demo_affineTransform01.m 8.22 KB
Newer Older
1
function demo_affineTransform01
2
% Affine transformations of raw data as pre-processing step to train a task-parameterized model. 
3
%
4 5 6 7
% 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.
8
%
9
% @article{Calinon16JIST,
10
%   author="Calinon, S.",
11 12
%   title="A Tutorial on Task-Parameterized Movement Learning and Retrieval",
%   journal="Intelligent Service Robotics",
13 14 15 16 17 18
%		publisher="Springer Berlin Heidelberg",
%		doi="10.1007/s11370-015-0187-9",
%		year="2016",
%		volume="9",
%		number="1",
%		pages="1--29"
19
% }
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
% 
% 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/>.
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192

addpath('./m_fcts/');


%% Parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
model.nbFrames = 2; %Number of candidate frames of reference
model.nbVar = 2; %Dimension of the datapoints in the dataset (here: x1,x2)
model.dt = 0.01; %Time step
nbData = 200; %Number of datapoints in a trajectory


%% Load 3rd order tensor data (for [x] encoding)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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=2 the dimension of a
% 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).
load('data/Data01.mat');


%% Task parameters and observed data for [t,x] encoding
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
model2.nbVar = 3; %Dimension of the datapoints in the dataset (here: t,x1,x2)
%Create 3rd order tensor data and task parameters for [t,x]
Data2 = zeros(model2.nbVar, model.nbFrames, nbSamples*nbData);
for n=1:nbSamples
	%size(s(n).Data)
	for m=1:model.nbFrames
		s2(n).p(m).b = [0; s(n).p(m).b];
		s2(n).p(m).A = eye(model2.nbVar);
		s2(n).p(m).A(2:end,2:end) = s(n).p(m).A;
		Data2(:,m,(n-1)*nbData+1:n*nbData) = s2(n).p(m).A \ (s(n).Data0 - repmat(s2(n).p(m).b, 1, nbData));
	end
end


%% Task parameters and observed data for [x,dx] encoding
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
model3.nbVarPos = 2; %Dimension of position data (here: x1,x2)
model3.nbDeriv = 2; %Number of static&dynamic features (D=2 for [x,dx], D=3 for [x,dx,ddx], etc.)
model3.nbVar = model3.nbVarPos * model3.nbDeriv; %Dimension of state vector
%Create transformation matrix to compute derivatives
D = (diag(ones(1,nbData-1),-1)-eye(nbData)) / model.dt;
D(end,end) = 0;
%Create 3rd order tensor data and task parameters for [x,dx]
Data3 = zeros(model3.nbVar, model.nbFrames, nbSamples*nbData);
for n=1:nbSamples
	s3(n).Data = zeros(model3.nbVar, model.nbFrames, nbData);
	s3(n).Data0 = s(n).Data0(2:end,:); %Remove time
	DataTmp = s3(n).Data0;
	for k=1:model3.nbDeriv-1
		DataTmp = [DataTmp; s3(n).Data0*D^k]; %Compute derivatives
	end
	for m=1:model.nbFrames
		s3(n).p(m).b = [s(n).p(m).b; zeros((model3.nbDeriv-1)*model3.nbVarPos,1)];
		s3(n).p(m).A = kron(eye(model3.nbDeriv), s(n).p(m).A);
		s3(n).Data(:,m,:) = s3(n).p(m).A \ (DataTmp - repmat(s3(n).p(m).b, 1, nbData));
		Data3(:,m,(n-1)*nbData+1:n*nbData) = s3(n).Data(:,m,:);
	end
end


%% Plots
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure('position',[10,10,1000,700]);
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]];

%DEMOS1
subplot(3,model.nbFrames+1,1); hold on; box on; title('Demonstrations [x]');
for n=1:nbSamples
	%Plot frames
	for m=1:model.nbFrames
		plot([s(n).p(m).b(1) s(n).p(m).b(1)+s(n).p(m).A(1,2)], [s(n).p(m).b(2) s(n).p(m).b(2)+s(n).p(m).A(2,2)], '-','linewidth',6,'color',colPegs(m,:));
		plot(s(n).p(m).b(1), s(n).p(m).b(2),'.','markersize',30,'color',colPegs(m,:)-[.05,.05,.05]);
	end
	%Plot trajectories
	plot(s(n).Data0(2,1), s(n).Data0(3,1),'.','markersize',12,'color',clrmap(n,:));
	plot(s(n).Data0(2,:), s(n).Data0(3,:),'-','linewidth',1.5,'color',clrmap(n,:));
end
axis(limAxes); axis square; set(gca,'xtick',[],'ytick',[]);

