BESOK BIMBINGAN !!!
a2nr
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@ -29,7 +29,7 @@ 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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berdasarkan tingkahlaku, menggunakan 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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@ -37,8 +37,9 @@ Ketiga bagian tersebut tertuju pada jawaban dari pertanyaan, "variable apa yang
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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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individu agent.
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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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@ -46,6 +47,7 @@ Metode formasi ini pada praktiknya, interaksi antar individu dilakukan untuk men
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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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@ -56,6 +58,7 @@ 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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@ -73,7 +76,7 @@ Dengan harapan penerapan real model tersebut dapat bermanfaat terhadap masyaraka
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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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%% referensi nya terhadap semua robot.
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%-----------------------------------------------------------------------------%
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@ -81,9 +84,9 @@ Dengan harapan penerapan real model tersebut dapat bermanfaat terhadap masyaraka
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%-----------------------------------------------------------------------------%
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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}(PI).
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Peneliti memberikan kecepatan refrensi secara konstan terhadap salah satu dari agent.
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Peneliti memberikan kecepatan referensi secara konstan terhadap salah satu dari agent.
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Lalu agent lainya memberikan respon untuk tetap menjaga formasi yang diinginkan.
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Tidak dejalaskan alasan oleh peneliti kenapa salah satu agent diberi kecepatan refrensi,
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Tidak dejalaskan alasan oleh peneliti kenapa salah satu agent diberi kecepatan referensi,
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akan tetapi metode tersebut hampir sama dengan strategi \textit{leader-follower}.
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\textit{Leader-follower} mengharuskan agent tetangga untuk beradaptasi terhadap perubahan tetangga lainnya secara spesifik.
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Akan tetapi ada perbedaan antara \textit{leader-follower} dengan metode berdasarkan jarak,
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@ -127,6 +130,6 @@ Tujuan dari penelitian ini adalah
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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 Memberikan referensi 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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@ -30,7 +30,7 @@ Agar robot bergerak kesegala arah, ketiga aktuator harus dikendalikan untuk meng
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Kinematika robot dapat dirumuskan menjadi
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\begin{align}
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\dot{\textbf{x}}_p & = R^T(\theta).\dot{\textbf{x}}_r, \label{eq:kinematika_robot}
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\dot{\textbf{x}}_p & = R^T(\theta)\dot{\textbf{x}}_r \label{eq:kinematika_robot}
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\end{align}
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dimana $R(\theta)$ adalah matrik rotasi ortogonal
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\begin{align*}
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@ -39,7 +39,7 @@ dimana $R(\theta)$ adalah matrik rotasi ortogonal
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\cos(\theta) & \sin(\theta) & 0 \\
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-\sin(\theta) & \cos(\theta) & 0 \\
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0 & 0 & 1 \\
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\end{bmatrix}.
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\end{bmatrix}
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\end{align*}
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Koordinat robot dideskripsikan menggunakan vector $\textbf{x}_p = \begin{bmatrix} x_p & y_p & \theta \end{bmatrix}^T$,
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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.
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@ -49,8 +49,8 @@ kecepatan pada titik pusat adalah sebuah fungsi dengan kecepatan roda sebagai pa
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Untuk mendapatkan persamaan tersebut, maka dapat dianalisis dengan hukum \textit{Power}.
