+plot distance error
+formationControl 1 dan 2 model +formationControl 2 +param sx/sy fncSpeedRefmaster
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*.csv
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INPUT /usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty
|
||||
INPUT /usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty
|
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INPUT /usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty
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INPUT /usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg
|
||||
INPUT /usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xcharter/XCharter-Roman-tlf-t1.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xcharter/XCharter-Roman-tlf-t1.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr12.tfm
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr8.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmr6.tfm
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi12.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi8.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmmi6.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmsy10.tfm
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmsy8.tfm
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmsy6.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/cm/cmex10.tfm
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm
|
||||
INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm
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INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd
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INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam7.tfm
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INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd
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INPUT /usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm
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INPUT /usr/share/texlive/texmf-dist/tex/latex/stmaryrd/Ustmry.fd
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INPUT /usr/share/texlive/texmf-dist/tex/latex/stmaryrd/Ustmry.fd
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/stmaryrd/stmary10.tfm
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/stmaryrd/stmary8.tfm
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/stmaryrd/stmary6.tfm
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INPUT /usr/share/texlive/texmf-dist/tex/latex/base/t1cmtt.fd
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INPUT /usr/share/texlive/texmf-dist/tex/latex/base/t1cmtt.fd
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/ectt1200.tfm
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xcharter/XCharter-Roman-tlf-t1.tfm
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xcharter/XCharter-Bold-tlf-t1.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xcharter/XCharter-Italic-tlf-t1.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam7.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam5.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm7.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm5.tfm
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/stmaryrd/stmary10.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/stmaryrd/stmary7.tfm
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/stmaryrd/stmary5.tfm
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OUTPUT ../DOC/RP_2015_Rozenheck.pdf
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INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/xcharter/XCharter-Roman-tlf-t1.vf
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xcharter/XCharter-Roman-tlf-t1--base.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/map/pdftex/updmap/pdftex.map
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INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/xcharter/XCharter-Roman-tlf-t1.vf
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xcharter/XCharter-Roman-tlf-t1--base.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/xcharter/XCharter-Bold-tlf-t1.vf
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xcharter/XCharter-Bold-tlf-t1--base.tfm
|
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INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/xcharter/XCharter-Roman-tlf-t1.vf
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xcharter/XCharter-Roman-tlf-t1--base.tfm
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INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/xcharter/XCharter-Italic-tlf-t1.vf
|
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xcharter/XCharter-Italic-tlf-t1--base.tfm
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xcharter/XCharter-Bold-tlf-t1.tfm
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INPUT ./IMG/fig2.png
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INPUT ./IMG/fig2.png
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INPUT ./IMG/fig2.png
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INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/xcharter/XCharter-Bold-tlf-t1.vf
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xcharter/XCharter-Bold-tlf-t1--base.tfm
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INPUT ./IMG/SIM_FIG1.png
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INPUT ./IMG/SIM_FIG1.png
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INPUT ./IMG/SIM_FIG1.png
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INPUT ./IMG/SIM_FIG2.png
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INPUT ./IMG/SIM_FIG2.png
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INPUT ./IMG/SIM_FIG2.png
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INPUT ./IMG/circle_form.png
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INPUT ./IMG/circle_form.png
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INPUT ./IMG/circle_form.png
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INPUT ./IMG/sin_form.png
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INPUT ./IMG/sin_form.png
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INPUT ./IMG/sin_form.png
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xcharter/XCharter-Bold-tlf-t1.tfm
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INPUT /usr/share/texlive/texmf-dist/fonts/vf/public/xcharter/XCharter-Bold-tlf-t1.vf
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INPUT /usr/share/texlive/texmf-dist/fonts/tfm/public/xcharter/XCharter-Bold-tlf-t1--base.tfm
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INPUT ../DOC/RP_2015_Rozenheck.aux
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INPUT /usr/share/texlive/texmf-dist/fonts/enc/dvips/xcharter/xch_tuu2ww.enc
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INPUT /usr/share/texlive/texmf-dist/fonts/enc/dvips/cm-super/cm-super-t1.enc
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/xcharter/XCharter-Bold.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/xcharter/XCharter-Italic.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/xcharter/XCharter-Roman.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr5.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/cm-super/sftt1200.pfb
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|
@ -204,7 +204,7 @@ Dalam bentuk matrix
|
|||
\end{bmatrix} +
|
||||
\begin{bmatrix}
|
||||
0 \\ k_{p2}R(x_1)^T \\ 0 \\ -k_{i2}
|
||||
\end{bmatrix} d
|
||||
\end{bmatrix} d \label{orde_dua_ss}
|
||||
\end{align}
|
||||
|
||||
\subsection{Implementasi}
|
||||
|
@ -226,6 +226,17 @@ dengan kecepatan vector $[-5;\ 5]$. Akan tetapi ada sebuah error apabila $vref$
|
|||
dengan kecepatan vector $[5;\, 5]$. Ini diakibatkan ada masalah pada rigiditas
|
||||
graph.
