benchmark_DS_GP_GMM02.m 10.3 KB
Newer Older
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262
function benchmark_DS_GP_GMM02
%Benchmark of task-parameterized model based on Gaussian process regression, 
%with trajectory model (Gaussian mixture model encoding), and DS-GMR used for reproduction
%Sylvain Calinon, 2015

addpath('./m_fcts/');

%% 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)
model.dt = 0.01; %Time step
model.kP = 100; %Stiffness gain
model.kV = (2*model.kP)^.5; %Damping gain (with ideal underdamped damping ratio)
nbRepros = 20; %Number of reproductions with new situations randomly generated
nbVarOut = model.nbVar-1;
L = [eye(nbVarOut)*model.kP, eye(nbVarOut)*model.kV];


%% 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
% datapoint, P=2 the number of candidate frames, and N=200x4 the number of datapoints in a trajectory (200)
% multiplied by the number of demonstrations (5).
load('data/DataLQR01.mat');


%% Transformation of 'Data' to learn the path of the spring-damper system
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
nbD = s(1).nbData;
nbVarOut = model.nbVar - 1;
%Create transformation matrix to compute [X; DX; DDX]
D = (diag(ones(1,nbD-1),-1)-eye(nbD)) / model.dt;
D(end,end) = 0;
%Create transformation matrix to compute XHAT = X + DX*kV/kP + DDX/kP
K1d = [1, model.kV/model.kP, 1/model.kP];
K = kron(K1d,eye(nbVarOut));
%Create 3rd order tensor data with XHAT instead of X, see Eq. (4.0.2) in doc/TechnicalReport.pdf
%Data = zeros(model.nbVar, model.nbFrames, nbD*nbSamples);
Data = s(1).Data0(1,:);
for n=1:nbSamples
	DataTmp = s(n).Data0(2:end,:);
	s(n).Data = K * [DataTmp; DataTmp*D; DataTmp*D*D];
	Data = [Data; s(n).Data]; %Data is a matrix of size M*D x T (stacking the different trajectory samples)
end

%% GPR with GMM encoding
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
fprintf('Parameters estimation of GPR with GMM encoding:');
%GMM encoding for each trajectory sample, learned at once by stacking the different trajectory samples in 'Data' matrix of size M*D x T
model.nbVar = size(Data,1); %Temporary modification of nbVar (for stacked data training)
model = init_GMM_timeBased(Data, model);
model = EM_GMM(Data, model);
model.nbVar = size(s(1).p(1).A,1); %Setting back the initial nbVar
for n=1:nbSamples
	id = (n-1)*2+2:n*2+1;
	s(n).Priors = model.Priors;
	s(n).Mu = model.Mu([1,id],:);
	s(n).Sigma = model.Sigma([1,id],[1,id],:);
% 	%Regularization of Sigma
% 	for i=1:model.nbStates
% 		[V,D] = eig(s(n).Sigma(:,:,i));
% 		U(:,:,i) = V * max(D,1E-3).^.5;
% 		s(n).Sigma(:,:,i) = U(:,:,i) * U(:,:,i)';
% 	end
	%Set query point vector (position and orientation of the two objects)
	s(n).DataIn = [s(n).p(1).b(2:3); s(n).p(1).A(2:3,3); s(n).p(2).b(2:3); s(n).p(2).A(2:3,3)];
	model.DataIn(:,n) = s(n).DataIn;
	%Set model output vector (Mu and Sigma)
	model.DataOut(:,n) = [reshape(s(n).Mu, model.nbVar*model.nbStates, 1); reshape(s(n).Sigma, model.nbVar^2*model.nbStates, 1)];
	%model.DataOut(:,n) = [reshape(s(n).Mu, model.nbVar*model.nbStates, 1); reshape(U, model.nbVar^2*model.nbStates, 1)];
end


