Division of demo01.m into 3 distinct examples

README.md

@@ -6,8 +6,8 @@
 
 ### Usage
 
-	Unzip the file and run 'demo01' in Matlab. Several reproduction algorithms can be selected by commenting/uncommenting 
-	lines 89-91 and 110-112 in demo01.m (finite/infinite horizon LQR or dynamical system with constant gains). 
+	Unzip the file and run 'demo_TPGMR_LQR01' (finite horizon LQR), 'demo_TPGMR_LQR02' (infinite horizon LQR) or
+	'demo_DSGMR01' (dynamical system with constant gains) in Matlab.  
 	'demo_testLQR01', 'demo_testLQR02' and 'demo_testLQR03' can also be run as additional examples of LQR.
 
 ### Reference  

demo_DSGMR01.m

+function demo_DSGMR01
+% Demonstration a task-parameterized probabilistic model encoding movements in the form of virtual spring-damper 
+% systems acting in multiple frames of reference. Each candidate coordinate system observes a set of 
+% demonstrations from its own perspective, by extracting an attractor path whose variations depend on the 
+% relevance of the frame through the task. This information is exploited to generate a new attractor path 
+% corresponding to new situations (new positions and orientation of the frames).
+%
+% This demo presents the results for a dynamical system with constant gains.
+%  
+% Author:	Sylvain Calinon, 2014
+%         http://programming-by-demonstration.org/SylvainCalinon
+%
+% This source code is given for free! In exchange, I would be grateful if you cite  
+% the following reference in any academic publication that uses this code or part of it: 
+%
+% @inproceedings{Calinon14ICRA,
+%   author="Calinon, S. and Bruno, D. and Caldwell, D. G.",
+%   title="A task-parameterized probabilistic model with minimal intervention control",
+%   booktitle="Proc. {IEEE} Intl Conf. on Robotics and Automation ({ICRA})",
+%   year="2014",
+%   month="May-June",
+%   address="Hong Kong, China",
+%   pages="3339--3344"
+% }
+
+%% 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 (required only if LQR is not used for reproduction)
+model.kV = (2*model.kP)^.5; %Damping gain (required only if LQR is not used for reproduction)
+nbRepros = 8; %Number of reproductions with new situations randomly generated
+rFactor = 1E-1; %Weighting term for the minimization of control commands in LQR
+
+
+%% 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
+for n=1:nbSamples
+	DataTmp = s(n).Data0(2:end,:);
+	DataTmp = [s(n).Data0(1,:); K * [DataTmp; DataTmp*D; DataTmp*D*D]];
+	for m=1:model.nbFrames
+		Data(:,m,(n-1)*nbD+1:n*nbD) = s(n).p(m).A \ (DataTmp - repmat(s(n).p(m).b, 1, nbD)); 
+	end
+end
+
+
+%% Tensor GMM learning
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+fprintf('Parameters estimation of tensor GMM with EM:');
+model = init_tensorGMM_timeBased(Data, model); %Initialization 
+model = EM_tensorGMM(Data, model);
+
+
+%% Reproduction with LQR for the task parameters used to train the model
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+disp('Reproductions with LQR...');
+DataIn = [1:s(1).nbData] * model.dt;
+for n=1:nbSamples
+  %Retrieval of attractor path through task-parameterized GMR
+  a(n) = estimateAttractorPath(DataIn, model, s(n));
+  r(n) = reproduction_DS(DataIn, model, a(n), a(n).currTar(:,1)); 
+end
+
+
+%% Reproduction with LQR for new task parameters
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+disp('New reproductions with LQR...');
+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);
+    rTmp.p(m).b = s(id(1)).p(m).b * w(1) + s(id(2)).p(m).b * w(2);
+    rTmp.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
+  anew(n) = estimateAttractorPath(DataIn, model, rTmp);
+  rnew(n) = reproduction_DS(DataIn, model, anew(n), anew(n).currTar(:,1)); 
+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).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',[]);
+
+%REPROS
+subplot(1,3,2); hold on; box on; title('Reproductions with DS-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
+  %Plot Gaussians
+  plotGMM(r(n).Mu(2:3,:,1), r(n).Sigma(2:3,2:3,:,1), [.7 .7 .7]);
+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
+axis(limAxes); axis square; set(gca,'xtick',[],'ytick',[]);
+
+%NEW REPROS
+subplot(1,3,3); hold on; box on; title('New reproductions with DS-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
+  %Plot Gaussians
+  plotGMM(rnew(n).Mu(2:3,:,1), rnew(n).Sigma(2:3,2:3,:,1), [.7 .7 .7]);
+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
+axis(limAxes); axis square; set(gca,'xtick',[],'ytick',[]);
+
+%print('-dpng','outTest1.png');
+
+%Plot additional information 
+figure; 
+%Plot norm of control commands
+subplot(1,2,1); hold on;
+for n=1:nbRepros
+  plot(DataIn, rnew(n).ddxNorm, 'k-', 'linewidth', 2);
+end
+xlabel('t'); ylabel('|ddx|');
+%Plot strength of the stiffness term
+subplot(1,2,2); hold on;
+for n=1:nbRepros
+  plot(DataIn, rnew(n).kpDet, 'k-', 'linewidth', 2);
+end
+xlabel('t'); ylabel('|Kp|');
+
+%Plot accelerations due to feedback and feedforward terms
+figure; hold on;
+n=1; k=1;
+plot(r(n).FB(k,:),'r-','linewidth',2);
+plot(r(n).FF(k,:),'b-','linewidth',2);
+legend('ddx feedback','ddx feedforward');
+xlabel('t'); ylabel(['ddx_' num2str(k)]);
+
+%print('-dpng','outTest2.png');
+%pause;
+%close all;
+
+