%DEMOS2
subplot(3,model.nbFrames+1,4); hold on; box on; title('Demonstrations [t,x]');
for n=1:nbSamples
	%Plot frames
	for m=1:model.nbFrames
		plot([s2(n).p(m).b(2) s2(n).p(m).b(2)+s2(n).p(m).A(2,3)], [s2(n).p(m).b(3) s2(n).p(m).b(3)+s2(n).p(m).A(3,3)], '-','linewidth',6,'color',colPegs(m,:));
		plot(s2(n).p(m).b(2), s2(n).p(m).b(3),'.','markersize',30,'color',colPegs(m,:)-[.05,.05,.05]);
	end
	%Plot trajectories
	plot(s(n).Data0(2,1), s(n).Data0(3,1),'.','markersize',12,'color',clrmap(n,:));
	plot(s(n).Data0(2,:), s(n).Data0(3,:),'-','linewidth',1.5,'color',clrmap(n,:));
end
axis(limAxes); axis square; set(gca,'xtick',[],'ytick',[]);

%DEMOS3
subplot(3,model.nbFrames+1,7); hold on; box on; title('Demonstrations [x,dx]');
for n=1:nbSamples
	%Plot frames
	for m=1:model.nbFrames
		plot([s3(n).p(m).b(1) s3(n).p(m).b(1)+s3(n).p(m).A(1,2)], [s3(n).p(m).b(2) s3(n).p(m).b(2)+s3(n).p(m).A(2,2)], '-','linewidth',6,'color',colPegs(m,:));
		plot(s3(n).p(m).b(1), s3(n).p(m).b(2),'.','markersize',30,'color',colPegs(m,:)-[.05,.05,.05]);
	end
	%Plot trajectories
	plot(s(n).Data0(2,1), s(n).Data0(3,1),'.','markersize',12,'color',clrmap(n,:));
	plot(s(n).Data0(2,:), s(n).Data0(3,:),'-','linewidth',1.5,'color',clrmap(n,:));
end
axis(limAxes); axis square; set(gca,'xtick',[],'ytick',[]);

%FRAMES
for m=1:model.nbFrames
	subplot(3,model.nbFrames+1,1+m); hold on; grid on; box on; title(['Frame ' num2str(m) ' [x]']);
	for n=1:nbSamples
		plot(squeeze(Data(1,m,(n-1)*s(1).nbData+1)), ...
			squeeze(Data(2,m,(n-1)*s(1).nbData+1)), '.','markersize',15,'color',clrmap(n,:));
		plot(squeeze(Data(1,m,(n-1)*s(1).nbData+1:n*s(1).nbData)), ...
			squeeze(Data(2,m,(n-1)*s(1).nbData+1:n*s(1).nbData)), '-','linewidth',1.5,'color',clrmap(n,:));
	end
	axis square; set(gca,'xtick',[0],'ytick',[0]);
end

%FRAMES2
for m=1:model.nbFrames
	subplot(3,model.nbFrames+1,4+m); hold on; grid on; box on; title(['Frame ' num2str(m) ' [t,x]']);
	for n=1:nbSamples
		plot(squeeze(Data2(2,m,(n-1)*s(1).nbData+1)), ...
			squeeze(Data2(3,m,(n-1)*s(1).nbData+1)), '.','markersize',15,'color',clrmap(n,:));
		plot(squeeze(Data2(2,m,(n-1)*s(1).nbData+1:n*s(1).nbData)), ...
			squeeze(Data2(3,m,(n-1)*s(1).nbData+1:n*s(1).nbData)), '-','linewidth',1.5,'color',clrmap(n,:));
	end
	axis square; set(gca,'xtick',[0],'ytick',[0]);
end

%FRAMES3
for m=1:model.nbFrames
	subplot(3,model.nbFrames+1,7+m); hold on; grid on; box on; title(['Frame ' num2str(m) ' [x,dx]']);
	for n=1:nbSamples
		plot(squeeze(Data3(1,m,(n-1)*s(1).nbData+1)), ...
			squeeze(Data3(2,m,(n-1)*s(1).nbData+1)), '.','markersize',15,'color',clrmap(n,:));
		plot(squeeze(Data3(1,m,(n-1)*s(1).nbData+1:n*s(1).nbData)), ...
			squeeze(Data3(2,m,(n-1)*s(1).nbData+1:n*s(1).nbData)), '-','linewidth',1.5,'color',clrmap(n,:));
	end
	axis square; set(gca,'xtick',[0],'ytick',[0]);
end

%print('-dpng','graphs/demo_affineTransform01.png');
%pause;
%close all;