{\dot{y}_r}.sgn(\dot{y}_r(t)) & = M.\ddot{y}_r(t) \\
|
||||
\Gamma(t) - B_{\dot{\theta}}.\dot{\theta}(t) - C_{\dot{\theta} }.sgn(\dot{\theta}(t) ) & = I.\ddot{\theta}(t)
|
||||
\end{align}
|
||||
Dimana $B_i$ adalah \textit{viscous firctions} yang mempresentasikan perbandingan terbalik dari gaya yang
|
||||
bersifat linier terhadap gaya dorong dan kecepatan robot. $C_i.sgn(\dot{i})$ adalah \textit{coulumb frictions}
|
||||
yang mempresentasikan perbandingan terbalik terhadap perubahan kecepatan, dimana tanda bilangan berubah kebalikan
|
||||
dari kecepatannya.
|
||||
\begin{align*}
|
||||
sgn(\alpha) = \begin{cases}
|
||||
1, & \alpha >0 \\
|
||||
0, & \alpha = 0 \\
|
||||
-1, & \alpha < 0.
|
||||
\end{cases}
|
||||
\end{align*}
|
||||
seperti pada persamaan~\eqref{eq:gaya_robot}, resultan gaya robot berhubungan dengan gaya roda.
|
||||
Maka gaya roda dapat dideskripsikan dengan menghubungkan antara gaya yang dihasilkan oleh motor
|
||||
\begin{align}
|
||||
F_{wi} & = \frac{\tau_i(t)}{r_i}
|
||||
\end{align}
|
||||
dimana $\tau_i(t)$ adalah torsi dari motor
|
||||
\begin{align}
|
||||
\tau_i(t) = l_i.K_{ti}.i_{ai}(t).
|
||||
\end{align}
|
||||
Untuk mendapatkan persamaan $i_{ai}(t)$, dapat digunakan deskripsi persamaan dinamika motor
|
||||
\begin{align}
|
||||
u_i(t) = L_{ai}.\frac{di_{ai}(t)}{dt} + R_{ai}.i_{ai}(t) + K_{vi}.w_{mi} \label{eq:dyn_motor}
|
||||
\end{align}
|
||||
dimana $L_{ai}$ dan $R_{ai}$ adalah Induktasi dan resistansi armature motornya.
|
||||
$K_{vi}$ adalah konstanta torsi motor dimana dalam satuan SI yang sama dengan $K_v$.
|
||||
Dalam praktiknya apabila motor dalam kecepatan \textit{stady state} maka $\frac{di_{ai}}{dt}$
|
||||
bernilai kecil, dan dalam persamaan~\eqref{eq:dyn_motor} nilai induktansi dapat diabaikan.
|
||||
|
||||
\begin{table}
|
||||
\centering
|
||||
\caption{Contoh Tabel}
|
||||
\label{tab:tab1}
|
||||
\begin{tabular}{| l | c r |}
|
||||
\hline
|
||||
& kol 1 & kol 2 \\
|
||||
\hline
|
||||
baris 1 & 1 & 2 \\
|
||||
baris 2 & 3 & 4 \\
|
||||
baris 3 & 5 & 6 \\
|
||||
jumlah & 9 & 12 \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
Penjabaran dinamika robot bisa diubah dalam bentuk \textit{state-space}
|
||||
\begin{align}
|
||||
\dot{x}(t) & = A_r.x(t) + B_r.u(t) + K.sgn(x(t)) \label{eq:ss1} \\
|
||||
y(t) & = C.x(t) \label{eq:ss2}
|
||||
\end{align}
|
||||
dimana vektor \textit{state} adalah $x(t) = \begin{bmatrix} x_p & y_p & \theta & \dot{x}_r & \dot{y}_r & \dot{\theta}_r \end{bmatrix}^T$, dan
|
||||
vektor output $y(t) = \begin{bmatrix} x_p & y_p & \theta \end{bmatrix}^T$ .
|
||||
Dimana $l = l_{1 \dots 3}, r = r_{1 \dots 3} R_a = R_{a1 \dots 3}$ and $K_t = K_{t1 \dots 3}$, maka didapat matriks yang dapat mendeskripsikan
|
||||
sistem robot
|
||||
\begin{align*}
|
||||
A_r & = \begin{bmatrix}
|
||||
0 & 0 & 0 & \cos(\theta) & -\sin(\theta) & 0 \\
|
||||
0 & 0 & 0 & \sin(\theta) & \cos(\theta) & 0 \\
|
||||
0 & 0 & 0 & 0 & 0 & 1 \\
|
||||
0 & 0 & 0 & -\frac{3.l^2.K_t^2}{2.M.R_a.r^2}-\frac{B_{\dot{x}_r}}{M} & 0 & 0 \\
|
||||
0 & 0 & 0 & 0 & -\frac{3.l^2.K_t^2}{2.M.R_a.r^2}-\frac{B_{\dot{y}_r}}{M} & 0 \\
|
||||
0 & 0 & 0 & 0 & 0 & -\frac{3.l^2.K_t^2}{2.I.R_a.r^2}-\frac{B_{\dot{\theta}_r}}{I} \\
|
||||
\end{bmatrix}, \\
|
||||
B_r & = \begin{bmatrix}
|
||||
0 & 0 & 0 & \\
|
||||
0 & 0 & 0 & \\
|
||||
0 & 0 & 0 & \\
|
||||
0 & \frac{l.K_t}{R_a.r}. \frac{\cos(30^\circ)}{M} & -\frac{l.K_t}{R_a.r}.\frac{\cos(30^\circ)}{M} \\
|
||||
\frac{l.K_t}{R_a.r}.\frac{-1}{M} & \frac{l.K_t}{R_a.r}.\frac{\cos(60^\circ)}{M} & \frac{l.K_t}{R_a.r}.\frac{\cos(60^\circ)}{M} \\
|
||||
\frac{l.K_t}{R_a.r}.\frac{b}{I} & \frac{l.K_t}{R_a.r}.\frac{b}{I} & \frac{l.K_t}{R_a.r}.\frac{b}{I} \\
|
||||
\end{bmatrix},
|
||||
%% \end{align*}
|
||||
%% \begin{align*}
|
||||
K = \begin{bmatrix}
|
||||
0 & 0 & 0 & 0 & 0 & 0 & \\
|
||||
0 & 0 & 0 & 0 & 0 & 0 & \\
|
||||
0 & 0 & 0 & 0 & 0 & 0 & \\
|
||||
0 & 0 & 0 & -\frac{C_{\dot{x}_r}}{M} & 0 & 0 \\
|
||||
0 & 0 & 0 & 0 & -\frac{C_{\dot{x}_r}}{M} & 0 \\
|
||||
0 & 0 & 0 & 0 & 0 & -\frac{C_{\dot{x}_r}}{M} \\
|
||||
\end{bmatrix}, \\
|
||||
C & = \begin{bmatrix}
|
||||
1 & 0 & 0 & 0 & 0 & 0 & \\
|
||||
0 & 1 & 0 & 0 & 0 & 0 & \\
|
||||
0 & 0 & 1 & 0 & 0 & 0 & \\
|
||||
\end{bmatrix}
|
||||
\end{align*}
|
||||
|
||||
Ada jenis tabel lain yang dapat dibuat dengan \latex~berikut
|
||||
beberapa diantaranya.
|
||||
Contoh-contoh ini bersumber dari
|
||||
\url{http://en.wikibooks.org/wiki/LaTeX/Tables}
|
||||
\section{Formasi Multi Robot}
|
||||
Pembahasan kendali formasi mutli-robot dikutip dari paper oleh \kutip{Rozenheck2015}.
|
||||
Dimana peneliti membahas mengenai kendali formasi robot berdasarkan jaraknya lalu dikendalikan dengan kendali PI.
|
||||
Dari subbab ini akan dirangkum dari paper tersebut, yaitu mulai dari pendahuluan sampai kendalinya.