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Apabila didefinisi hubungan antara gaya resultan robot dengan gaya yang dihasilkan roda
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\begin{align*}
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F_{\dot{x}_r} & = \cos{90^\circ}.F_{w1}(t) + \cos{30^\circ}.F_{w2}(t) + (-\cos{30^\circ}).F_{w3}(t) \\
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F_{\dot{y}_r} & = (-1).F_{w1}(t) + \cos{60^\circ}.F_{w2}(t) + \cos{60^{\circ}}.F_{w3}(t) \\
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F_{\dot{x}_r} & = F_{w1}(t)\cos({90^\circ})+ F_{w2}(t) \cos({30^\circ})+ -F_{w3}(t) \cos({30^\circ}) \\
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F_{\dot{y}_r} & = -F_{w1}(t) + F_{w2}(t) \cos({60^\circ})+ F_{w3}(t) \cos({60^{\circ}}) \\
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\Gamma & = d.F_{w1}(t) + d.F_{w2}(t) + d.F_{w3}(t)
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\end{align*}
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dimana $d$ adalah jarak dari titik $P$ ke lokasi roda, maka akan didapat matriks geometri
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@ -61,29 +61,29 @@ $F_w = \begin{bmatrix} F_{w1} & F_{w2} & F_{w3} \end{bmatrix}^T$
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0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2} \\
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-1 & \frac{1}{2} & \frac{1}{2} \\
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l & l & l
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\end{bmatrix}.F_W \nonumber \\
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F_R & = A.F_w. \label{eq:gaya_robot}
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\end{bmatrix}F_W \nonumber \\
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F_R & = AF_w \label{eq:gaya_robot}
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\end{align}
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Dalam kasus robot, \textit{power} yang dihasilkan oleh setiap roda sama dengan \textit{power} dari robot itu sendiri
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(\kutip{Hacene2019}).
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Dengan menggunakan persamaan~\eqref{eq:gaya_robot} akan menghasilkan persamaan kinematika robot menggunakan 3 roda
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\textit{omniwheel} \begin{align}
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P_{w} & = P_{R} \nonumber \\
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F_w^T.\dot{x}_w & = F_R^T.\dot{\textbf{x}}_r \nonumber \\
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F_w^T.\dot{x}_w & = {(A.F_w)}^T.\dot{\textbf{x}}_r \nonumber \\
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\dot{x}_w & = A^T.\dot{\textbf{x}}_r \nonumber \\
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\dot{\textbf{x}}_r & = {(A^T)}^{-1}.\dot{x}_w.\label{eq:kecepatan_robot}
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P_{w} & = P_{R} \nonumber \\
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F_w^T\dot{x}_w & = F_R^T\dot{\textbf{x}}_r \nonumber \\
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F_w^T\dot{x}_w & = {(A.F_w)}^T\dot{\textbf{x}}_r \nonumber \\
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\dot{x}_w & = A^T\dot{\textbf{x}}_r \nonumber \\
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\dot{\textbf{x}}_r & = {(A^T)}^{-1}\dot{x}_w\label{eq:kecepatan_robot}
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\end{align}
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dengan mensubtitusi persamaan~\eqref{eq:kecepatan_robot} pada~\eqref{eq:kinematika_robot}
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\begin{align}
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\dot{\textbf{x}}_p & = R^T{(\theta)}.{(A^T)}^{-1}.\dot{x}_w
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\dot{\textbf{x}}_p & = R^T{(\theta)}{(A^T)}^{-1}\dot{x}_w
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\end{align}
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Pergerakan robot juga dideskripsikan secara dinamika menggunakan hukum pergerakan dari \textit{Newton}.
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\begin{align}
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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) \\
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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) \\
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\Gamma(t) - B_{\dot{\theta}}.\dot{\theta}(t) - C_{\dot{\theta} }.sgn(\dot{\theta}(t) ) & = I.\ddot{\theta}(t)
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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) \\
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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) \\
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\Gamma(t) - B_{\dot{\theta}}\dot{\theta}(t) - C_{\dot{\theta} }sgn(\dot{\theta}(t) ) & = I\ddot{\theta}(t)
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\end{align}
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Dimana $B_i$ adalah \textit{viscous firctions} yang mempresentasikan perbandingan terbalik dari gaya yang
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bersifat linier terhadap gaya dorong dan kecepatan robot. $C_i.sgn(\dot{i})$ adalah \textit{coulumb frictions}
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@ -91,9 +91,9 @@ yang mempresentasikan perbandingan terbalik terhadap perubahan kecepatan, dimana
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dari kecepatannya.
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\begin{align*}
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sgn(\alpha) = \begin{cases}
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1, & \alpha >0 \\
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0, & \alpha = 0 \\
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-1, & \alpha < 0.