demo_TPGMR_LQR01.m

+function demo_TPGMR_LQR01
+% Demonstration a task-parameterized probabilistic model encoding movements in the form of virtual spring-damper 
+% systems acting in multiple frames of reference. Each candidate coordinate system observes a set of 
+% demonstrations from its own perspective, by extracting an attractor path whose variations depend on the 
+% relevance of the frame through the task. This information is exploited to generate a new attractor path 
+% corresponding to new situations (new positions and orientation of the frames), while the predicted covariances 
+% are exploited by a linear quadratic regulator (LQR) to estimate the stiffness and damping feedback terms of 
+% the spring-damper systems, resulting in a minimal intervention control strategy.
+%
+% This demo presents the results for a finite horizon LQR.
+%  
+% Author:	Sylvain Calinon, 2014
+%         http://programming-by-demonstration.org/SylvainCalinon
+%
+% This source code is given for free! In exchange, I would be grateful if you cite  
+% the following reference in any academic publication that uses this code or part of it: 
+%
+% @inproceedings{Calinon14ICRA,
+%   author="Calinon, S. and Bruno, D. and Caldwell, D. G.",
+%   title="A task-parameterized probabilistic model with minimal intervention control",
+%   booktitle="Proc. {IEEE} Intl Conf. on Robotics and Automation ({ICRA})",
+%   year="2014",
+%   month="May-June",
+%   address="Hong Kong, China",
+%   pages="3339--3344"
+% }
+
+%% 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 
+nbRepros = 8; %Number of reproductions with new situations randomly generated
+rFactor = 1E-1; %Weighting term for the minimization of control commands in LQR
+
+
+%% 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');
+
+
+%% Tensor GMM learning
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+fprintf('Parameters estimation of tensor GMM with EM:');
+model = init_tensorGMM_timeBased(Data, model); %Initialization 
+model = EM_tensorGMM(Data, model);
+
+
+%% Reproduction with LQR for the task parameters used to train the model
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+disp('Reproductions with LQR...');
+DataIn = [1:s(1).nbData] * model.dt;
+for n=1:nbSamples
+  %Retrieval of attractor path through task-parameterized GMR
+  a(n) = estimateAttractorPath(DataIn, model, s(n));
+  r(n) = reproduction_LQR_finiteHorizon(DataIn, model, a(n), a(n).currTar(:,1), rFactor);
+end
+
+
+%% Reproduction with LQR for new task parameters
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+disp('New reproductions with LQR...');
+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);
+    rTmp.p(m).b = s(id(1)).p(m).b * w(1) + s(id(2)).p(m).b * w(2);
+    rTmp.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
+  anew(n) = estimateAttractorPath(DataIn, model, rTmp);
+  rnew(n) = reproduction_LQR_finiteHorizon(DataIn, model, anew(n), anew(n).currTar(:,1), rFactor);
+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).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',[]);
+
+%REPROS
+subplot(1,3,2); hold on; box on; title('Reproductions with finite horizon LQR');
+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 Gaussians
+  plotGMM(r(n).Mu(2:3,:,1), r(n).Sigma(2:3,2:3,:,1), [.7 .7 .7]);
+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
+axis(limAxes); axis square; set(gca,'xtick',[],'ytick',[]);
+
+%NEW REPROS
+subplot(1,3,3); hold on; box on; title('New reproductions with finite horizon LQR');
+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
+  %Plot Gaussians
+  plotGMM(rnew(n).Mu(2:3,:,1), rnew(n).Sigma(2:3,2:3,:,1), [.7 .7 .7]);
+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
+axis(limAxes); axis square; set(gca,'xtick',[],'ytick',[]);
+
+%print('-dpng','outTest1.png');
+
+%Plot additional information 
+figure; 
+%Plot norm of control commands
+subplot(1,2,1); hold on;
+for n=1:nbRepros
+  plot(DataIn, rnew(n).ddxNorm, 'k-', 'linewidth', 2);
+end
+xlabel('t'); ylabel('|ddx|');
+%Plot strength of the stiffness term
+subplot(1,2,2); hold on;
+for n=1:nbRepros
+  plot(DataIn, rnew(n).kpDet, 'k-', 'linewidth', 2);
+end
+xlabel('t'); ylabel('|Kp|');
+
+%Plot accelerations due to feedback and feedforward terms
+figure; hold on;
+n=1; k=1;
+plot(r(n).FB(k,:),'r-','linewidth',2);
+plot(r(n).FF(k,:),'b-','linewidth',2);
+legend('ddx feedback','ddx feedforward');
+xlabel('t'); ylabel(['ddx_' num2str(k)]);
+
+%print('-dpng','outTest2.png');
+%pause;
+%close all;
+
+