|
||||
|
||||
\begin{table}
|
||||
\centering
|
||||
\caption{An Example of Rows Spanning Multiple Columns}
|
||||
\label{row.spanning}
|
||||
\begin{tabular}{|l|l|*{6}{c|}}
|
||||
\hline % create horizontal line
|
||||
No & Name & \multicolumn{3}{|c|}{Week 1} & \multicolumn{3}{|c|}{Week 2} \\
|
||||
\cline{3-8} % create line from 3rd column till 8th column
|
||||
& & A & B & C & A & B & C\\
|
||||
\hline
|
||||
1 & Lala & 1 & 2 & 3 & 4 & 5 & 6\\
|
||||
2 & Lili & 1 & 2 & 3 & 4 & 5 & 6\\
|
||||
3 & Lulu & 1 & 2 & 3 & 4 & 5 & 6\\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
|
||||
\begin{table}
|
||||
\centering
|
||||
\caption{An Example of Columns Spanning Multiple Rows}
|
||||
\label{column.spanning}
|
||||
\begin{tabular}{|l|c|l|}
|
||||
\hline
|
||||
Percobaan & Iterasi & Waktu \\
|
||||
\hline
|
||||
Pertama & 1 & 0.1 sec \\ \hline
|
||||
\multirow{2}{*}{Kedua} & 1 & 0.1 sec \\
|
||||
& 3 & 0.15 sec \\
|
||||
\hline
|
||||
\multirow{3}{*}{Ketiga} & 1 & 0.09 sec \\
|
||||
& 2 & 0.16 sec \\
|
||||
& 3 & 0.21 sec \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
\subsection{Pendahuluan Formasi Multi Robot}
|
||||
|
||||
\begin{table}
|
||||
\centering
|
||||
\caption{An Example of Spanning in Both Directions Simultaneously}
|
||||
\label{mix.spanning}
|
||||
\begin{tabular}{cc|c|c|c|c|}
|
||||
\cline{3-6}
|
||||
& & \multicolumn{4}{|c|}{Title} \\ \cline{3-6}
|
||||
& & A & B & C & D \\ \hline
|
||||
\multicolumn{1}{|c|}{\multirow{2}{*}{Type}} &
|
||||
\multicolumn{1}{|c|}{X} & 1 & 2 & 3 & 4\\ \cline{2-6}
|
||||
\multicolumn{1}{|c|}{} &
|
||||
\multicolumn{1}{|c|}{Y} & 0.5 & 1.0 & 1.5 & 2.0\\ \cline{1-6}
|
||||
\multicolumn{1}{|c|}{\multirow{2}{*}{Resource}} &
|
||||
\multicolumn{1}{|c|}{I} & 10 & 20 & 30 & 40\\ \cline{2-6}
|
||||
\multicolumn{1}{|c|}{} &
|
||||
\multicolumn{1}{|c|}{J} & 5 & 10 & 15 & 20\\ \cline{1-6}
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
|
||||
\subsubsection{Teori Graf}
|
||||
Suatu graf $\graf$, dinotasikan sebagai $\graf=(\simpul, \sisi)$, merupakan pasangan $\simpul$ dan $\sisi$,
|
||||
di mana $\simpul$ merupakan himpunan tak kosong berisikan simpul pada graf tersebut dan $\sisi$
|
||||
merupakan himpunan sisi pada graf tersebut. Secara formal,
|
||||
himpunan $\sisi$ dapat dinyatakan sebagai suatu koleksi subhimpunan berkardinalitas dua dari himpunan $\simpul$,
|
||||
atau dalam notasi matematika $\sisi \subseteq \simpul \times \simpul $.
|
||||
Sebuah $\graf$ diakatakan tak berarah (\textit{undirected graph}),
|
||||
dimana himpunan sisi terdiri dari pasangan node $(i,j)$,
|
||||
maka sisi tersebut tidak memiliki urutan arah antara node $i$ dengan $j$. Dinotasikan
|
||||
$n \triangleq | \simpul |$ sebagai jumlah dari node dan $m \triangleq | \sisi |$ sebagai jumlah dari sisinya.
|
||||
Apabila $(i,j) \in \sisi$ maka dapat disebut node $i$ dan $j$ berdekatan(\textit{adjecent}).
|
||||
Himpunan dari node yang terhubung dari setiap simpul $i$ dinotasikan dengan $\tetangga_i \triangleq \{ j \in \simpul: (i,j) \in \sisi \}$, dan juga $i \sim j$.
|
||||
Matiks insidensi (\textit{incidence}), $E \in \mathbb{R}^{n\times m}$, adalah matrik $\{0,\pm 1\}$ dimana
|
||||
baris matrik mengindikasikan simpulnya dan kolomnya sebagai sisinya.
|
||||
Matriks \textit{laplacian} didefinisikan dengan $L(\simpul)=EE^T$
|
||||
|
||||
\subsubsection{Teori Kekakuan Graf}
|
||||
Koordinat multi dimensi adalah konfigurasi matrik vector yang terdisi dari beberapa koordinat node,
|
||||
$x = \begin{bmatrix} x_1^T & \dots & x_n^T \end{bmatrix}^T \mathbb{R}^{2n}$, dimana
|
||||
$x_i \in \mathbb{R}^2$ dan $x_i \neq x_j$ untuk semua $i \neq j$.
|
||||
Difinisi sebuah kerangka (\textit{framework}), dinotasikan dengan $\graf(x)$,
|
||||
adalah graf tak berarah $\graf$ dengan konfigurasi $x$, dimana simpul $i$ pada graf dipetakan
|
||||
kedalam koordinat $x_i$. Misalkan $(i,j)\in \sisi$ sama dengan sisi ke $k$ dari graf langsung
|
||||
dan mendefinisikan vektor sisi dari kerangka, atau dapat disebut sebagai vektor posisi relatif,
|
||||
dengan $ e_k \triangleq x_j - x_i$. Untuk semua vektor sisi dapat dinotasikan dengan
|
||||
$e=\begin{bmatrix}e_1^t & \dots & e_m^T\end{bmatrix} \in \mathbb{R}^{2m}$.
|
||||
|
||||
Apabila kerangka $\simpul(x)$ dengan vektor sisi $\{e_k\}_{k=1}^m$, maka didefinisisi fungsi sisi (\textit{edge function}), $F:\mathbb{R}^{2n} \times \simpul \rightarrow \mathbb{R}^m$
|
||||
dengan
|
||||
\begin{align}
|
||||
F(x,\sisi) &\triangleq
|
||||
\begin{bmatrix}
|
||||
||e_1||^2 & \dots & ||e_m||^2
|
||||
\end{bmatrix}^T
|
||||
\end{align}
|
||||
Matrik kekakuan $R(x)$ yang berhubungan erat dengan kerangka $\graf(x)$ dapat didefinisikan
|
||||
dengan \textit{Jacobian} dari fungsi sisi (\kutip{Rozenheck2015}),
|
||||
\begin{align}
|
||||
R(x) &\triangleq \frac{\partial F(x,\graf)}{\partial x} \in \mathbb{R}^{m\times 2n} \nonumber\\
|
||||
&\triangleq diag(e_i^T)(E^T \otimes I_2)
|
||||
\end{align}
|
||||
|
||||
\subsection{Kendali Formasi Multi-Robot}
|
||||
\label{subbab:KendaliFormasi}
|
||||
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}
|
||||
\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
|
||||
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.
|
||||
\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.
|
||||
\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) + B.v_{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 refrensinya
|
||||
, $v_{ref} \in \mathbb{R}^2$ sebagai kecepatan refrensi,
|
||||
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.
|
||||
\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).