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1, & \alpha >0 \\
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0, & \alpha = 0 \\
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-1, & \alpha < 0
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\end{cases}
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\end{align*}
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seperti pada persamaan~\eqref{eq:gaya_robot}, resultan gaya robot berhubungan dengan gaya roda.
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@ -103,11 +103,11 @@ Maka gaya roda dapat dideskripsikan dengan menghubungkan antara gaya yang dihasi
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\end{align}
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dimana $\tau_i(t)$ adalah torsi dari motor
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\begin{align}
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\tau_i(t) = l_i.K_{ti}.i_{ai}(t).
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\tau_i(t) = l_iK_{ti}i_{ai}(t)
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\end{align}
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Untuk mendapatkan persamaan $i_{ai}(t)$, dapat digunakan deskripsi persamaan dinamika motor
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\begin{align}
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u_i(t) = L_{ai}.\frac{di_{ai}(t)}{dt} + R_{ai}.i_{ai}(t) + K_{vi}.w_{mi} \label{eq:dyn_motor}
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u_i(t) = L_{ai}\frac{di_{ai}(t)}{dt} + R_{ai}i_{ai}(t) + K_{vi}w_{mi} \label{eq:dyn_motor}
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\end{align}
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dimana $L_{ai}$ dan $R_{ai}$ adalah Induktasi dan resistansi armature motornya.
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$K_{vi}$ adalah konstanta torsi motor dimana dalam satuan SI yang sama dengan $K_v$.
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@ -116,8 +116,8 @@ bernilai kecil, dan dalam persamaan~\eqref{eq:dyn_motor} nilai induktansi dapat
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Penjabaran dinamika robot bisa diubah dalam bentuk \textit{state-space}
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\begin{align}
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\dot{x}(t) & = A_r.x(t) + B_r.u(t) + K.sgn(x(t)) \label{eq:ss1} \\
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y(t) & = C.x(t) \label{eq:ss2}
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\dot{x}(t) & = A_rx(t) + B_ru(t) + Ksgn(x(t)) \label{eq:ss1} \\
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y(t) & = Cx(t) \label{eq:ss2}
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\end{align}
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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
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vektor output $y(t) = \begin{bmatrix} x_p & y_p & \theta \end{bmatrix}^T$ .
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@ -230,12 +230,12 @@ setiap robot $i$ dan $j$ untuk sisi $(i,j)\in \sisi$.
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Lalu didefinisi persamaan potensial yang memiliki hubungan antara jarak robot yang diinginkan
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dengan jarak yang sekarang
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\begin{align}
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\Phi(e) & = \frac{1}{2} \sum_{k=1}^{m} \big( ||e_k||^2 - d_k^2 \big)^2.
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\Phi(e) & = \frac{1}{2} \sum_{k=1}^{m} \big( ||e_k||^2 - d_k^2 \big)^2
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\end{align}
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Pengamatan dilakukan agar $\Phi(e) =0$ jika dan hanya jika $||e_k||^2 = d_k^2,$ $\forall k = 1, \dots, m$.
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Kendali dari setiap robot menggunakan gradien negatif dari fungsi potensial
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\begin{align}
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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.
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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
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\end{align}
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Dengan itu, dapat disubtitusi kedalam persamaan dinamika pada persamaan~\eqref{eq:modelorde1}
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\begin{align}
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@ -244,22 +244,22 @@ Dengan itu, dapat disubtitusi kedalam persamaan dinamika pada persamaan~\eqref{e
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Penambahan refresni kecepatan pada salah satu robot dapat menjadikan formasi bermanuver.