|
||||
|
||||
\subsubsection{ time varian bentuk diskrit }
|
||||
Sederhana dari persamaan-()\ref{orde_dua_ss})
|
||||
\begin{align}
|
||||
\dot{x} &= A(x)x + B(x) d \\
|
||||
\frac{x[k+1]-x[k]}{h} &= A(x[k])x[k] + B(x[k])d \\
|
||||
x[k+1] &= I + hA(x[k])x[k] + hB(x[k])d\\
|
||||
x]k+1] &= A_d[k] x[k] + B_d[k]d \\
|
||||
A_d[k] &= I +hA(x[k]) \\
|
||||
B_d[k] &= hB(x[k])
|
||||
\end{align}
|
||||
|
||||
\section{Kesimpulan}
|
||||
Implementasi berhasil. Penelitian mengalami kekurangan apabila vref diberikan
|
||||
pada robot yang berpotensi menghasilkan lipatan pada graph.
|
||||
|
|
|
@ -1,5 +1,7 @@
|
|||
clear -all
|
||||
|
||||
graphics_toolkit('gnuplot')
|
||||
omni = omni = omnidirectional(0.94, 0.96, 0.01, 2.2, 1.5,0.099,0.1,1.5,0.025,30,0.035,19,0.00011,1.69,0.0059,0.0059,0.9,9.1,6,'./');
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% config nang kene
|
||||
conRobot = [1 2 1;
|
||||
3 2 1;
|
||||
|
@ -14,22 +16,25 @@ corRobot = [1.5; 1.7;0;
|
|||
2; 2.5;0;
|
||||
2.5; 2.8;0;
|
||||
]; % xy xy xy
|
||||
robStateLen = length(corRobot)/length(dRobot)
|
||||
robStateLen = size(omni.origin.A,1);
|
||||
B = [
|
||||
1 0; 0 1;
|
||||
0 0; 0 0;
|
||||
0 0; 0 0;
|
||||
];
|
||||
kp = 80;
|
||||
ki = 1;
|
||||
kp = 150;
|
||||
ki = 3;
|
||||
% fvref = fncSpeedRef('ysin',50,2,robStateLen);
|
||||
% fvref = fncSpeedRef('xsin',50,2,robStateLen);
|
||||
% fvref = fncSpeedRef('cw',-300,1,robStateLen);
|
||||
% fvref = fncSpeedRef('s',50,50,robStateLen);
|
||||
fvref = fncSpeedRef('s',0,0,robStateLen);
|
||||
h = .1;
|
||||
h = .01;
|
||||
tspan = 1:h:10;
|
||||
sys = formationControl2ndBuilder(conRobot,robStateLen,kp,kp,ki,ki,length_d,1);
|
||||
% sys = formationControl2ndModelBuilder(conRobot,omni.origin,kp,kp,ki,ki,length_d,1);
|
||||
% sys = formationControl1stModelBuilder(conRobot,omni.origin,kp,kp,ki,ki,length_d,1);
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% config nang nduwur
|
||||
|
||||
[R,K,d] = rigidityMatrixFnc(conRobot,robStateLen);
|
||||
|
@ -37,16 +42,34 @@ _zero = zeros(size(R(corRobot,K),1),1);
|
|||
sInit = [corRobot; _zero;];
|
||||
sAnsInit =[_zero; _zero;];
|
||||
s2ndInit = [corRobot; %x1
|
||||
zeros(length(corRobot),1); %x2
|
||||
zeros(length(corRobot),1); %xi1
|
||||
_zero]; %xi2
|
||||
zeros(length(corRobot),1); %x2
|
||||
zeros(length(corRobot),1); %xi1
|
||||
_zero;]; %xi2
|
||||
% _zero; zeros(length(corRobot),1);]; %x2*
|
||||
s1stInit = [corRobot; zeros(size(corRobot)); zeros(size(dRobot))];
|
||||
|
||||
% state_init = sInit;
|
||||
state_init = s2ndInit;
|
||||
% state_init = s1stInit;
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% start solving
|
||||
printf("Mulai memecakan masalah \n\n");
|
||||
startExe = tic;
|
||||
|
||||
dydt = @(t, y) sys.ss(y,fvref(t));
|
||||
[t,y] = ode45(dydt, tspan, s2ndInit);
|
||||
% continue
|
||||
% dydt = @(t, y) sys.ss(y,fvref(t));
|
||||
% [t,y] = ode45(dydt, tspan, state_init);
|
||||
|
||||
% discrate taylor methode