|
||||
\end{align}
|
||||
Dengan itu dapat digabungkan menjadi persamaan \textit{state-space} menggunakan persamaan~\eqref{eq:dynmState}
|
||||
\begin{align}
|
||||
\begin{bmatrix}
|
||||
\dot{x}(t) \\ \dot{\xi}(t)
|
||||
\end{bmatrix} =
|
||||
\begin{bmatrix}
|
||||
-k_pR(x)^TR(x) & -R(x)^T \\
|
||||
k_iR(x) & 0
|
||||
\end{bmatrix}
|
||||
\begin{bmatrix}
|
||||
x(t) \\ \xi(t)
|
||||
\end{bmatrix}+
|
||||
\begin{bmatrix}
|
||||
k_pR(x)^T \\ -k_iI
|
||||
\end{bmatrix} d +
|
||||
\begin{bmatrix}
|
||||
B \\ 0
|
||||
\end{bmatrix} v_{ref}
|
||||
\label{eq:ss-formasi}
|
||||
\end{align}
|
||||
|
||||
|
||||
\section{Solusi Persamaan Differensial Secara Numerik}
|
||||
\label{bab: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.
|
||||
Dalam kasus kendali, persamaan differensial dikalkulasi menggunakan komputer, sehingga persamaan tersebut
|
||||
dapat dicari solusi pendekatannya menggunakan cara numerik. Persamaan orde satu dapat direpresentasikan
|
||||
dengan persamaan
|
||||
\begin{align}
|
||||
\dot{x}(t) & = f(x,t), t_0 \leq t \leq t_f \label{eq:ode1.a} \\
|
||||
y(t_0) & = x(t_0).\label{eq:ode1.b}
|
||||
\end{align}
|
||||
Dimana $x(t) \in \mathbb{R}^n$, adalah vector yang setiap iterasi waktu berubah, $f(x,t)\in \mathbb{R}^n$
|
||||
adalah fungsi sistem, $t_0$ dan $t_f$ adalah waktu inisial dan waktu akhir.
|
||||
Pada persamaan~\eqref{eq:ode1.a} dan~\eqref{eq:ode1.b} adalah persamaan dengan permasalahan nilai inisial~\kutip{Fabien2009}.
|
||||
|
||||
Apablia $t(0) = t(t_i)$ maka $t(1) = t(0)+ h$, dimana $h$ adalah perubahan kecil yang memiliki hubungan terhadap waktu.
|
||||
Didalam metode algoritma yang akan dibahas, $h$ juga dapat disebut sebagai \textit{step size}, dan juga
|
||||
$t[k] = t[k-1] + h$ adalah bentuk diskretnya untuk $k = 0,1,2,3\dots$.
|
||||
|
||||
Apabila $y(t[k])$ adalah nilai inisial ketika waktu $t[k]$, maka menggunakan deret \textit{taylor} akan didapat
|
||||
pendekapan solusi untuk $y(t[k+1])$. Menggunakan orde pertama deret \textit{taylor} saja maka didapat
|
||||
persamaan diskret solusi pendekatan $y(t[k])~\approx y[k]$
|
||||
\begin{align}
|
||||
y[k+1] = y[k]+f(y[k])h. \label{eq:desode1}
|
||||
\end{align}
|
||||
|
||||
Pendekatan lain dari persamaan~\eqref{eq:desode1} dengan mendefinisikan turunan $y(t[k])$ sebagai
|
||||
\begin{align}
|
||||
\dot{y}(t[k]) & = \frac{y[k+1] - y[k]}{h}. \label{eq:desdotode1}
|
||||
\end{align}
|
||||
Persamaan~\eqref{eq:desode1} dan~\eqref{eq:desdotode1} dinamakan dengan persamaan \textit{explicite Euler method} dan \textit{forward Euler formula}.
|
||||
Apabila persamaan~\eqref{eq:desdotode1} disubtitusikan pada~\eqref{eq:ode1.a}
|
||||
dan~\eqref{eq:ode1.b} maka didapat persamaan~\eqref{eq:desode1}.
|
||||
Untuk diterapkan dalam komputer, dapat mengikuti algoritme~\ref{algo:eEuler}.
|
||||
|
||||
\begin{algorithm}
|
||||
\DontPrintSemicolon
|
||||
\KwInput{Integer $N > 0$, $h=(t_f-t_i)/N$, $t[0]=t_i$, $y[0]=y[t_i]=y_i$).}
|
||||
\KwOutput{$y[k]$, $k=1,2,\dots,N$.}
|
||||
\For{ $k=0,1,\dots,N-1$}
|
||||
{
|
||||
$y[k+1] = y[k]+h.f(y[k])$\;
|
||||
$t[k+1] = t[k] + h$
|
||||
}
|
||||
\caption{\textit{Explicite Euler Method}}
|
||||
\label{algo:eEuler}
|
||||
\end{algorithm}
|
||||
|
||||
\subsection{Stabilitas Metode Euler}
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[scale=.5]{BAB2/img/equler_explicit.png}
|
||||
\caption[]{Area stabilitas metode explicit euler. (\kutip{Fabien2009})}
|
||||
\label{fig:explicit_euler}
|
||||
\end{figure}
|
||||
Properti dari stabilitas metode Euler dapat diperoleh dengan mendefinisikan persamaan differensial secara general $\dot{x}=\alpha x$,dimana $\alpha$ adalah bilangan complex
|
||||
dari parameter sistem.
|
||||
Dengan menggunakan pendekatan sebelumnya maka persamaan masalah dapat didefinisikan
|
||||
\begin{align}
|
||||
y[k+1] = (1+h\lambda)y[k] = (1 + z)y[k]= R(z)y[k]. \label{eq:disstab}
|
||||
\end{align}
|
||||
Dari persamaan~\eqref{eq:disstab}, sistem akan stabil apabila $|R(z)|\leq 1$.
|
||||
Jika digambarkan dalam grafik complex stabilitas maka dapat dilihat pada gambar~\ref{fig:explicit_euler}
|
||||
|
|
|
|||
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|
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245
BAB3/bab3.tex
245
BAB3/bab3.tex
|
|
@ -1,71 +1,198 @@
|
|||
%-----------------------------------------------------------------------------%
|
||||
\chapter{\babTiga}
|
||||
%-----------------------------------------------------------------------------%
|
||||
\todo{tambahkan kata-kata pengantar bab 1 disini}
|
||||
|
||||
\section{Strategi Kendali Multi Robot}
|
||||
|
||||
%-----------------------------------------------------------------------------%
|
||||
\section{Satu Persamaan}
|
||||
%-----------------------------------------------------------------------------%
|
||||
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.\
|
||||
|
||||
\noindent \begin{align}\label{eq:garis}
|
||||
\cfrac{y - y_{1}}{y_{2} - y_{1}} =
|
||||
\cfrac{x - x_{1}}{x_{2} - x_{1}}
|
||||
\subsection{Kendali Robot}
|
||||
\todo{akan dijelaskan tentang metode yang digunakan untuk mengendalikan robot pada bagian robot saja}
|
||||
|
||||
\subsection{Kendali Formasi Multi Robot}
|
||||
Pada sub bab~\ref{subbab:KendaliFormasi} dijabarkan bagaimana kendali formasi menggunakan
|
||||
kendali-PI dan menghasilkan persamaan~\eqref{eq:ss-formasi}.
|
||||
Persamaan tersebut adalah persamaan \textit{state-space} kendali formasi.
|
||||
Apabila diperhatikan \textit{state} yang digunakan adalah koordinat relatif dari robot.
|
||||
Akan tetapi dalam batasanya, robot hanya bisa mengetahui nilai jarak dari robot lain.
|
||||
Dengan kata lain, yang dibutuhkan dalam metode kendali formasi adalah jarak dalam bentuk koordinat,
|
||||
$x \in \mathbb{R}^2$. Sedangkan dalam kenyataanya yang diketahui adalah jarak, $r \in \mathbb{R}$.
|
||||
Apabila hanya variable jarak tersebut sebagai acuan kendali, maka robot tidak mengerti kearah mana
|
||||
harusnya robot itu bergerak untuk meminimalisasi error jaraknya.
|
||||
|
||||
\subsubsection{Strategi Penentuan 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.
|
||||
|
||||
\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 $\alpha[k+1]$
|
||||
\begin{align}
|
||||
\alpha[k+1] = cos^{-1}\Bigg[ \frac{l_a^2 + d[k+1]^2 -d_a[k]^2}{2d_a[k+1]l_a} \Bigg].