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Skema kendali secara general dapat didefinisi dengan
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\begin{align}
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\dot{x}(t) & = u(t) + B.v_{ref} \\
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\dot{x}(t) & = u(t) + Bv_{ref} \\
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u(t) & = -R(x)^TC\Big(R(x)x(t)- d\Big) \label{eq:kontrolinput}
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\end{align}
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dimana $B \in \mathbb{R}^{2n \times 2}$ digunakan untuk indikasi robot ke $i$ sebagai leader atau penerima kecepatan refrensinya
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, $v_{ref} \in \mathbb{R}^2$ sebagai kecepatan refrensi,
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dimana $B \in \mathbb{R}^{2n \times 2}$ digunakan untuk indikasi robot ke $i$ sebagai leader atau penerima kecepatan referensinya
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, $v_{ref} \in \mathbb{R}^2$ sebagai kecepatan referensi,
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dan $C$ adalah konstanta pengendali yang akan digantikan dengan algoritma kendali.
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Dengan menerapkan kendali Proportional-Integral, konstanta $C$ pada persamaan~\eqref{eq:kontrolinput}
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dapat diubah dengan
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\begin{align}
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u(t) & = u_{k_p}(t) + u_{k_i}(t) \\
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u_{k_p}(t) & = -R(x)^Tk_p\Big(R(x)x(t)- d\Big) \\
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u_{k_i}(t) & = -R(x)^Tk_i\int_0^T\Big(R(x)x(\tau)- d\Big)d\tau.
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u(t) & = u_{k_p}(t) + u_{k_i}(t) \\
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u_{k_p}(t) & = -R(x)^Tk_p\Big(R(x)x(t)- d\Big) \\
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u_{k_i}(t) & = -R(x)^Tk_i\int_0^T\Big(R(x)x(\tau)- d\Big)d\tau
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\end{align}
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Lalu pada bagian integrator( $k_i$ ), menghasilkan \textit{state} baru
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\begin{align}
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\dot{\xi}(t) & = k_i\Big(R(x)x(t)- d\Big).
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\dot{\xi}(t) & = k_i\Big(R(x)x(t)- d\Big)
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\end{align}
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Dengan itu dapat digabungkan menjadi persamaan \textit{state-space} menggunakan persamaan~\eqref{eq:dynmState}
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\begin{align}
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@ -294,7 +294,7 @@ dapat dicari solusi pendekatannya menggunakan cara numerik. Persamaan orde satu
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dengan persamaan
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\begin{align}
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\dot{x}(t) & = f(x,t), t_0 \leq t \leq t_f \label{eq:ode1.a} \\
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y(t_0) & = x(t_0).\label{eq:ode1.b}
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y(t_0) & = x(t_0)\label{eq:ode1.b}
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\end{align}
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Dimana $x(t) \in \mathbb{R}^n$, adalah vector yang setiap iterasi waktu berubah, $f(x,t)\in \mathbb{R}^n$
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adalah fungsi sistem, $t_0$ dan $t_f$ adalah waktu inisial dan waktu akhir.
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@ -308,12 +308,12 @@ Apabila $y(t[k])$ adalah nilai inisial ketika waktu $t[k]$, maka menggunakan der
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pendekatan solusi untuk $y(t[k+1])$. Menggunakan orde pertama deret \textit{taylor} saja maka didapat
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persamaan diskret solusi pendekatan $y(t[k])~\approx y[k]$
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\begin{align}
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y[k+1] = y[k]+f(y[k])h. \label{eq:desode1}
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y[k+1] = y[k]+f(y[k])h \label{eq:desode1}
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\end{align}
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Pendekatan lain dari persamaan~\eqref{eq:desode1} dengan mendefinisikan turunan $y(t[k])$ sebagai
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\begin{align}
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\dot{y}(t[k]) & = \frac{y[k+1] - y[k]}{h}. \label{eq:desdotode1}
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\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}
|
||||
|
|
@ -326,7 +326,7 @@ Untuk diterapkan dalam komputer, dapat mengikuti algoritme~\ref{algo:eEuler}.
|
|||
\KwOutput{$y[k]$, $k=1,2,\dots,N$.}
|
||||
\For{ $k=0,1,\dots,N-1$}
|
||||
{
|
||||
$y[k+1] = y[k]+h.f(y[k])$\;
|
||||
$y[k+1] = y[k]+hf(y[k])$\;
|
||||
$t[k+1] = t[k] + h$
|
||||
}
|
||||
\caption{\textit{Explicite Euler Method}}
|
||||
|
|
@ -337,14 +337,14 @@ Untuk diterapkan dalam komputer, dapat mengikuti algoritme~\ref{algo:eEuler}.