|
||||
dydt = @(t, y) sys.dss(y, h, fvref(t))
|
||||
t(1,:) = tspan(1);
|
||||
y(1,:) = dydt(t(1), state_init);
|
||||
Dd(1,:) = [norm((K*y(1,1:9)')(1:3)) norm((K*y(1,1:9)')(4:6)) norm((K*y(1,1:9)')(7:9))]';
|
||||
for i = 2:length(tspan)
|
||||
t(i,:) = tspan(i);
|
||||
y(i,:) = dydt(t(i),y(i-1,:)');
|
||||
Dd(i,:) = [norm((K*y(i,1:9)')(1:3)) norm((K*y(i,1:9)')(4:6)) norm((K*y(i,1:9)')(7:9))]';
|
||||
endfor
|
||||
|
||||
endExe = toc(startExe);
|
||||
printf("Membutuhkan waktu %i menit, %i detik \n untuk memecahkan masalah mu \n\n",
|
||||
|
@ -111,6 +134,11 @@ str_tmp =strcat(str_tmp,sprintf("\"R%i \" )",++i));
|
|||
eval(str_tmp)
|
||||
title("Motion dari Robot");
|
||||
|
||||
figure(2)
|
||||
plot(t,Dd(:,1),t,Dd(:,2),t,Dd(:,3))
|
||||
title("distance error")
|
||||
legend()
|
||||
|
||||
csvwrite("DataOutMotion.csv", [t y])
|
||||
% save DataOutMotion.data y
|
||||
% save DataErrorEdge.data yans
|
||||
|
|
|
@ -24,9 +24,21 @@ function fncSr = fncSpeedRef(param,r,v,robStateLen)
|
|||
strSfy = strcat(sprintf("%i*cos(%i*t)",r,v));
|
||||
endif
|
||||
|
||||
elseif (param == 's')
|
||||
strSfx = strcat(sprintf("%i",r));
|
||||
strSfy = strcat(sprintf("%i",v));
|
||||
elseif (param(1) == 's')
|
||||
strSinOcos = strcat(sprintf("%s", param(3:end)));
|
||||
if (length(param) > 1)
|
||||
if (param(2) == 'y')
|
||||
strSfx = strcat(sprintf("%i*%s(%i*t)",r,strSinOcos,v));
|
||||
strSfy = strcat(sprintf("%i",0));
|
||||
% 'ysin' / 'ycos'
|
||||
else %if (param(2) == 'x')
|
||||
strSfx = strcat(sprintf("%i",0));
|
||||
strSfy = strcat(sprintf("%i*%s(%i*t)",r,strSinOcos,v));
|
||||
endif
|
||||
else
|
||||
strSfx = strcat(sprintf("%i",r));
|
||||
strSfy = strcat(sprintf("%i",v));
|
||||
endif
|
||||
else
|
||||
printf("Karepmu opo ? \n\n bukak fungsi speedRef sek diwoco komen e \n\n");
|
||||
endif
|
||||
|
|
|
@ -0,0 +1,30 @@
|
|||
function obj = formationControl1stModelBuilder(edgeL,model,kp1,kp2,ki1,ki2,dScale,nNodeVref)
|
||||
addpath("./networks-toolbox");
|
||||
obj = struct();
|
||||
robStateLen = size(model.A,1)
|
||||
[obj.R, obj.K, obj.d] = rigidityMatrixFnc(edgeL,robStateLen);
|
||||
obj.m = length(obj.d);
|
||||
obj.n = numNodes(edgeL);
|
||||
obj.nodeStateLength = robStateLen*obj.n;
|
||||
obj.stateLength = 2 * obj.nodeStateLength + obj.m;
|
||||
_nst = kron(eye(obj.n), model.Nst);
|
||||
_kst = kron([zeros(obj.n) eye(obj.n)], model.Kst);
|
||||
%obj.A = kron([zeros(obj.n) zeros(obj.n);zeros(obj.n) eye(obj.n)],model.A) + kron([zeros(obj.n) eye(obj.n);zeros(obj.n) zeros(obj.n)],eye(obj.n));
|
||||
% pilih robot mana yang ingin dijalankan dengan mengganti 0 menjadi 1
|
||||
% r 1 2 3 r 1 2 3
|
||||
% v v v v v v
|
||||
obj.A = kron([zeros(obj.n) zeros(obj.n);zeros(obj.n) diag([1 0 0])],model.A) + kron([zeros(obj.n) diag([1 0 0]);zeros(obj.n) zeros(obj.n)],eye(obj.n));
|
||||
obj.B = kron([zeros(obj.n); eye(obj.n)],model.B);
|
||||
obj.Ksgn = kron([zeros(obj.n) zeros(obj.n);zeros(obj.n) eye(obj.n)],model.K);