|
||||
\end{align}
|
||||
Sebelum $\alpha[k+1]$ digunakan, jarak $d_a[k+1]$ dan $d_a[k]$ berpengaruh dalam penentuan koordinat.
|
||||
Sehingga diperlukan sedikit algoritma
|
||||
\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}
|
||||
|
||||
\equ~\ref{eq:garis} diatas adalah persamaan garis.
|
||||
\equ~\ref{eq:garis} dan \ref{eq:bola} sama-sama dibuat dengan perintah \bslash
|
||||
align.
|
||||
Perintah ini juga dapat digunakan untuk menulis lebih dari satu persamaan.
|
||||
|
||||
\noindent \begin{align}\label{eq:bola}
|
||||
\underbrace{|\overline{ab}|}_{\text{pada bola $|\overline{ab}| = r$}}
|
||||
= \sqrt[2]{(x_{b} - x_{a})^{2} + (y_{b} - y_{a})^{2} +
|
||||
\vert\vert(z_{b} - z_{a})^{2}}
|
||||
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.
|
||||
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}
|
||||
|
||||
%-----------------------------------------------------------------------------%
|
||||
\section{Lebih dari Satu Persamaan}
|
||||
\label{sec:multiEqu}
|
||||
%-----------------------------------------------------------------------------%
|
||||
\noindent \begin{align}\label{eq:matriks}
|
||||
|\overline{a} * \overline{b}| &= |\overline{a}| |\overline{b}| \sin\theta
|
||||
\\[0.2cm]
|
||||
\overline{a} * \overline{b} &=
|
||||
\begin{array}{| c c c |}
|
||||
\hat{i} & x_{1} & x_{2} \\
|
||||
\hat{j} & y_{1} & y_{2} \\
|
||||
\hat{k} & z_{1} & z_{2} \\
|
||||
\end{array} \nonumber \\[0.2cm]
|
||||
&= \hat{i} \,
|
||||
\begin{array}{ | c c | }
|
||||
y_{1} & y_{2} \\
|
||||
z_{1} & z_{2} \\
|
||||
\end{array}
|
||||
+ \hat{j} \,
|
||||
\begin{array}{ | c c | }
|
||||
z_{1} & z_{2} \\
|
||||
x_{1} & x_{2} \\
|
||||
\end{array}
|
||||
+ \hat{k} \,
|
||||
\begin{array}{ | c c | }
|
||||
x_{1} & x_{2} \\
|
||||
y_{1} & y_{2} \\
|
||||
\end{array}
|
||||
\nonumber
|
||||
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]
|
||||
\end{bmatrix}
|
||||
\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 pada kondisi inisial.
|
||||
|
||||
Pada \equ~\ref{eq:matriks} dapat dilihat beberapa baris menjadi satu bagian
|
||||
dari \equ~\ref{eq:matriks}.
|
||||
Sedangkan dibawah ini dapat dilihat bahwa dengan cara yang sama, \equ~
|
||||
\ref{eq:gabungan1}, \ref{eq:gabungan2}, dan \ref{eq:gabungan3} memiliki nomor
|
||||
persamaannya masing-masing.
|
||||
\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}.
|
||||
\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. }
|
||||
\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.
|
||||
|
||||
\noindent \begin{align}\label{eq:gabungan1}
|
||||
\int_{a}^{b} f(x)\, dx + \int_{b}^{c} f(x) \, dx = \int_{a}^{c} f(x) \, dx
|
||||
\\\label{eq:gabungan2}
|
||||
\lim_{x \to \infty} \frac{f(x)}{g(x)} = 0 \hspace{1cm}
|
||||
\text{jika pangkat $f(x)$ $<$ pangkat $g(x)$} \\\label{eq:gabungan3}
|
||||
a^{m^{a \, ^{n}\log b }} = b^{\frac{m}{n}}
|
||||
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.
|
||||
|
||||
\subsection{Kestabilan Model}
|
||||
Pada persamaan~\eqref{eq:disstab} apabila model dikalkulasi akan bergantung dengan besarnya \textit{step size}, $h$.
|
||||
Oleh karena itu, setelah persamaan~\eqref{eq:ss1}-\eqref{eq:ss2} dilakukan parameterisasi harus dilakukan penentuan \textit{step size} agar model tersebut stabil dalam mensimulasikan modelnya.
|
||||
Penentuan \textit{step size} harus berdasarkan kriteria kestabilan pada gamabar~\ref{fig:explicit_euler}.
|
||||
|
||||
Apabila didefinisi ulang \textit{state} pada persamaan~\eqref{eq:ss1}-\eqref{eq:ss2} dengan
|
||||
$x(t) = \begin{bmatrix}\dot{x}_r & \dot{y}_r & \dot{\theta}_r \end{bmatrix}^T$,
|
||||
maka akan lebih mudah untuk menghitung kestabilan dari matriks $A \in \mathbb{R}^{3 \times 3}$.
|
||||
Dengan menggunakan parameter dari penelitian oleh \kutip{CORREIA20127}, maka akan diperoleh matriks $A, B, K,$ dan $C$.
|
||||
\begin{align*}
|
||||
A & = \begin{bmatrix}
|
||||
-6.69666 & 0.00000 & 0.00000 \\
|
||||
0.00000 & -6.71000 & 0.00000 \\
|
||||
0.00000 & 0.00000 & -4.04200 \\
|
||||
\end{bmatrix} ; \quad
|
||||
B = \begin{bmatrix}
|
||||
0.00000 & 0.57735 & -0.57735 \\
|
||||
-0.66667 & 0.33333 & 0.33333 \\
|
||||
4.00000 & 4.00000 & 4.00000 \\
|
||||
\end{bmatrix} ; \\
|
||||
K & = \begin{bmatrix}
|
||||
-1.46667 & 0.00000 & 0.00000 \\
|
||||
0.00000 & -1.00000 & 0.00000 \\
|
||||
0.00000 & 0.00000 & -0.06600 \\
|
||||
\end{bmatrix}; \quad
|
||||
C = \begin{bmatrix}
|
||||
1 & 0 & 0 \\
|
||||
0 & 1 & 0 \\
|
||||
0 & 0 & 1
|
||||
\end{bmatrix}.
|
||||
\end{align*}
|
||||
|
||||
Dengan menggunakan pendekatan pada persamaan~\eqref{eq:desdotode1} untuk persamaan~\eqref{eq:ss1} maka diperoleh bentuk diskretnya
|
||||
\begin{align}
|
||||
x[k+1] & = (I + A.h).x[k] + B.h.u[k] + K.h.sgn(x[k]). \\
|
||||
\end{align}
|
||||
Pengali $sgn(.)$ bersifat penambah dari sistem, maka dalam penentuan kestabilan ini akan dianggap penambah dari matriks sistem.
|
||||
\begin{align}
|
||||
x[k+1] & = (I + (A+K).h).x[k] + B.h.u[k]. \\
|
||||
\end{align}
|
||||
Kriteria kestabilan akan bergantung dari hasil penentuan $h$ pada $I+(A+K)h~=~\Lambda$.
|
||||
Untuk semua nilai $\lambda$ pada matriks $\Lambda$ harus memenuhi kriteris $\lambda \leq 1$.
|
||||
Dimungkinkan akan mengalami kebingungan ketika menentukan besar $h$,
|
||||
akan tetapi nantinya persamaan ini akan diterapkan dan diselesaikan oleh komputer.
|
||||
Alangkah baiknya apabila diidentifikasi terlebih dahulu konsumsi waktu yang dibutuhkan untuk menyelesaikan
|
||||
satu iterasi dari persamaan tersebut.
|
||||
Setelah dilakukan identifikasi, waktu yang dibutuhkan untuk satu kali iterasi berkisar $0.001$ ms (Pembulatan).
|
||||
Sehingga penentuan \textit{step size} sebesar $0.1$ ms sangat dimungkinkan, dengan pertimbangan
|
||||
sisa dari waktu yang digunakan kalkulasi dapat digunakan untuk waktu \textit{idle} dan menjalankan program yang lain. Berikut adalah matriks $\Lambda$ setelah dikalkulasi menggunakan $h=0.1$
|
||||
\begin{align*}
|
||||
\Lambda = \begin{bmatrix}
|
||||
0.18367 & 0.00000 & 0.00000 \\
|
||||
0.00000 & 0.22900 & 0.00000 \\
|
||||
0.00000 & 0.00000 & 0.58920 \\
|
||||
\end{bmatrix}.