|
|||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[scale=.5]{BAB2/img/equler_explicit.png}
|
||||
\caption[]{Area stabilitas metode explicit euler. (\kutip{Fabien2009})}
|
||||
\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}
|
||||
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}
|
||||
|
|
|
|||
|
|
@ -7,7 +7,8 @@ bidan kendali multi-robot, khususnya dalam kendali formasi.
|
|||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[scale=.8]{BAB3/img/kerangka_pen.png}
|
||||
% \includegraphics[scale=.8]{BAB3/img/kerangka_pen.png}
|
||||
\input{BAB3/img/structur.tex}
|
||||
\caption{Kerangka Penelitian}
|
||||
\label{fig:krangka_pen}
|
||||
\end{figure}
|
||||
|
|
@ -17,19 +18,21 @@ bidan kendali multi-robot, khususnya dalam kendali formasi.
|
|||
Kendali formasi adalah kendali multi-agent untuk mencapai suatu formasi yang diinginkan.
|
||||
Banyak metode yang telah digunakan berdasarkan berbagai macam kategori.
|
||||
Dapat diperhatikan dalam gambar~\ref{fig:krangka_pen}, dari berbagai metode teresebut
|
||||
dapat disimpulkan dalam 3 kategori secara general.
|
||||
dapat disimpulkan dalam 3 kategori secara general.
|
||||
Yaitu berbasis posisi, pergerakan, dan jarak.
|
||||
Pembagian kategori tersebut berdasarkan kemampuan sensor yang digunakan dan
|
||||
penggunaan komunikasi dalam metodenya.
|
||||
penggunaan komunikasi dalam metodenya.
|
||||
Dari ketiga kategori tersebut, kendali formati berbasis jarak sangat dibutuhkan pembahasan
|
||||
mengenai penerapan metode tersebut pada agent yang nyata.
|
||||
Pada penelitian oleh \kutip{Rozenheck2015}, kendali formasi berdasarkan jarak menggunakan
|
||||
kendali PI untuk mengendalikan multi-robot dan menghasilkan pergerakan yang baik.
|
||||
Maka dari itu sebagai langkah awal, kerangka kendali-PI dapat terapkan menggunakan agent nyata.
|
||||
Pada penelitian oleh \kutip{Rozenheck2015}, kendali formasi berdasarkan jarak dikendalikan
|
||||
menggunakan kendali PI dan menghasilkan pergerakan yang baik.
|
||||
Dalam penelitian ini akan difokuskan pada kendali formasi berbasis jarak
|
||||
dengan mengembangkan kendali PI yang telah dilakukan sebelumnya beserta menggunakan
|
||||
model nyata.
|
||||
|
||||
\section{Permasalah dan Solusi}
|
||||
|
||||
Pada krangka kendali-PI pada persamaan~\eqref{eq:ss-formasi}, state yang digunakan membutuhkan
|
||||
Pada krangka kendali-PI pada persamaan~\eqref{eq:ss-formasi}, state yang digunakan membutuhkan
|
||||
koordinat relatif dari tetangganya. Akan tetapi pada batasan penelitian ini, sensor yang digunakan
|
||||
hanya memberikan jarak terhadap tetangganya. Secara pendekatan, digunakan koordinat polar dan diubah
|
||||
ke koordinat kartesian. Akan tetapi koordinat polar membutuhkan sudut antara agent dan tetangganya.
|
||||
|
|
@ -39,6 +42,6 @@ untuk menentukan sudutnya.
|
|||
Algoritma \textit{cosinus} tersebut hanya berlaku apabila tetangga tidak melakukan pergerakan dan
|
||||
akan dijalankan algoritma tersebut ketika inisialisasi.
