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rli
pbdlib-matlab
Commits
a4047af2
Commit
a4047af2
authored
Jul 24, 2017
by
Sylvain CALINON
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New example demo_LWR01.m added
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a4047af2
function
demo_LWR01
% Polynomial fitting with locally weighted regression (LWR).
%
% Writing code takes time. Polishing it and making it available to others takes longer!
% If some parts of the code were useful for your research of for a better understanding
% of the algorithms, please reward the authors by citing the related publications,
% and consider making your own research available in this way.
%
% @article{Calinon16JIST,
% author="Calinon, S.",
% title="A Tutorial on Task-Parameterized Movement Learning and Retrieval",
% journal="Intelligent Service Robotics",
% publisher="Springer Berlin Heidelberg",
% doi="10.1007/s11370-015-0187-9",
% year="2016",
% volume="9",
% number="1",
% pages="1--29"
% }
%
% Copyright (c) 2015 Idiap Research Institute, http://idiap.ch/
% Written by Sylvain Calinon, http://calinon.ch/
%
% This file is part of PbDlib, http://www.idiap.ch/software/pbdlib/
%
% PbDlib is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License version 3 as
% published by the Free Software Foundation.
%
% PbDlib is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with PbDlib. If not, see <http://www.gnu.org/licenses/>.
addpath
(
'./m_fcts/'
);
%% Parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
model
.
nbStates
=
3
;
%Number of activation functions (i.e., number of states in the GMM)
model
.
nbVarIn
=
2
;
%Degree of the polynomial (based on time input)
model
.
nbVarOut
=
2
;
%Number of motion variables [x1,x2]
nbData
=
200
;
%Length of a trajectory
nbSamples
=
5
;
%Number of demonstrations
tIn
=
linspace
(
0
,
1
,
nbData
);
%% Load handwriting data
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
demos
=
[];
load
(
'data/2Dletters/G.mat'
);
Data
=
[];
for
n
=
1
:
nbSamples
s
(
n
)
.
Data
=
spline
(
1
:
size
(
demos
{
n
}
.
pos
,
2
),
demos
{
n
}
.
pos
,
linspace
(
1
,
size
(
demos
{
n
}
.
pos
,
2
),
nbData
));
%Resampling
Data
=
[
Data
s
(
n
)
.
Data
];
%Concatenation of the multiple demonstrations
end
%% Setting of the basis functions and reproduction
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Set centroids equally spread in time
model
=
init_GMM_timeBased
(
tIn
,
model
);
%Set constant shared covariance
for
i
=
1
:
model
.
nbStates
model
.
Sigma
(:,:,
i
)
=
1E-2
;
end
%Compute activation weights
H
=
zeros
(
model
.
nbStates
,
nbData
);
for
i
=
1
:
model
.
nbStates
H
(
i
,:)
=
gaussPDF
(
tIn
,
model
.
Mu
(:,
i
),
model
.
Sigma
(:,:,
i
));
end
H
=
H
.
/
repmat
(
sum
(
H
,
1
),
model
.
nbStates
,
1
);
H2
=
repmat
(
H
,
1
,
nbSamples
);
%Nonlinear profile retrieval - LWR version 1
X
=
[];
Xr
=
[];
for
d
=
0
:
model
.
nbVarIn
X
=
[
X
,
repmat
(
tIn
.^
d
,
1
,
nbSamples
)
'
];
Xr
=
[
Xr
,
tIn
.^
d
'
];
end
Y
=
Data
'
;
for
i
=
1
:
model
.
nbStates
W
=
diag
(
H2
(
i
,:));
MuP
(:,:,
i
)
=
X
'*W*X \ X'
*
W
*
Y
;
%Weighted least squares
end
Yr
=
zeros
(
nbData
,
model
.
nbVarOut
);
for
t
=
1
:
nbData
for
i
=
1
:
model
.