|
||||
\end{align*}
|
||||
Terbukti bahwa semua nilai item didalam matriks kurang dari sama dengan satu.
|
||||
Sehingga menggunakan algoritma \textit{Expilicit Euler} sudah cukup untuk menjalankan model robot \textit{omni 3-wheel} sebagai model \textit{holonomic} yang akan digunakan untuk percobaan kendali multi robot.
|
||||
Hasil plot dari simulasi model dapat dilihat pada gambar~\ref{fig:sim_model}.
|
||||
\begin{figure}
|
||||
\centering
|
||||
\begin{subfigure}[t]{.6\textwidth}
|
||||
\includegraphics[scale=.4]{BAB3/img/speedRobot_-6_3_3.png}
|
||||
\caption{}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.6\textwidth}
|
||||
\includegraphics[scale=.4]{BAB3/img/speedRobot_0_6_-6.png}
|
||||
\caption{}
|
||||
\end{subfigure}
|
||||
\begin{subfigure}[t]{.6\textwidth}
|
||||
\includegraphics[scale=.4]{BAB3/img/speedRobot_6_6_6.png}
|
||||
\caption{}
|
||||
\end{subfigure}
|
||||
\caption{(a)$w_1=-6; w_2=3; w_3=3$. (b) $w_1=0; w_2=6; w_3=-6$ (c) $w_1=6; w_2=6; w_3=6$}
|
||||
\label{fig:sim_model}
|
||||
\end{figure}
|
||||
\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}
|
||||
|
|
|
|||
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author="Fabien, Brian",
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||||
title="Numerical Solution of ODEs and DAEs",
|
||||
bookTitle="Analytical System Dynamics: Modeling and Simulation",
|
||||
year="2009",
|
||||
publisher="Springer US",
|
||||
address="Boston, MA",
|
||||
pages="1--59",
|
||||
isbn="978-0-387-85605-6",
|
||||
doi="10.1007/978-0-387-85605-6_5",
|
||||
url="https://doi.org/10.1007/978-0-387-85605-6_5"
|
||||
}
|
||||
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||||
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|
@ -0,0 +1,17 @@
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|||
@Article{Hacene2019,
|
||||
author="Hacene, Nacer
|
||||
and Mendil, Boubekeur",
|
||||
title="Fuzzy Behavior-based Control of Three Wheeled Omnidirectional Mobile Robot",
|
||||
journal="International Journal of Automation and Computing",
|
||||
year="2019",
|
||||
month="Apr",
|
||||
day="01",
|
||||
volume="16",
|
||||
number="2",
|
||||
pages="163--185",
|
||||
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.",
|
||||
issn="1751-8520",
|
||||
doi="10.1007/s11633-018-1135-x",
|
||||
url="https://doi.org/10.1007/s11633-018-1135-x"
|
||||
}
|
||||
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
@article{CORREIA20127,
|
||||
title = "Modeling of a Three Wheeled Omnidirectional Robot Including Friction Models",
|
||||
journal = "IFAC Proceedings Volumes",
|
||||
volume = "45",
|
||||
number = "22",
|
||||
pages = "7 - 12",
|
||||
year = "2012",
|
||||
note = "10th IFAC Symposium on Robot Control",
|
||||
issn = "1474-6670",
|
||||
doi = "https://doi.org/10.3182/20120905-3-HR-2030.00002",
|
||||
url = "http://www.sciencedirect.com/science/article/pii/S1474667016335807",
|
||||
author = "Mariane Dourado Correia and André Gustavo and Scolari Conceição",
|
||||
keywords = "Models, Friction, Parameter estimation, Autonomous mobile robots",
|
||||
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."
|
||||
}
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
@article{QUESADA2019275,
|
||||
title = "Open-source low-cost Hardware-in-the-loop simulation platform for testing control strategies for artificial pancreas research",
|
||||
journal = "IFAC-PapersOnLine",
|
||||
volume = "52",
|
||||
number = "1",
|
||||
pages = "275 - 280",
|
||||
year = "2019",
|
||||
note = "12th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems DYCOPS 2019",
|
||||
issn = "2405-8963",
|
||||
doi = "https://doi.org/10.1016/j.ifacol.2019.06.074",
|
||||
url = "http://www.sciencedirect.com/science/article/pii/S2405896319301594",
|
||||
author = "Luisa Fernanda Quesada and José David Rojas and Orlando Arrieta and Ramon Vilanova",
|
||||
keywords = "Controlled system, insulin control, Hardware in the loop, PID control, Optimal control",
|
||||
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."
|
||||
}
|
||||
|
|
@ -0,0 +1,10 @@
|
|||
@article{article,
|
||||
author = {Parker, Lynne},
|
||||
year = {2003},
|
||||
month = {03},
|
||||
pages = {1-5},
|
||||
title = {Current research in multirobot systems},
|
||||
volume = {7},
|
||||
journal = {Artificial Life and Robotics},
|
||||
doi = {10.1007/BF02480877}
|
||||
}
|
||||
|
|
@ -0,0 +1,9 @@
|
|||
@inproceedings{inproceedings,
|
||||
author = {Guanghua, Wang and Deyi, Li and Wenyan, Gan and Peng, Jia},
|
||||
year = {2013},
|
||||
month = {01},
|
||||
pages = {1335-1339},
|
||||
title = {Study on Formation Control of Multi-Robot Systems},
|
||||
isbn = {978-1-4673-4893-5},
|
||||
doi = {10.1109/ISDEA.2012.316}
|
||||
}
|
||||
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Before Width: | Height: | Size: 264 KiB After Width: | Height: | Size: 318 KiB |
|
|
@ -6,11 +6,7 @@
|
|||
% Tambahkan pustaka yang digunakan setelah perintah berikut.
|
||||
%
|
||||
\phantomsection %hack to add clickable section for pustaka
|
||||
\begin{thebibliography}{4}
|
||||
|
||||
\bibitem{latex.intro}
|
||||
{Jeff Clark. (n.d). \f{Introduction to LaTeX}.
|
||||
26 Januari 2010. \url{http://frodo.elon.edu/tutorial/tutorial/node3.html}.}
|
||||
|
||||
\end{thebibliography}
|
||||
\renewcommand{\bibname}{Daftar Referensi}
|
||||
\addChapter{\bibname}
|
||||
\printbibliography[title=\bibname]
|
||||
|
||||
|
|
|
|||
|
|
@ -0,0 +1,169 @@
|
|||
@Inbook{Jim1999,
|
||||
author="Jim A. Ledin",
|
||||
title= "Hardware-in-the-Loop Simulation",
|
||||
bookTitle="Embedded Systems Programming",
|
||||
year=1999,
|
||||
month="February",
|
||||
page="42"
|
||||
}
|
||||
|
||||
@Articel{Irwanto2018,
|
||||
author="Herma Yudhi Irwanto ",
|
||||
title="Development of Mobile Ground Control System and GPS Base Auto Tracking Antenna",
|
||||
journal="Jurnal Teknologi Dirgantara",
|
||||
volume="16",
|
||||
number="1",
|
||||
year=2018,
|
||||
month="Juni"
|
||||
}
|
||||
@article{QUESADA2019275,
|
||||
title = "Open-source low-cost Hardware-in-the-loop simulation platform for testing control strategies for artificial pancreas research",
|
||||
journal = "IFAC-PapersOnLine",
|
||||
volume = "52",
|
||||
number = "1",
|
||||
pages = "275 - 280",
|
||||
year = "2019",
|
||||
note = "12th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems DYCOPS 2019",
|
||||
issn = "2405-8963",
|
||||
doi = "https://doi.org/10.1016/j.ifacol.2019.06.074",
|
||||
url = "http://www.sciencedirect.com/science/article/pii/S2405896319301594",
|
||||
author = "Luisa Fernanda Quesada and José David Rojas and Orlando Arrieta and Ramon Vilanova",
|
||||
keywords = "Controlled system, insulin control, Hardware in the loop, PID control, Optimal control",
|
||||
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."