|
||||
Ketika tetangga melakukan pergerakan, tetangga mengirimkan informasi percepatan koordinatnya pada agent.
|
||||
Kegunaannya adalah sebagai refrensi perubahan koordinat terhadap tetangga.
|
||||
Kegunaannya adalah sebagai referensi perubahan koordinat terhadap tetangga.
|
||||
Sehingga harapanya adalah kerangka kendali-PI dapat digunakan menggunakan sensor yang hanya mendeteksi jarak saja.
|
||||
|
||||
|
|
|
|||
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|
||||
|
|
@ -18,7 +18,12 @@ set point dan membahas parameter kendali state-space feedback agar mencapai kri-
|
|||
teria yang diinginkan.
|
||||
|
||||
\subsubsection{State Feedback}
|
||||
\todo{Gambar grafik state space feedback}
|
||||
\begin{figure}
|
||||
\centering
|
||||
\input{BAB4/img/statefeedback.tex}
|
||||
\caption{State-feedback Sistem}
|
||||
\label{fig:state-feedback}
|
||||
\end{figure}
|
||||
Pada persamaan~\eqref{eq:ss1} diketahui bahwa state memiliki dimensi $6 \times 1$. Dimensi
|
||||
tersebut tidak menunjukan sistem memiliki orde 6. Apabila diperhatikan orde
|
||||
dari sistem adalah orde 2. Dengan membaginya kedalam 3 persamaan state-space
|
||||
|
|
@ -156,7 +161,7 @@ Untuk mendesain parameter K pada \textit{state feedback},
|
|||
diasumsikan bahwa \textit{state} pada sistem dapat diperoleh dari sensor, $x(t)$ untuk semua $t$.
|
||||
Persamaan rumus masukan ke sistem menjadi
|
||||
\begin{align}
|
||||
u(t) = -K_sx(t)
|
||||
u(t) = -K_s x(t)
|
||||
\end{align}
|
||||
sehingga persamaan \textit{state space} menjadi berikut.
|
||||
\begin{align}
|
||||
|
|
@ -268,7 +273,7 @@ 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].
|
||||
\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
|
||||
|
|
@ -293,8 +298,8 @@ Dengan memanfaatkan kedua strategi tersebut dapat digunakan untuk
|
|||
mengkalkulasi koordinat robot $B$ relatif terhadap robot $A$
|
||||
\begin{align}
|
||||
x_B^A = \begin{bmatrix}
|
||||
x_B = d_a[k].\cos \alpha[k] \\
|
||||
y_B = d_a[k].\sin \alpha[k]
|
||||
x_B = 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
|
||||
|
|
@ -376,11 +381,11 @@ Dengan menggunakan parameter dari penelitian oleh \kutip{CORREIA20127}, maka aka
|
|||
|
||||
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]). \\
|
||||
x[k+1] & = (I + Ah)x[k] + Bhu[k] + Khsgn(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]. \\
|
||||
x[k+1] & = (I + (A+K)h)x[k] + Bhu[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 $\lambda \leq 1$.
|
||||
|
|
|
|||
Binary file not shown.