% %% Reproduction with GPR and DS-GMR for the task parameters used to train the model
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% disp('Reproductions with DS-GMR...');
% DataIn = [1:s(1).nbData] * model.dt;
% for n=1:nbSamples
% 	%Rebuild model parameters with GPR
% 	vOut = GPR(model.DataIn, model.DataOut, s(n).DataIn);
% 	
% 	%Re-arrange GPR output as GMM parameters
% 	r(n).Mu = reshape(vOut(1:model.nbVar*model.nbStates), model.nbVar, model.nbStates);
% 	r(n).Sigma = reshape(vOut(model.nbVar*model.nbStates+1:end), model.nbVar, model.nbVar, model.nbStates);
% % 	U = reshape(vOut(model.nbVar*model.nbStates+1:end), model.nbVar, model.nbVar, model.nbStates);
% % 	for i=1:model.nbStates
% % 		r(n).Sigma(:,:,i) = U(:,:,i) * U(:,:,i)';
% % 	end
% 	r(n).Priors = model.Priors;
% 	r(n).nbStates = model.nbStates;
% 	
% 	%Regularization of Sigma
% 	for i=1:model.nbStates
% 		[V,D] = eig(r(n).Sigma(:,:,i));
% 		r(n).Sigma(:,:,i) = V * max(D,1E-3) * V';
% 	end
% 	
% % 	%Retrieval of attractor path through GMR
% % 	currTar = GMR(r(n), DataIn, 1, [2:model.nbVar]); %See Eq. (3.0.2) to (3.0.5) in doc/TechnicalReport.pdf
% % 	
% % 	%Motion retrieval with spring-damper system
% % 	x = s(n).p(1).b(2:model.nbVar);
% % 	dx = zeros(nbVarOut,1);
% % 	for t=1:s(n).nbData
% % 		%Compute acceleration, velocity and position
% % 		ddx =  -L * [x-currTar(:,t); dx]; %See Eq. (4.0.1) in doc/TechnicalReport.pdf
% % 		dx = dx + ddx * model.dt;
% % 		x = x + dx * model.dt;
% % 		r(n).Data(:,t) = x;
% % 	end
% end


%% Reproduction with GPR and DS-GMR for new task parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('New reproductions with DS-GMR...');

% %Random generation of new task parameters
% for n=1:10
% 	id=ceil(rand(2,1)*nbSamples);
% 	w=rand(2); w=w/sum(w);
% 	taskParams(n).p(1) = s(1).p(1);
% 	taskParams(n).p(2).b = s(id(1)).p(2).b * w(1) + s(id(2)).p(2).b * w(2);
% 	taskParams(n).p(2).A = s(id(1)).p(2).A * w(1) + s(id(2)).p(2).A * w(2);
% end
% for n=11:20
%   taskParams(n).p(1) = s(1).p(1);
% 	taskParams(n).p(2).b = [0; rand(1,1) * 2; rand(1,1)];
% 	aTmp = rand(1) * pi + pi;
% 	taskParams(n).p(2).A = [[1;0;0] [0;cos(aTmp);-sin(aTmp)] [0;sin(aTmp);cos(aTmp)]];
% 	taskParams(n).p(2).A(2:end,2:end) = taskParams(n).p(2).A(2:end,2:end) * norm(s(1).p(1).A(:,2));
% end
% save('data/taskParams3.mat','taskParams');

load('data/taskParams3.mat'); %Load new task parameters (new situation)

DataIn = [1:s(1).nbData] * model.dt;
for n=1:nbRepros
	rnew(n).p = taskParams(n).p;
	%Query point vector (position and orientation of the two objects)
	rnew(n).DataIn = [rnew(n).p(1).b(2:3); rnew(n).p(1).A(2:3,3); rnew(n).p(2).b(2:3); rnew(n).p(2).A(2:3,3)];
	
	%Rebuild model parameters with GPR
	vOut = GPR(model.DataIn, model.DataOut, rnew(n).DataIn);
	
	%Re-arrange GPR output as GMM parameters
	rnew(n).Mu = reshape(vOut(1:model.nbVar*model.nbStates), model.nbVar, model.nbStates);
	rnew(n).Sigma = reshape(vOut(model.nbVar*model.nbStates+1:end), model.nbVar, model.nbVar, model.nbStates);
% 	U = reshape(vOut(model.nbVar*model.nbStates+1:end), model.nbVar, model.nbVar, model.nbStates);
% 	for i=1:model.nbStates
% 		rnew(n).Sigma(:,:,i) = U(:,:,i) * U(:,:,i)';
% 	end
	rnew(n).Priors = model.Priors;
	rnew(n).nbStates = model.nbStates;
	
	%Regularization of Sigma
	for i=1:model.nbStates
		[V,D] = eig(rnew(n).Sigma(:,:,i));
		rnew(n).Sigma(:,:,i) = V * max(D,1E-3) * V';
	end
	
	%Retrieval of attractor path through GMR
	[rnew(n).currTar, rnew(n).currSigma] = GMR(rnew(n), DataIn, 1, [2:model.nbVar]); %See Eq. (3.0.2) to (3.0.5) in doc/TechnicalReport.pdf
	