|
||||
}
|
||||
@Article{Hacene2019,
|
||||
author="Hacene, Nacer
|
||||
and Mendil, Boubekeur",
|
||||
title="Fuzzy Behavior-based Control of Three Wheeled Omnidirectional Mobile Robot",
|
||||
journal="International Journal of Automation and Computing",
|
||||
year="2019",
|
||||
month=Apr,
|
||||
day="01",
|
||||
volume="16",
|
||||
number="2",
|
||||
pages="163--185",
|
||||
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.",
|
||||
issn="1751-8520",
|
||||
doi="10.1007/s11633-018-1135-x",
|
||||
url="https://doi.org/10.1007/s11633-018-1135-x"
|
||||
}
|
||||
|
||||
@Inbook{Fabien2009,
|
||||
author="Fabien, Brian",
|
||||
title="Numerical Solution of ODEs and DAEs",
|
||||
bookTitle="Analytical System Dynamics: Modeling and Simulation",
|
||||
year="2009",
|
||||
publisher="Springer US",
|
||||
address="Boston, MA",
|
||||
pages="1--59",
|
||||
isbn="978-0-387-85605-6",
|
||||
doi="10.1007/978-0-387-85605-6_5",
|
||||
url="https://doi.org/10.1007/978-0-387-85605-6_5"
|
||||
}
|
||||
|
||||
|
||||
|
||||
@article{CORREIA20127,
|
||||
title = "Modeling of a Three Wheeled Omnidirectional Robot Including Friction Models",
|
||||
journal = "IFAC Proceedings Volumes",
|
||||
volume = "45",
|
||||
number = "22",
|
||||
pages = "7 - 12",
|
||||
year = "2012",
|
||||
note = "10th IFAC Symposium on Robot Control",
|
||||
issn = "1474-6670",
|
||||
doi = "https://doi.org/10.3182/20120905-3-HR-2030.00002",
|
||||
url = "http://www.sciencedirect.com/science/article/pii/S1474667016335807",
|
||||
author = "Mariane Dourado Correia and André Gustavo and Scolari Conceição",
|
||||
keywords = "Models, Friction, Parameter estimation, Autonomous mobile robots",
|
||||
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."
|
||||
}
|
||||
|
||||
|
||||
@INPROCEEDINGS{Khaledyan2018,
|
||||
author={M. {Khaledyan} and M. {de Queiroz}},
|
||||
booktitle={2018 Annual American Control Conference (ACC)},
|
||||
title={Translational Maneuvering Control of Nonholonomic Kinematic Formations: Theory and Experiments},
|
||||
year={2018},
|
||||
volume={},
|
||||
number={},
|
||||
pages={2910-2915},
|
||||
keywords={control system synthesis;mobile robots;motion control;multi-robot systems;path planning;position control;robot dynamics;robot kinematics;translational maneuvering control;nonholonomic kinematic formations;distance-based formation maneuvering problem;control law;kinematic level;rigidity properties;sensing/control interactions;simple input transformation;control design;nonholonomic model;single-integrator equation;formation maneuvers;multiple nonholonomic unicycle-type robots;time-varying translational velocity;Robot kinematics;Atmospheric modeling;Trajectory;Kinematics;Mobile robots;Robot sensing systems},
|
||||
doi={10.23919/ACC.2018.8431562},
|
||||
ISSN={2378-5861},
|
||||
month={June},}
|
||||
|
||||
@INPROCEEDINGS{Rozenheck2015,
|
||||
author={O. {Rozenheck} and S. {Zhao} and D. {Zelazo}},
|
||||
booktitle={2015 European Control Conference (ECC)},
|
||||
title={A proportional-integral controller for distance-based formation tracking},
|
||||
year={2015},
|
||||
volume={},
|
||||
number={},
|
||||
pages={1693-1698},
|
||||
keywords={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},
|
||||
doi={10.1109/ECC.2015.7330781},
|
||||
ISSN={},
|
||||
month={July},}
|
||||
|
||||
@article{Parker2003,
|
||||
author = {Parker, Lynne},
|
||||
year = {2003},
|
||||
month = {03},
|
||||
pages = {1-5},
|
||||
title = {Current research in multirobot systems},
|
||||
volume = {7},
|
||||
journal = {Artificial Life and Robotics},
|
||||
doi = {10.1007/BF02480877}
|
||||
}
|
||||
@inproceedings{Guanghua2013,
|
||||
author = {Guanghua, Wang and Deyi, Li and Wenyan, Gan and Peng, Jia},
|
||||
year = {2013},
|
||||
month = {01},
|
||||
pages = {1335-1339},
|
||||
title = {Study on Formation Control of Multi-Robot Systems},
|
||||
isbn = {978-1-4673-4893-5},
|
||||
doi = {10.1109/ISDEA.2012.316}
|
||||
}
|
||||
@INPROCEEDINGS{YQC2005,
|
||||
author={Yang Quan Chen and Zhongmin Wang},
|
||||
booktitle={2005 IEEE/RSJ International Conference on Intelligent Robots and Systems},
|
||||
title={Formation control: a review and a new consideration},
|
||||
year={2005},
|
||||
volume={},
|
||||
number={},
|
||||
pages={3181-3186},
|
||||
keywords={mobile robots;remotely operated vehicles;multi-robot systems;position control;motion control;distributed parameter systems;unmanned autonomous vehicle formation;unmanned autonomous robot formation;distributed parameter systems;formation regulation control;formation tracking control;pattern formation;Robot kinematics;Mobile robots;Control systems;Remotely operated vehicles;Robot sensing systems;Robot control;Intelligent robots;Distributed parameter systems;Road vehicles;Intelligent systems;Formation control;stability analysis;graph theory;Lyapunov analysis;distributed parameter system;pattern formation;formation regulation control;formation tracking control;morphological pattern formation tracking control;adaptive mesh},
|
||||
doi={10.1109/IROS.2005.1545539},
|
||||
ISSN={2153-0858},
|
||||
month={Aug},}
|
||||
|
||||
|
||||
@article{OH2015424,
|
||||
title = "A survey of multi-agent formation control",
|
||||
journal = "Automatica",
|
||||
volume = "53",
|
||||
pages = "424 - 440",
|
||||
year = "2015",
|
||||
issn = "0005-1098",
|
||||
doi = "https://doi.org/10.1016/j.automatica.2014.10.022",
|
||||
url = "http://www.sciencedirect.com/science/article/pii/S0005109814004038",
|
||||
author = "Kwang-Kyo Oh and Myoung-Chul Park and Hyo-Sung Ahn",
|
||||
keywords = "Formation control, Position-based control, Displacement-based control, Distance-based control",
|
||||
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."}
|
||||
|
||||
@INPROCEEDINGS{Cao2007,
|
||||
author={M. {Cao} and A. S. {Morse} and C. {Yu} and B. D. O. {Anderson} and S. {Dasguvta}},
|
||||
booktitle={2007 46th IEEE Conference on Decision and Control},