|
|
@ -0,0 +1,428 @@
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\pgfpathcurveto{\pgfpoint{24.278153\du}{13.718589\du}}{\pgfpoint{24.419243\du}{13.843394\du}}{\pgfpoint{24.419243\du}{14.059213\du}}
|
||||
\pgfpathcurveto{\pgfpoint{24.419243\du}{14.275031\du}}{\pgfpoint{24.278153\du}{14.399839\du}}{\pgfpoint{24.278153\du}{14.399839\du}}
|
||||
\pgfpathlineto{\pgfpoint{23.937528\du}{14.059213\du}}
|
||||
\pgfpathlineto{\pgfpoint{24.278153\du}{13.718589\du}}
|
||||
\pgfusepath{fill}
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\pgfpathmoveto{\pgfpoint{24.278153\du}{13.718589\du}}
|
||||
\pgfpathcurveto{\pgfpoint{24.278153\du}{13.718589\du}}{\pgfpoint{24.419243\du}{13.843394\du}}{\pgfpoint{24.419243\du}{14.059213\du}}
|
||||
\pgfpathcurveto{\pgfpoint{24.419243\du}{14.275031\du}}{\pgfpoint{24.278153\du}{14.399839\du}}{\pgfpoint{24.278153\du}{14.399839\du}}
|
||||
\pgfpathlineto{\pgfpoint{23.937528\du}{14.059213\du}}
|
||||
\pgfpathlineto{\pgfpoint{24.278153\du}{13.718589\du}}
|
||||
\pgfusepath{stroke}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\pgfsetarrowsend{stealth}
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (24.419243\du,14.059213\du)--(25.883795\du,14.041967\du);
|
||||
}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\pgfsetarrowsend{stealth}
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (21.904601\du,14.049286\du)--(23.455813\du,14.059213\du);
|
||||
}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetmiterjoin
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\pgfsetarrowsend{stealth}
|
||||
{\pgfsetcornersarced{\pgfpoint{0.000000\du}{0.000000\du}}\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (25.811887\du,18.975969\du)--(23.916019\du,18.963903\du)--(23.935195\du,14.591173\du);
|
||||
}}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetmiterjoin
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\pgfsetarrowsend{stealth}
|
||||
{\pgfsetcornersarced{\pgfpoint{0.000000\du}{0.000000\du}}\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (37.129244\du,14.043446\du)--(37.128188\du,18.934303\du)--(28.186438\du,18.977751\du);
|
||||
}}
|
||||
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
\fill (29.809367\du,9.974961\du)--(29.809367\du,11.874961\du)--(31.809367\du,11.874961\du)--(31.809367\du,9.974961\du)--cycle;
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetmiterjoin
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (29.809367\du,9.974961\du)--(29.809367\du,11.874961\du)--(31.809367\du,11.874961\du)--(31.809367\du,9.974961\du)--cycle;
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node at (30.809367\du,11.042461\du){K};
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\pgfsetarrowsend{stealth}
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (35.480929\du,10.935868\du)--(31.858859\du,10.927412\du);
|
||||
}
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\pgfsetarrowsend{stealth}
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (18.222764\du,13.998829\du)--(19.805582\du,14.025131\du);
|
||||
}
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node[anchor=west] at (17.372771\du,13.998829\du){r};
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node[anchor=west] at (24.698449\du,13.515596\du){u};
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node[anchor=west] at (29.042810\du,13.272441\du){};
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node[anchor=west] at (25.646752\du,13.975968\du){};
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node[anchor=west] at (36.896701\du,13.603131\du){x};
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetbuttcap
|
||||
{
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
% was here!!!
|
||||
\pgfsetarrowsend{stealth}
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (41.281747\du,14.049635\du)--(43.230090\du,14.016749\du);
|
||||
}
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node[anchor=west] at (43.530186\du,14.041749\du){y};
|
||||
\definecolor{dialinecolor}{rgb}{1.000000, 1.000000, 1.000000}
|
||||
\pgfsetfillcolor{dialinecolor}
|
||||
\fill (34.048344\du,13.077600\du)--(34.048344\du,14.977600\du)--(36.048344\du,14.977600\du)--(36.048344\du,13.077600\du)--cycle;
|
||||
\pgfsetlinewidth{0.100000\du}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetdash{}{0pt}
|
||||
\pgfsetmiterjoin
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\draw (34.048344\du,13.077600\du)--(34.048344\du,14.977600\du)--(36.048344\du,14.977600\du)--(36.048344\du,13.077600\du)--cycle;
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node at (35.048344\du,14.145100\du){$\int$};
|
||||
% setfont left to latex
|
||||
\definecolor{dialinecolor}{rgb}{0.000000, 0.000000, 0.000000}
|
||||
\pgfsetstrokecolor{dialinecolor}
|
||||
\node[anchor=west] at (31.923591\du,13.615528\du){$\dot{x}$};
|
||||
\end{tikzpicture}
|
||||
Loading…
Reference in New Issue