|
||||
obj.controller = @(set_point,st) arrayfun(model.limit_motor,_nst * set_point + _kst * st(1:(2 * obj.nodeStateLength)));
|
||||
obj.formation_controller = @(st) -obj.R(st(1:obj.nodeStateLength),obj.K)'*kp1*(obj.R(st(1:obj.nodeStateLength),obj.K)*st(1:obj.nodeStateLength)-(obj.d*dScale)) -obj.R(st(1:obj.nodeStateLength),obj.K)'*ki1*st(obj.stateLength-obj.m+1:obj.stateLength,1);
|
||||
obj.formation_control_dot = @(st) [obj.R(st(1:obj.nodeStateLength),obj.K) zeros(obj.m, obj.nodeStateLength + obj.m)];
|
||||
obj.stateA = @(st) [obj.A zeros(obj.stateLength-obj.m, obj.m); obj.formation_control_dot(st)];
|
||||
obj.stateB = [obj.B zeros(obj.stateLength-obj.m, obj.m); zeros(obj.m, size(model.B,2)*obj.n) eye(obj.m)];
|
||||
obj.stateKsgn = @(st,h) (h*[obj.Ksgn zeros(obj.stateLength-obj.m, obj.m); zeros(obj.m,obj.stateLength)])*arrayfun(model.sgn,st);
|
||||
obj.stateInput = @(st) [obj.controller(obj.formation_controller(st), st); obj.d*dScale];
|
||||
|
||||
obj.ss = @(st,vRef) obj.stateA(st)*st + obj.stateKsgn(st,1) + obj.stateB *obj.stateInput(st);
|
||||
|
||||
obj.dss = @(st,h,vRef) (eye(size(obj.stateA(st))) + (h*obj.stateA(st)))*st + obj.stateKsgn(st,h) + (h*obj.stateB)*obj.stateInput(st);
|
||||
endfunction
|
|
@ -24,10 +24,11 @@ function obj = formationControl2ndBuilder(edgeL,robStateLen,kp1,kp2,ki1,ki2,dSca
|
|||
obj.Kb(obj.n+nNodeVref) = 1;
|
||||
obj.Kb = [kron(obj.Kb,eye(robStateLen)); zeros(obj.m,robStateLen)];
|
||||
obj.d = obj.d*dScale;
|
||||
obj.ssDisc = @(st,vRef,h) (eye(obj.sizeA) + (obj.A(st)*h))*st + obj.B(st)*h*obj.d + obj.Kb*vRef;
|
||||
obj.dss = @(st,h,vRef) (eye(obj.sizeA) + (obj.A(st)*h))*st + (obj.B(st)*h)*obj.d + (obj.Kb*h)*vRef;
|
||||
obj.ss = @(st,vRef) obj.A(st)*st + obj.B(st)*obj.d + obj.Kb*vRef;
|
||||
|
||||
printf("============== Formation Control ============ \n");
|
||||
printf(" state model : %i \n", obj.nodeStateLength);
|
||||
printf(" Node : %i \n", obj.n);
|
||||
printf(" Edge : %i \n", obj.m);
|
||||
printf("Dimention State : %i \n", obj.stateLength);
|
||||
|
|
|
@ -0,0 +1,44 @@
|
|||
function obj = formationControl2ndModelBuilder(edgeL,model,kp1,kp2,ki1,ki2,dScale,nNodeVref)
|
||||
addpath("./networks-toolbox");
|
||||
% pkg load parallel
|
||||
obj = struct();
|
||||
robStateLen = size(model.syscl.A,1)
|
||||
[obj.R, obj.K, obj.d] = rigidityMatrixFnc(edgeL,robStateLen);
|
||||
obj.m = length(obj.d);
|
||||
obj.n = numNodes(edgeL);
|
||||
obj.nodeStateLength = robStateLen*obj.n;
|
||||
obj.stateLength = 4 * obj.nodeStateLength + obj.m;
|
||||
|
||||
% build matrix sistem
|
||||
obj.A1 = @(st) [zeros(obj.nodeStateLength), zeros(obj.nodeStateLength), zeros(obj.nodeStateLength),zeros(obj.nodeStateLength,obj.m), eye(obj.nodeStateLength)];
|
||||
obj.A2 = @(st) [-kp2*obj.R(st(1:(obj.nodeStateLength)),obj.K)'*obj.R(st(1:(obj.nodeStateLength)),obj.K), -kp1*eye(obj.nodeStateLength), -eye(obj.nodeStateLength), -obj.R(st(1:(obj.nodeStateLength)),obj.K)',zeros(obj.nodeStateLength)];