	%Motion retrieval with spring-damper system
	x = rnew(n).p(1).b(2:model.nbVar);
	dx = zeros(nbVarOut,1);
	for t=1:nbD
		%Compute acceleration, velocity and position
		ddx =  -L * [x-rnew(n).currTar(:,t); dx]; %See Eq. (4.0.1) in doc/TechnicalReport.pdf 
		dx = dx + ddx * model.dt;
		x = x + dx * model.dt;
		rnew(n).Data(:,t) = x;
	end
end


%% Plots
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure('PaperPosition',[0 0 4 3],'position',[20,50,600,450]);
axes('Position',[0 0 1 1]); axis off; hold on;
set(0,'DefaultAxesLooseInset',[0,0,0,0]);
limAxes = [-1.5 2.5 -1.6 1.4]*.8;
myclr = [0.2863 0.0392 0.2392; 0.9137 0.4980 0.0078; 0.7412 0.0824 0.3137];

%Plot step-by-step
plotPegs(s(1).p(1), myclr(1,:), .5);
for n=1:nbSamples
	plotPegs(s(n).p(2), myclr(2,:), .1);
	patch([s(n).Data0(2,1:end) s(n).Data0(2,end:-1:1)], [s(n).Data0(3,1:end) s(n).Data0(3,end:-1:1)],...
		[1 1 1],'linewidth',1.5,'edgecolor',[0 0 0],'facealpha',0,'edgealpha',0.04);
end
axis equal; axis(limAxes);
h=[];
for n=1:nbSamples
	delete(h)
	h = plotPegs(s(n).p(2), myclr(2,:), .5);
	h = [h plotGMM(s(n).Mu(2:3,:),s(n).Sigma(2:3,2:3,:), [0 0 0], 1)];
	print('-dpng','-r600',['graphs/benchmark_DS_GP_GMM_intro_step' num2str(n) 'a.png']);
	h = [h plot2DArrow(s(n).p(2).b(2:3), s(n).p(2).A(2:3,3), [.8 0 0])];
	print('-dpng','-r600',['graphs/benchmark_DS_GP_GMM_intro_step' num2str(n) 'b.png']);
end

pause;
close all;
return;

%Plot demonstrations
plotPegs(s(1).p(1), myclr(1,:), .1);
for n=1:nbSamples
	plotPegs(s(n).p(2), myclr(2,:), .1);
	patch([s(n).Data0(2,1:end) s(n).Data0(2,end:-1:1)], [s(n).Data0(3,1:end) s(n).Data0(3,end:-1:1)],...
		[1 1 1],'linewidth',1.5,'edgecolor',[0 0 0],'facealpha',0,'edgealpha',0.04);
end
for n=1:nbSamples
	plotGMM(s(n).Mu(2:3,:),s(n).Sigma(2:3,2:3,:), [0 0 0], .04);
end
axis equal; axis(limAxes);
%print('-dpng','-r600',['graphs/benchmark_DS_GP_GMM_intro00.png']);

%Plot reproductions in new situations
h=[];
for n=1:nbRepros
	delete(h);
	h = plotPegs(rnew(n).p);
	%h = [h plotGMM(rnew(n).currTar, rnew(n).currSigma,  [0 .8 0], .2)];
	%h = [h plotGMM(rnew(n).Mu(2:3,:), rnew(n).Sigma(2:3,2:3,:),  myclr(3,:), .6)];
	h = [h patch([rnew(n).Data(1,:) rnew(n).Data(1,fliplr(1:nbD))], [rnew(n).Data(2,:) rnew(n).Data(2,fliplr(1:nbD))],...
		[1 1 1],'linewidth',1.5,'edgecolor',[0 0 0],'facealpha',0,'edgealpha',0.4)];
	h = [h plot(rnew(n).Data(1,1), rnew(n).Data(2,1),'.','markersize',12,'color',[0 0 0])];
	axis equal; axis(limAxes);
	print('-dpng','-r600',['graphs/benchmark_DS_GP_GMM_intro' num2str(n,'%.2d') '.png']);
	%pause
end

pause;
close all;

end

%Function to plot pegs
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function h = plotPegs(p, colPegs, fa)
if ~exist('colPegs')
	colPegs = [0.2863 0.0392 0.2392; 0.9137 0.4980 0.0078];
	fa = 0.4;
end
pegMesh = [-4 -3.5; -4 10; -1.5 10; -1.5 -1; 1.5 -1; 1.5 10; 4 10; 4 -3.5; -4 -3.5]' *1E-1;
for m=1:length(p)
	dispMesh = p(m).A(2:3,2:3) * pegMesh + repmat(p(m).b(2:3),1,size(pegMesh,2));
	h(m) = patch(dispMesh(1,:),dispMesh(2,:),colPegs(m,:),'linewidth',1,'edgecolor','none','facealpha',fa);
end
end