|
||||
title={Controlling a triangular formation of mobile autonomous agents},
|
||||
year={2007},
|
||||
volume={},
|
||||
number={},
|
||||
pages={3603-3608},
|
||||
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.},
|
||||
keywords={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},
|
||||
doi={10.1109/CDC.2007.4434757},
|
||||
ISSN={0191-2216},
|
||||
month={Dec},}
|
||||
|
||||
|
||||
|
|
@ -4,43 +4,54 @@
|
|||
%
|
||||
% @author unknown
|
||||
% @version 1.01
|
||||
% @edit by Andreas Febrian
|
||||
% @edit by 1. Andreas Febrian
|
||||
% 2. Anggoro Dwi Nur Rohman
|
||||
%
|
||||
|
||||
\begin{titlepage}
|
||||
\begin{center}
|
||||
\begin{figure}
|
||||
|
||||
%% \vspace*{1.0cm}
|
||||
|
||||
|
||||
% judul thesis harus dalam 14pt Times New Roman
|
||||
\bo{ \Judul} \\
|
||||
\vspace*{14pt}
|
||||
\vspace*{14pt}
|
||||
|
||||
% harus dalam 16pt Times New Roman
|
||||
\bo{ \fontsize{16}{6}\selectfont \Type}
|
||||
\vspace*{10pt}
|
||||
|
||||
\bo{TEKNIK {\Jurusan} KONSENTRASI TEKNIK \Program}
|
||||
\vspace*{14pt}
|
||||
\vspace*{14pt}
|
||||
\vspace*{14pt}
|
||||
|
||||
\bo{\fontsize{12}{2}\selectfont Ditujukan untuk memenuhi persyaratan\\
|
||||
memperoleh gelar \gelar}
|
||||
\vspace*{14pt}
|
||||
\vspace*{14pt}
|
||||
|
||||
\begin{figure}
|
||||
\begin{center}
|
||||
% \includegraphics[width=2.5cm]{pics/makara.png}
|
||||
\includegraphics[width=2.5cm]{OTHER/img/makara.png}
|
||||
\includegraphics[width=5cm]{OTHER/img/makara.png}
|
||||
\end{center}
|
||||
\end{figure}
|
||||
\vspace*{0cm}
|
||||
\bo{
|
||||
UNIVERSITAS INDONESIA\\
|
||||
}
|
||||
|
||||
\vspace*{1.0cm}
|
||||
% judul thesis harus dalam 14pt Times New Roman
|
||||
\bo{\Judul} \\[1.0cm]
|
||||
|
||||
\vspace*{2.5 cm}
|
||||
% harus dalam 14pt Times New Roman
|
||||
\bo{\Type}
|
||||
|
||||
\vspace*{3 cm}
|
||||
% penulis dan npm
|
||||
\bo{\Penulis} \\
|
||||
\bo{\npm} \\
|
||||
\bo{ \fontsize{12}{2}\selectfont \Penulis \\ \npm} \\
|
||||
|
||||
\vspace*{5.0cm}
|
||||
|
||||
% informasi mengenai fakultas dan program studi
|
||||
\bo{
|
||||
\NamaUni \\
|
||||
FAKULTAS \Fakultas\\
|
||||
PROGRAM STUDI \Program \\
|
||||
DEPOK \\
|
||||
\Kota \\
|
||||
\bulanTahun
|
||||
}
|
||||
\end{center}
|
||||
\end{titlepage}
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -2,6 +2,14 @@
|
|||
% Informasi Mengenai Dokumen
|
||||
%-----------------------------------------------------------------------------%
|
||||
%
|
||||
% Nama universitas
|
||||
\var{\namaUni}{Universitas Brawijaya}
|
||||
\Var{\NamaUni}{Universitas Brawijaya}
|
||||
|
||||
% Kota universitas
|
||||
\var{\kota} {Malang}
|
||||
\Var{\Kota} {Malang}
|
||||
|
||||
% Judul laporan.
|
||||
\var{\judul}{Judul Skripsi/Thesis/Disertasi}
|
||||
%
|
||||
|
|
@ -13,33 +21,37 @@
|
|||
|
||||
%
|
||||
% Tipe laporan, dapat berisi Skripsi, Tugas Akhir, Thesis, atau Disertasi
|
||||
\var{\type}{Tugas Akhir}
|
||||
\var{\type}{Thesis}
|
||||
%
|
||||
% Tulis kembali tipe laporan, kali ini akan diubah menjadi huruf kapital
|
||||
\Var{\Type}{Tugas Akhir}
|
||||
\Var{\Type}{Thesis}
|
||||
%
|
||||
% Tulis nama penulis
|
||||
\var{\penulis}{Tidak Diketahui}
|
||||
\var{\penulis}{anggoro dwi nur rohman}
|
||||
%
|
||||
% Tulis kembali nama penulis, kali ini akan diubah menjadi huruf kapital
|
||||
\Var{\Penulis}{Tidak Diketahui}
|
||||
\Var{\Penulis}{Anggoro Dwi Nur Rohman}
|
||||
%
|
||||
% Tulis NPM penulis
|
||||
\var{\npm}{XXXXXXXXXX}
|
||||
\var{\npm}{186060300111007}
|
||||
%
|
||||
% Tuliskan Fakultas dimana penulis berada
|
||||
\Var{\Fakultas}{??}
|
||||
\var{\fakultas}{??}
|
||||
\Var{\Fakultas}{Teknik}
|
||||
\var{\fakultas}{Teknik}
|
||||
%
|
||||
% Jurusan
|
||||
\Var{\Jurusan}{Elektro}
|
||||
\var{\jurusan}{Elektro}
|
||||
%
|
||||
% Tuliskan Program Studi yang diambil penulis
|
||||
\Var{\Program}{??}
|
||||
\var{\program}{??}
|
||||
\Var{\Program}{Kontrol dan Elektronika}
|
||||
\var{\program}{Kontrol dan Elektronika}
|
||||
%
|
||||
% Tuliskan tahun publikasi laporan
|
||||
\Var{\bulanTahun}{Januari 2010}
|
||||
\Var{\bulanTahun}{Januari 2019}
|
||||
%
|
||||
% Tuliskan gelar yang akan diperoleh dengan menyerahkan laporan ini
|
||||
\var{\gelar}{Sarjana ??}
|
||||
\var{\gelar}{Magister Teknik}
|
||||
%
|
||||
% Tuliskan tanggal pengesahan laporan, waktu dimana laporan diserahkan ke
|
||||
% penguji/sekretariat
|
||||
|
|
@ -64,9 +76,14 @@
|
|||
%
|
||||
\Var{\kataPengantar}{Kata Pengantar}
|
||||
\Var{\babSatu}{Pendahuluan}
|
||||
\Var{\babDua}{Sekilas Mengenai \latex}
|
||||
\Var{\babTiga}{Notasi Matematik}
|
||||
\Var{\babEmpat}{Struktur Berkas}
|
||||
\Var{\babDua}{Kajian Pustaka}
|
||||
\Var{\babTiga}{Kerangka Konsep Penelitian}
|
||||
\Var{\babEmpat}{Metode Penelitian}
|
||||
\Var{\babLima}{Perintah dalam uithesis.sty}
|
||||
\Var{\babEnam}{??}
|
||||
\Var{\kesimpulan}{Kesimpulan dan Saran}
|
||||
|
||||
\var{\graf}{\mathcal{G}}
|
||||
\var{\simpul}{\mathcal{V}}
|
||||
\Var{\sisi}{\epsilon}
|
||||
\Var{\tetangga}{\mathcal{N}}
|
||||
|
|
|
|||
File diff suppressed because it is too large
Load Diff
Binary file not shown.
|
After Width: | Height: | Size: 318 KiB |
|
|
@ -0,0 +1,11 @@
|
|||
@Comment{$ biblatex control file $}
|
||||
@Comment{$ biblatex version 2.9 $}
|
||||
Do not modify this file!
|
||||
|
||||
This is an auxiliary file used by the 'biblatex' package.
|
||||
This file may safely be deleted. It will be recreated as
|
||||
required.
|
||||
|
||||
@Control{biblatex-control,
|
||||
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|
||||
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|
||||
|
|
@ -0,0 +1,524 @@
|
|||
% $ biblatex auxiliary file $
|
||||
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|
||||
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|
||||
%
|
||||
% This is an auxiliary file used by the 'biblatex' package.
|
||||
% This file may safely be deleted. It will be recreated as
|
||||
% required.