|
||||
obj.A3 = @(st) [zeros(obj.nodeStateLength), ki1*eye(obj.nodeStateLength), zeros(obj.nodeStateLength), zeros(obj.nodeStateLength,obj.m), zeros(obj.nodeStateLength)];
|
||||
obj.A4 = @(st) [ki2*obj.R(st(1:(obj.nodeStateLength)),obj.K), zeros(obj.m,obj.nodeStateLength), zeros(obj.m,obj.nodeStateLength), zeros(obj.m), zeros(obj.m,obj.nodeStateLength)];
|
||||
obj.MOsgn =@(st) diag([model.sgn(st(1)) model.sgn(st(2)) model.sgn(st(3))]);
|
||||
obj.MOdist = @(st) [obj.MOsgn(st(31:33)) zeros(robStateLen) zeros(robStateLen); zeros(robStateLen) obj.MOsgn(st(34:36)) zeros(robStateLen); zeros(robStateLen) zeros(robStateLen) obj.MOsgn(st(37:39))];
|
||||
obj.MO = @(st) [zeros(obj.nodeStateLength), kron(eye(robStateLen),model.syscl.B) , zeros(obj.nodeStateLength), zeros(obj.nodeStateLength,obj.m), kron(eye(robStateLen),model.syscl.A)+obj.MOdist(st)];
|
||||
obj.A = @(st) [obj.A1(st); obj.A2(st); obj.A3(st); obj.A4(st); obj.MO(st)];
|
||||
obj.sizeA = size(obj.A(ones(obj.stateLength,1)));
|
||||
|
||||
% build matrix input
|
||||
obj.B = @(st) [zeros(obj.nodeStateLength,obj.m); kp2*obj.R(st(1:(obj.nodeStateLength)),obj.K)'; zeros(obj.nodeStateLength,obj.m); -ki2*eye(obj.m,obj.m); zeros(obj.nodeStateLength,obj.m)]
|
||||
obj.sizeB = size(obj.B(ones(obj.stateLength,1)));
|
||||
|
||||
%build state space
|
||||
obj.Kb = zeros(obj.n*3,1);
|
||||
obj.Kb(obj.n+nNodeVref) = 1;
|
||||
obj.Kb = [kron(obj.Kb,eye(robStateLen)); zeros(obj.m,robStateLen); zeros(obj.nodeStateLength,robStateLen)];
|
||||
obj.d = obj.d*dScale;
|
||||
obj.dss = @(st,h,vRef) (eye(obj.sizeA) + (obj.A(st)*h))*st + obj.B(st)*h*obj.d + obj.Kb*h*vRef;
|
||||
obj.ss = @(st,vRef) obj.A(st)*st + obj.B(st)*obj.d + obj.Kb*vRef;
|
||||
|
||||
printf("============== Formation Control ============ \n");
|
||||
printf(" state model : %i \n", obj.nodeStateLength);
|
||||
printf(" Node : %i \n", obj.n);
|
||||
printf(" Edge : %i \n", obj.m);
|
||||
printf("Dimention State : %i \n", obj.stateLength);
|
||||
printf(" Dimention A : %i x %i \n", obj.sizeA);
|
||||
printf(" Dimention B : %i x %i \n", obj.sizeB);
|
||||
printf("============================================= \n");
|
||||
|
||||
endfunction
|
|
@ -0,0 +1,37 @@
|
|||
omni = omnidirectional(0.94, 0.96, 0.01, 2.2, 1.5,0.099,0.1,1.5,0.025,30,0.035,19,0.00011,1.69,0.0059,0.0059,0.9,9.1,6,'./');
|
||||
|
||||
A = kron(eye(3), [zeros(size(omni.origin.syscl.a)) eye(size(omni.origin.syscl.a)); zeros(size(omni.origin.syscl.a)) omni.origin.syscl.a]);
|
||||
B = kron(eye(3),kron([0;1],omni.origin.syscl.b));
|
||||
R = @(the) [[cos(deg2rad(the)) -sin(deg2rad(the)) 0; sin(deg2rad(the)) cos(deg2rad(the)) 0; [0 0 1];] zeros(size(omni.origin.syscl.a)); zeros(size(omni.origin.syscl.a)) zeros(size(omni.origin.syscl.a))];
|
||||
C = @(the1,the2, the3) kron(diag([1 0 0]), R(the1)) + kron(diag([0 1 0]), R(the2)) + kron(diag([0 0 1]), R(the3));
|
||||
fvref_cw = fncSpeedRef('cw',4,6,3);
|
||||
fvref_ysin = fncSpeedRef('sysin',8,6,3);