nbStates
Yr
(
t
,:)
=
Yr
(
t
,:)
+
H
(
i
,
t
)
*
Xr
(
t
,:)
*
MuP
(:,:,
i
);
end
end
% %Nonlinear profile retrieval - LWR version 2
% for i=1:model.nbStates
% st(i).X = [];
% st(i).Xr = [];
% for d=0:model.polDeg
% st(i).X = [st(i).X, repmat((tIn-model.Mu(1,i)).^d,1,nbSamples)'];
% st(i).Xr = [st(i).Xr, (tIn-model.Mu(1,i)).^d'];
% end
% end
% Y = DataDMP';
% for i=1:model.nbStates
% W = diag(H2(i,:));
% MuP(:,:,i) = st(i).X' * W * st(i).X \ st(i).X' * W * Y; %Weighted least squares
% end
% Yr = zeros(nbData,model.nbVarPos);
% for t=1:nbData
% for i=1:model.nbStates
% Yr(t,:) = Yr(t,:) + H(i,t) * st(i).Xr(t,:) * MuP(:,:,i);
% end
% end
r
(
1
)
.
Data
=
Yr
'
;
%% Plots
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure
(
'PaperPosition'
,[
0
0
16
4
],
'position'
,[
10
,
10
,
1300
,
500
],
'color'
,[
1
1
1
]);
xx
=
round
(
linspace
(
1
,
64
,
model
.
nbStates
));
clrmap
=
colormap
(
'jet'
)
*
0.5
;
clrmap
=
min
(
clrmap
(
xx
,:),
.
9
);
%Spatial plot
axes
(
'Position'
,[
0
0
.
2
1
]);
hold
on
;
axis
off
;
plot
(
Data
(
1
,:),
Data
(
2
,:),
'.'
,
'markersize'
,
8
,
'color'
,[
.
7
.
7
.
7
]);
plot
(
r
(
1
)
.
Data
(
1
,:),
r
(
1
)
.
Data
(
2
,:),
'.'
,
'markersize'
,
16
,
'linewidth'
,
3
,
'color'
,[
.
8
0
0
]);
axis
square
;
axis
equal
;
%Timeline plot
axes
(
'Position'
,[
.
25
.
58
.
7
.
4
]);
hold
on
;
for
n
=
1
:
nbSamples
plot
(
tIn
,
Data
(
1
,(
n
-
1
)
*
nbData
+
1
:
n
*
nbData
),
'-'
,
'linewidth'
,
1
,
'color'
,[
.
7
.
7
.
7
]);
end
[
~
,
id
]
=
max
(
H
,[],
1
);
for
i
=
1
:
model
.
nbStates
Xr
=
[];
for
d
=
0
:
model
.
nbVarIn
Xr
=
[
Xr
,
tIn
(
id
==
i
)
.^
d
'
];
%Version 1
%Xr = [Xr, (tIn(id==i)-model.Mu(1,i)).^d']; %Version 2
end
plot
(
tIn
(
id
==
i
),
Xr
*
MuP
(:,
1
,
i
),
'.'
,
'linewidth'
,
6
,
'markersize'
,
26
,
'color'
,
min
(
clrmap
(
i
,:)
+
0.5
,
1
));
end
plot
(
tIn
,
Yr
(:,
1
),
'-'
,
'linewidth'
,
2
,
'color'
,[
.
8
0
0
]);
axis
([
min
(
tIn
)
max
(
tIn
)
min
(
Data
(
1
,:))
-
1
max
(
Data
(
1
,:))
+
1
]);
ylabel
(
'$y_{t,1}$'
,
'fontsize'
,
16
,
'interpreter'
,
'latex'
);
%Timeline plot of the basis functions activation
axes
(
'Position'
,[
.
25
.
12
.
7
.
4
]);
hold
on
;
for
i
=
1
:
model
.
nbStates
patch
([
tIn
(
1
),
tIn
,
tIn
(
end
)],
[
0
,
H
(
i
,:),
0
],
min
(
clrmap
(
i
,:)
+
0.5
,
1
),
'EdgeColor'
,
min
(
clrmap
(
i
,:)
+
0.2
,
1
),
...
'linewidth'
,
2
,
'facealpha'
,
.
4
,
'edgealpha'
,
.
4
);
end
axis
([
min
(
tIn
)
max
(
tIn
)
0
1.1
]);
xlabel
(
'$t$'
,
'fontsize'
,
16
,
'interpreter'
,
'latex'
);
ylabel
(
'$\phi(x_t)$'
,
'fontsize'
,
16
,
'interpreter'
,
'latex'
);
%print('-dpng','-r300','graphs/demo_LWR01.png');
%pause;
%close all;
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