|
||||
%
|
||||
\begingroup
|
||||
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|
||||
\@ifundefined{ver@biblatex.sty}
|
||||
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|
||||
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|
||||
{The bibliography requires the 'biblatex' package.}
|
||||
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|
||||
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|
||||
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|
||||
|
||||
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|
||||
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|
||||
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|
||||
{{hash=CM}{%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
{{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},
|
||||
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|
||||
{{hash=ABDO}{%
|
||||
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|
||||
familyi={A\bibinitperiod},
|
||||
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|
||||
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|
||||
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|
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|
||||
{{hash=DS}{%
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
}
|
||||
\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}
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\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}
|
||||
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|
||||
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|
||||
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|
||||
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
{{hash=GA}{%
|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\keyw{Models, Friction, Parameter estimation, Autonomous mobile robots}
|
||||
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|
||||
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||||
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||||
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||||
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||||
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|
||||
\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}
|
||||
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|
||||
|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\field{pages}{1\bibrangedash 59}
|
||||
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|
||||
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|
||||
\verb https://doi.org/10.1007/978-0-387-85605-6_5
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\field{isbn}{978-1-4673-4893-5}
|
||||
\field{pages}{1335\bibrangedash 1339}
|
||||
\field{title}{Study on Formation Control of Multi-Robot Systems}
|
||||
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|
||||
\field{year}{2013}
|
||||
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|
||||
|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\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
|
||||
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|
||||
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|
||||
\field{journaltitle}{International Journal of Automation and Computing}
|
||||
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|
||||
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|
||||
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|
||||
|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
\field{title}{Development of Mobile Ground Control System and GPS Base Auto
|
||||
Tracking Antenna}
|
||||
\field{volume}{16}
|
||||
\field{journaltitle}{Jurnal Teknologi Dirgantara}
|
||||
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|
||||
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|
||||
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|
||||
|
||||
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
\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},
|
||||
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|
||||
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|
||||
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|
||||
{{hash=AHS}{%
|
||||
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|
||||
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|
||||
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|
||||
giveni={H\bibinitperiod-S\bibinitperiod},
|
||||
}}%
|
||||
}
|
||||
\keyw{Formation control, Position-based control, Displacement-based
|
||||
control, Distance-based control}
|
||||
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|
||||
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|
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||||
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|
||||
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|
||||
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|
||||
\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}{%
|
||||
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|
||||
familyi={P\bibinitperiod},
|
||||
given={Lynne},
|
||||
giveni={L\bibinitperiod},
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\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
|
||||
|
||||
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|
||||
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|
||||
{{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},
|
||||
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|
||||
{{hash=VR}{%
|
||||
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|
||||
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}
|
||||
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|
||||
\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}
|
||||
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|
||||
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|
||||
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|
||||
\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}
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
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|
||||
<file>thesis.aux</file>
|
||||
<file>thesis-blx.bib</file>
|
||||
</requires>
|
||||
<requires type="editable">
|
||||
<file>OTHER/references.bib</file>
|
||||
</requires>
|
||||
<requires type="static">
|
||||
<file>biblatex.bst</file>
|
||||
</requires>
|
||||
</external>
|
||||
</requests>
|
||||
|
|
@ -17,7 +17,7 @@
|
|||
|
||||
% Load konfigurasi LaTeX untuk tipe laporan thesis
|
||||
\usepackage{uithesis}
|
||||
|
||||
\addbibresource{OTHER/references.bib}
|
||||
|
||||
% Load konfigurasi khusus untuk laporan yang sedang dibuat
|
||||
\input{laporan_setting}
|
||||
|
|
|
|||
55
uithesis.sty
55
uithesis.sty
|
|
@ -3,6 +3,7 @@
|
|||
%
|
||||
% @author Andreas Febrian
|
||||
% @version 1.03
|
||||
% @edit by Anggoro Dwi Nur Rohman
|
||||
%
|
||||
% Terima kasih untuk:
|
||||
% 1. Lia Sadita
|
||||
|
|
@ -100,11 +101,17 @@
|
|||
%
|
||||
\usepackage[font=footnotesize,format=plain,labelfont=bf,up,textfont=up]{caption}
|
||||
|
||||
% digunakan untuk membuat sub gambar didalam figure
|
||||
% usepackage dilakukan setelah caption,
|
||||
%
|
||||
\usepackage{subcaption}
|
||||
|
||||
%
|
||||
% Membantu penulisan notasi matematika terutama untuk dokumen dengan banyak
|
||||
% rumus.
|
||||
%
|
||||
\usepackage{amsmath}
|
||||
%% \usepackage{amsmath}
|
||||
\usepackage{amsmath, amsfonts, stmaryrd, amssymb}
|
||||
|
||||
%
|
||||
% Membuat seluruh tulisan menjadi Times New Roman.
|
||||
|
|
@ -135,9 +142,28 @@
|
|||
%
|
||||
%
|
||||
\usepackage{float}
|
||||
\floatplacement{figure}{H}
|
||||
\floatplacement{table}{H}
|
||||
\floatplacement{figure}{H}
|
||||
\floatplacement{table}{H}
|
||||
|
||||
% Untuk mengatur ukuran font
|
||||
%
|
||||
\usepackage{anyfontsize}
|
||||
%
|
||||
% Digunakan untuk nomor dengan format inline
|
||||
%
|
||||
\usepackage[inline]{enumitem}
|
||||
%
|
||||
% Menggunakan biblatex untuk referensi
|
||||
%
|
||||
\usepackage[backend=bibtex, style=authoryear-icomp,autocite=inline]{biblatex}
|
||||
%
|
||||
% Digunakan untuk menghasilkan tabel pseudocode
|
||||
%
|
||||
% \usepackage[chapter]{algorithm}
|
||||
% \usepackage[noend]{algpseudocode}
|
||||
|
||||
\usepackage{xcolor}
|
||||
\usepackage[linesnumbered,ruled,vlined,algochapter]{algorithm2e}
|
||||
|
||||
%-----------------------------------------------------------------------------%
|
||||
% Konfigurasi
|
||||
|
|
@ -188,7 +214,7 @@
|
|||
\fancyhead[C]{}
|
||||
\fancyhead[R]{\thepage}
|
||||
\renewcommand{\headrulewidth}{0.0pt}
|
||||
\fancyfoot[R]{\footnotesize \bo{Universitas Indonesia}}
|
||||
\fancyfoot[R]{\footnotesize \bo{ }}
|
||||
\renewcommand{\footrulewidth}{0.0pt}
|
||||
\pagestyle{fancy}
|
||||
|
||||
|
|
@ -260,8 +286,15 @@
|
|||
%
|
||||
% Alias untuk perintah \LaTeX
|
||||
\newcommand{\latex}{\LaTeX}
|
||||
|
||||
|
||||
%
|
||||
%
|
||||
% fix link daftar isi yang sebelumnya ngelink ke halaman sebelumnya
|
||||
\newcommand{\daftaIsi}{\phantomsection \tableofcontents}
|
||||
\newcommand{\daftarGambar}{\phantomsection \listoffigures}
|
||||
\newcommand{\daftarTabel}{\phantomsection \listoftables}
|
||||
\newcommand{\kutip}[1]{\citeauthor*{#1}(\citeyear{#1})}
|
||||
\newcommand{\kutipLs}[1]{\citeauthor*{#1},\citeyear{#1}}
|
||||
\newcommand{\kutipLsHal}[2]{\citeauthor*{#1}, \citeyear{#1}, #2}
|
||||
|
||||
%-----------------------------------------------------------------------------%
|
||||
% Ubah Istilah Penulisan
|
||||
|
|
@ -296,4 +329,12 @@
|
|||
%
|
||||
%
|
||||
\newcommand{\equ}{Persamaan}
|
||||
|
||||
%
|
||||
%
|
||||
%%% Coloring the comment as blue in algorthm
|
||||
\newcommand\mycommfont[1]{\footnotesize\ttfamily\textcolor{blue}{#1}}
|
||||
\SetCommentSty{mycommfont}
|
||||
\SetKwInput{KwInput}{Masukan} % Set the Input
|
||||
\SetKwInput{KwOutput}{Keluaran} % set the Output
|
||||
\SetKwFor{For}{Untuk}{Lakukan}{}
|
||||
\SetAlgorithmName{Algoritme}{\autoref}{Daftar Algoritme}
|
||||
|
|
|
|||
Loading…
Reference in New Issue