|
||||
fvref_xsin = fncSpeedRef('sxsin',8,6,3);
|
||||
finput = @(t) [fvref_cw(t)+[0 0 90*sin(deg2rad(5*t))]'; fvref_xsin(t); fvref_ysin(t);]
|
||||
|
||||
sys = @(st, input) A*st + B* input;
|
||||
dydt = @(t, y) sys(y, finput(t));
|
||||
RX = @(x,y,the) x*cos(deg2rad(the))-y*sin(deg2rad(the));
|
||||
RY = @(x,y,the) y*cos(deg2rad(the))+x*sin(deg2rad(the));
|
||||
|
||||
init = [0 0 0 0 0 0 5 7 45 0 0 0 -8 4 270 0 0 0]';
|
||||
tSpan = 1:.1:50;
|
||||
[t, y] = ode45(dydt,tSpan,init);
|
||||
for i=1:size(t,1)
|
||||
out(i,:) = C(y(i,3),y(i,9)+y(i,3),y(i,15)+y(i,3))*y(i,:)';
|
||||
u(i,:) = finput(t(i))';
|
||||
d1(i,1) = hypot(out(i,7)-out(i,1),out(i,8)-out(i,2));
|
||||
d2(i,1) = hypot(out(i,13)-out(i,1),out(i,14)-out(i,2));
|
||||
endfor
|
||||
|
||||
close all
|
||||
figure(1)
|
||||
plot(out(:,1), out(:,2), out(:,7), out(:,8), out(:,13), out(:,14));
|
||||
figure(2)
|
||||
plot(t(:,1), d1(:,1), t(:,1), d2(:,1));
|
||||
figure(3)
|
||||
plot(t(:,1), u(:,1), t(:,1), u(:,2), t(:,1), u(:,3));
|
||||
% figure(4)
|
||||
% plot(t(:,1), u(:,4), t(:,1), u(:,5),t(:,1), u(:,6));
|
||||
% figure(5)
|
||||
% plot(t(:,1), u(:,7), t(:,1), u(:,8),t(:,1), u(:,9));
|
|
@ -0,0 +1,180 @@
|
|||
## Omnidirectional Modeling API of Octave by Adnr
|
||||
function obj = omnidirectional(
|
||||
%% viscous friction coefficient related to v
|
||||
%B v (N/m/s)
|
||||
cBv%0.94
|
||||
%% viscous friction coefficient related to v n
|
||||
%B vn (N/m/s)
|
||||
, cBvn%0.96
|
||||
%% viscous friction coefficient related to ω
|
||||
%B ω (N/rad/s)
|
||||
, cBw%0.01
|
||||
%% coulomb friction coefficient related to v
|
||||
%C v (N )
|
||||
, cCv%2.2
|
||||
%% coulomb friction coefficient related to v n
|
||||
%C vn (N )
|
||||
, cCvn%1.5
|
||||
%% coulomb friction coefficient related to ω
|
||||
%C ω (N.m)
|
||||
, cCw%0.099
|
||||
%% radius of the robot
|
||||
%b(m)
|
||||
, cb%0.1
|
||||
%% mass of the robot
|
||||
%M (kg)
|
||||
, cM%1.5
|
||||
%% inertia moment of the robot
|
||||
%I n (kg.m 2 )
|
||||
, cIn%0.025
|
||||
%% angle
|
||||
%δ
|
||||
, cdlt%30
|
||||
%% radius of the wheels
|
||||
%r 1 , r 2 , r 3 (m)
|
||||
, cri%0.035
|
||||
%% reduction of the motors
|
||||
%l 1 , l 2 , l 3
|
||||
, cli%19
|
||||
%% motor’s armature inductance
|
||||
%L a 1...3 (H)
|
||||
, cLi%0.00011
|
||||
%% motor’s armature resistance
|
||||
%R a 1...3 (Ω)
|
||||
, cRai%1.69
|
||||
%% motor’s emf constant
|
||||
%K v 1...3 (V olts/rad/s)
|
||||
, cKv%0.0059
|
||||
%% motor’s torque constant
|
||||
%K t 1...3 (N.m/A)
|
||||
, cKt%0.0059
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%% Criterion of canonical second-orde system
|
||||
, zeta
|
||||
, omega
|
||||
%% Input constrain
|
||||
, InCon
|
||||
, path_file
|
||||
)
|
||||
|
||||
pkg load control
|
||||
obj = struct();
|
||||
|
||||
%%%%%%% Origin builder
|
||||
|
||||
obj.origin = struct();
|
||||
obj.origin.A = [-((3*(cli^2)*(cKt^2))/(2*cM*cRai*(cri^2)))-(cBv/cM),0,0;
|
||||
