demo_TPGMR01.m 6.46 KB
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function demo_TPGMR01
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% Task-parameterized Gaussian mixture model (TP-GMM), with time-based GMR used for reproduction. 
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%
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% 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.
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%
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% @article{Calinon16JIST,
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%   author="Calinon, S.",
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%   title="A Tutorial on Task-Parameterized Movement Learning and Retrieval",
%   journal="Intelligent Service Robotics",
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%		publisher="Springer Berlin Heidelberg",
%		doi="10.1007/s11370-015-0187-9",
%		year="2016",
%		volume="9",
%		number="1",
%		pages="1--29"
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% }
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% 
% 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/>.
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addpath('./m_fcts/');

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%% Parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
model.nbStates = 3; %Number of Gaussians in the GMM
model.nbFrames = 2; %Number of candidate frames of reference
model.nbVar = 3; %Dimension of the datapoints in the dataset (here: t,x1,x2)
nbRepros = 8; %Number of reproductions with new situations randomly generated


%% Load 3rd order tensor data
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('Load 3rd order tensor data...');
% The MAT file contains a structure 's' with the multiple demonstrations. 's(n).Data' is a matrix data for
% sample n (with 's(n).nbData' datapoints). 's(n).p(m).b' and 's(n).p(m).A' contain the position and
% orientation of the m-th candidate coordinate system for this demonstration. 'Data' contains the observations
% in the different frames. It is a 3rd order tensor of dimension D x P x N, with D=3 the dimension of a
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% datapoint, P=2 the number of candidate frames, and N=TM the number of datapoints in a trajectory (T=200)
% multiplied by the number of demonstrations (M=5).
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load('data/Data02.mat');


%% TP-GMM learning
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
fprintf('Parameters estimation of TP-GMM with EM:');
%model = init_tensorGMM_kmeans(Data, model); 
model = init_tensorGMM_timeBased(Data, model); 
model = EM_tensorGMM(Data, model);


%% Reproduction with GMR for the task parameters used to train the model
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('Reproductions with GMR...');
DataIn = s(1).Data(1,:);
for n=1:nbSamples
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	[r(n).Mu, r(n).Sigma] = productTPGMM0(model, s(n).p); %See Eq. (6)
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	r(n).Priors = model.Priors;
	r(n).nbStates = model.nbStates;
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	r(n).Data = [DataIn; GMR(r(n), DataIn, 1, 2:model.nbVar)]; %See Eq. (17)-(19)
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end


%% Reproduction with GMR for new task parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('New reproductions with GMR...');
for n=1:nbRepros
	for m=1:model.nbFrames
		%Random generation of new task parameters
		id=ceil(rand(2,1)*nbSamples);
		w=rand(2); w=w/sum(w);
		rnew(n).p(m).b = s(id(1)).p(m).b * w(1) + s(id(2)).p(m).b * w(2);
		rnew(n).p(m).A = s(id(1)).p(m).A * w(1) + s(id(2)).p(m).A * w(2);
	end
	%Retrieval of attractor path through task-parameterized GMR
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	[rnew(n).Mu, rnew(n).Sigma] = productTPGMM0(model, rnew(n).p); %See Eq. (6)
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	rnew(n).Priors = model.Priors;
	rnew(n).nbStates = model.nbStates;
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	rnew(n).Data = [DataIn; GMR(rnew(n), DataIn, 1, 2:model.nbVar)]; %See Eq. (17)-(19)
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end


%% Plots
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure('position',[20,50,1300,500]);
xx = round(linspace(1,64,nbSamples));
clrmap = colormap('jet');
clrmap = min(clrmap(xx,:),.95);
limAxes = [-1.2 0.8 -1.1 0.9];
colPegs = [[.9,.5,.9];[.5,.9,.5]];

%DEMOS
subplot(1,3,1); hold on; box on; title('Demonstrations');
for n=1:nbSamples
	%Plot frames
	for m=1:model.nbFrames
		plot([s(n).p(m).b(2) s(n).p(m).b(2)+s(n).p(m).A(2,3)], [s(n).p(m).b(3) s(n).p(m).b(3)+s(n).p(m).A(3,3)], '-','linewidth',6,'color',colPegs(m,:));
		plot(s(n).p(m).b(2), s(n).p(m).b(3),'.','markersize',30,'color',colPegs(m,:)-[.05,.05,.05]);
	end
	%Plot trajectories
	plot(s(n).Data(2,1), s(n).Data(3,1),'.','markersize',12,'color',clrmap(n,:));
	plot(s(n).Data(2,:), s(n).Data(3,:),'-','linewidth',1.5,'color',clrmap(n,:));
end
axis(limAxes); axis square; set(gca,'xtick',[],'ytick',[]);

%REPROS
subplot(1,3,2); hold on; box on; title('Reproductions with GMR');
for n=1:nbSamples
	%Plot frames
	for m=1:model.nbFrames
		plot([s(n).p(m).b(2) s(n).p(m).b(2)+s(n).p(m).A(2,3)], [s(n).p(m).b(3) s(n).p(m).b(3)+s(n).p(m).A(3,3)], '-','linewidth',6,'color',colPegs(m,:));
		plot(s(n).p(m).b(2), s(n).p(m).b(3),'.','markersize',30,'color',colPegs(m,:)-[.05,.05,.05]);
	end
end
for n=1:nbSamples
	%Plot trajectories
	plot(r(n).Data(2,1), r(n).Data(3,1),'.','markersize',12,'color',clrmap(n,:));
	plot(r(n).Data(2,:), r(n).Data(3,:),'-','linewidth',1.5,'color',clrmap(n,:));
end
for n=1:nbSamples
	%Plot Gaussians
	plotGMM(r(n).Mu(2:3,:,1), r(n).Sigma(2:3,2:3,:,1), [.5 .5 .5],.8);
end
axis(limAxes); axis square; set(gca,'xtick',[],'ytick',[]);

%NEW REPROS
subplot(1,3,3); hold on; box on; title('New reproductions with GMR');
for n=1:nbRepros
	%Plot frames
	for m=1:model.nbFrames
		plot([rnew(n).p(m).b(2) rnew(n).p(m).b(2)+rnew(n).p(m).A(2,3)], [rnew(n).p(m).b(3) rnew(n).p(m).b(3)+rnew(n).p(m).A(3,3)], '-','linewidth',6,'color',colPegs(m,:));
		plot(rnew(n).p(m).b(2), rnew(n).p(m).b(3), '.','markersize',30,'color',colPegs(m,:)-[.05,.05,.05]);
	end
end
for n=1:nbRepros
	%Plot trajectories
	plot(rnew(n).Data(2,1), rnew(n).Data(3,1),'.','markersize',12,'color',[.2 .2 .2]);
	plot(rnew(n).Data(2,:), rnew(n).Data(3,:),'-','linewidth',1.5,'color',[.2 .2 .2]);
end
for n=1:nbRepros
	%Plot Gaussians
	plotGMM(rnew(n).Mu(2:3,:,1), rnew(n).Sigma(2:3,2:3,:,1), [.5 .5 .5],.8);
end
axis(limAxes); axis square; set(gca,'xtick',[],'ytick',[]);

%print('-dpng','graphs/demo_TPGMR01.png');
%pause;
%close all;