0, -((3*(cli^2)*(cKt^2))/(2*cM*cRai*(cri^2)))-(cBvn/cM),0;
|
||||
0,0,-((3*(cb^2)*(cli^2)*(cKt^2))/(2*cIn*cRai*(cri^2)))-(cBw/cIn)];
|
||||
obj.origin.B = [0, (cos(cdlt*pi/180)/cM), -(cos(cdlt*pi/180)/cM);
|
||||
-1/cM, sin(cdlt*pi/180)/cM, sin(cdlt*pi/180)/cM;
|
||||
cb/cIn, cb/cIn, cb/cIn];
|
||||
obj.origin.K = [-cCv/cM, 0,0;
|
||||
0, -cCvn/cM, 0;
|
||||
0,0,-cCw/cM];
|
||||
obj.LENGTH_STATE = size(obj.origin.A,1);
|
||||
obj.LENGTH_INTPUT = size(obj.origin.B,1);
|
||||
Q = [500 0 0; 0 500 0; 0 0 5;]
|
||||
R = eye(3)*0.3;
|
||||
kst_ = lqr(obj.origin.A,obj.origin.B,Q,R);
|
||||
nst_ = -pinv(eye(size(obj.origin.A))*inv(obj.origin.A-obj.origin.B*kst_)*obj.origin.B);
|
||||
syscl = ss(obj.origin.A-obj.origin.B*kst_, obj.origin.B*nst_, eye(3),0);
|
||||
% step(syscl);
|
||||
obj.origin.Kst = kst_;
|
||||
obj.origin.Nst = nst_;
|
||||
obj.origin.syscl = syscl
|
||||
%%%%%%%
|
||||
|
||||
A = obj.origin.A;
|
||||
B = obj.origin.B;
|
||||
K = obj.origin.K;
|
||||
obj.LENGTH_STATE = size(A,1)+3;
|
||||
obj.LENGTH_INPUT = size(B,1);
|
||||
obj.A = [zeros(size(A)),eye(size(A));zeros(size(A)),A;];
|
||||
obj.B = [zeros(size(B));B;];
|
||||
obj.K = [zeros(size(B,2),size(B,2));K];
|
||||
obj.getState = @(o) zeros(size(A,1)+3,1);
|
||||
obj.getInput = @(o) zeros(size(B,2),1);
|
||||
obj.InCon = ones(obj.LENGTH_INPUT)*InCon;
|
||||
|
||||
|
||||
%%%%%%%%% Make Controller
|
||||
obj.controllabilityTest = @(a,b) rank(ctrb(a,b));
|
||||
obj.observabilityTest = @(a,c) rank(obsv(a,c));
|
||||
s = tf('s');
|
||||
obj.Gref = omega^2/(s^2+(2*zeta*omega)*s+omega^2);
|
||||
p = pole(obj.Gref);
|
||||
Kst = zeros(3,6);
|
||||
Nst = zeros(3,6);
|
||||
Q = {
|
||||
[ 100 0; 0 10;], %x
|
||||
[ 100 0; 0 10;], %y
|
||||
[2000 0; 0 10;] %theta
|
||||
};
|
||||
R = eye(3)*1;
|
||||
for i = [1:3]
|
||||
A_ = [0 1;
|
||||
0 A(i,i)];
|
||||
B_ = [0 0 0;
|
||||
B(i,1) B(i,2) B(i,3)];
|
||||
kst_ = lqr(A_,B_,Q{i},R);
|
||||
nst_ = -pinv(eye(size(A_))*inv(A_-B_*kst_)*B_);
|
||||
% syscl = ss(A_-B_*kst_, B_*nst_, eye(2),0); % uncomment for debugging
|
||||
% step(syscl);
|
||||
j = ((i-1)*2);
|
||||
Kst(:,1+j:2+j) = kst_;
|
||||
Nst(:,1+j:2+j) = nst_;
|
||||
endfor
|
||||
obj.Kst = [Kst(:,1) Kst(:,3) Kst(:,5) Kst(:,2) Kst(:,4) Kst(:,6)];
|
||||
obj.Nst = [Nst(:,1) Nst(:,3) Nst(:,5) Nst(:,2) Nst(:,4) Nst(:,6)];
|
||||
obj.syscl = ss(obj.A-obj.B*obj.Kst,obj.B*obj.Nst,eye(size(obj.A)),[0]);
|
||||
|
||||
%%%%%%%%% Generate discrete state space function
|
||||
% sgn function, in octave comparison (x compare value) return integer
|
||||
% result of comparison used to address to value in matrix
|
||||
obj.sgn = @(x) [0,1,-1](4-(1*(x<0))-(2*(x>0))-(3*(x==0)));
|
||||
obj.origin.sgn = obj.sgn;
|
||||
obj.limit_motor = @(x) [x,6,-6](4-(1*(x<-6))-(2*(x>6))-(3*(x<6 & x>-6)));
|
||||
obj.origin.limit_motor = obj.limit_motor;
|
||||
|
||||
% Kinematic function for coordinate robot to global
|
||||
obj.rotationOrtogonal = @(the) [cos(the) sin(the) 0; -sin(the) cos(the) 0; 0 0 1];
|
||||
|
||||
% https://en.wikibooks.org/wiki/Control_Systems/State-Space_Equations#Discretization
|
||||
% x[k+1] = (1 + AT)x[k] + TBu[k] + TKsgn(x[k])
|
||||
% Not using function from control package becouse the system have K term
|
||||
obj.Aterm = @(o,T,st) (eye(o.LENGTH_STATE,o.LENGTH_STATE)+(o.A*T))*st;
|
||||
obj.Bterm = @(o,T,st,in) (T*o.B)*in;
|
||||
obj.Kterm = @(o,T,st,in) ((T*o.K)*[o.sgn(st(4));o.sgn(st(5));o.sgn(st(6))]);
|
||||
% Original state space robot
|
||||
obj.disDotState = @(o,T,st,in) o.Aterm(o,T,st)+o.Bterm(o,T,st,in)+o.Kterm(o,T,st,in);
|
||||
|
||||
obj.Uterm = @(o,st,ref) (o.Nst*ref - o.Kst*st);
|
||||
obj.Cons = @(u) [u,InCon,-InCon](1+(2*(u<-InCon)+(1*(u>InCon))));
|
||||
obj.UCons = @(o,u) [o.Cons(u(1)); o.Cons(u(2)); o.Cons(u(3))];
|
||||
obj.UIn = @(o,st,ref) o.UCons(o,o.Uterm(o,st,ref));
|
||||
% State space included controller
|
||||
obj.disDotStateCl = @(o,T,st,ref) o.disDotState(o,T,st,o.UCons(o,o.Uterm(o,st,ref)));
|
||||
obj.Y = @(o,st) [o.rotationOrtogonal(st(3))', zeros(size(A))]*st;
|
||||
|
||||
|
||||
% Time eq
|
||||
obj.disTime = @(T,ti) (ti + abs(T));
|
||||
obj.testStabilityExplicit = @(h) abs(eye(size(A))+(h*(A+K)));
|
||||
obj.testStabilityImplicit = @(h) abs(eye(size(A))-(h*(A+K)));
|
||||
|
||||
%%%%%%%%% PRINT the matrix to file used matrix in python app
|
||||
csvwrite(strcat(path_file,'A.matrix'),obj.A);
|
||||
csvwrite(strcat(path_file,'B.matrix'),obj.B);
|
||||
csvwrite(strcat(path_file,'C.matrix'),[eye(size(A)), zeros(size(A))]);
|
||||
csvwrite(strcat(path_file,'K.matrix'),obj.K);
|
||||
csvwrite(strcat(path_file,'Kst.matrix'),obj.Kst);
|
||||
csvwrite(strcat(path_file,'Nst.matrix'),obj.Nst);
|
||||
|
||||
[y,t] = step(obj.Gref);
|
||||
csvwrite(strcat(path_file,'Gref.csv'),[y,t]);
|
||||
csvwrite(strcat(path_file,'poleGref.csv'),pole(obj.Gref));
|
||||
|
||||
|
||||
endfunction
|
||||
|
|
@ -12,8 +12,9 @@ function [R,K, d] = rigidityMatrixFnc (edgeL,stateLen)
|
|||
printf("Jumlah Robot : %i \n", tmp);
|
||||
% generasi vector error menggunakan matrix
|
||||
% koneksi
|
||||
tmp = getNodes(gInc,'adjacency');
|
||||
% tmp = getNodes(gInc,'adjacency');
|
||||
K = kron(adj2inc(edgeL2adj(edgeL))',eye(stateLen));
|
||||
tmp = 1:(size(K,1)/stateLen);
|
||||
edgeVector = @(x,k) k*x;
|
||||
% hasil turunan dari fungsi edge
|
||||
str = "errBlockDiagonal = @(errVec) (blkdiag(";
|
||||
|
|
|
@ -0,0 +1,26 @@
|
|||
#Friction multiplied
|
||||
function xo = sgn( x=[x1; x2; x3])
|
||||
xo = [0;0;0;];
|
||||
if x(1) > 0 ;
|
||||
xo(1) = 1;
|
||||
elseif x(1) < 0;
|
||||
xo(1) = -1;
|
||||
else;
|
||||
%% xo(1) = x(1);
|
||||
endif;
|
||||
if x(2) > 0 ;
|
||||
xo(2) = 1;
|
||||
elseif x(2) < 0;
|
||||
xo(2) = -1;
|
||||
else;
|
||||
%% xo(2) = x(2);
|
||||
endif;
|
||||
if x(3) > 0 ;
|
||||
xo(3) = 1;
|
||||
elseif x(3) < 0;
|
||||
xo(3) = -1;
|
||||
else;
|
||||
%% xo(3) = x(3);
|
||||
endif;
|
||||
endfunction
|
||||
|
Loading…
Reference in New Issue