demo01.m → demo_TPGMR_LQR02.m

-function demo01
+function demo_TPGMR_LQR02
 % Demonstration a task-parameterized probabilistic model encoding movements in the form of virtual spring-damper 
 % systems acting in multiple frames of reference. Each candidate coordinate system observes a set of 
 % demonstrations from its own perspective, by extracting an attractor path whose variations depend on the 
@@ -7,8 +7,7 @@ function demo01
 % are exploited by a linear quadratic regulator (LQR) to estimate the stiffness and damping feedback terms of 
 % the spring-damper systems, resulting in a minimal intervention control strategy.
 %
-% Several reproduction algorithms can be selected by commenting/uncommenting lines 89-91 and 110-112
-% (finite/infinite horizon LQR or dynamical system with constant gains).
+% This demo presents the results for an infinite horizon LQR.
 %  
 % Author:	Sylvain Calinon, 2014
 %         http://programming-by-demonstration.org/SylvainCalinon
@@ -48,28 +47,6 @@ disp('Load 3rd order tensor data...');
 load('data/DataLQR01.mat');
 
 
-% %% Optional recomputation of 'Data' (only required when using reproduction_DS)
-% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% model.kP = 100; %Stiffness gain (required only if LQR is not used for reproduction)
-% model.kV = (2*model.kP)^.5; %Damping gain (required only if LQR is not used for reproduction)
-% 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
-% for n=1:nbSamples
-%   DataTmp = s(n).Data0(2:end,:);
-%   DataTmp = [s(n).Data0(1,:); K * [DataTmp; DataTmp*D; DataTmp*D*D]];
-%   for m=1:model.nbFrames
-%     Data(:,m,(n-1)*nbD+1:n*nbD) = s(n).p(m).A \ (DataTmp - repmat(s(n).p(m).b, 1, nbD)); 
-%   end
-% end
-
-
 %% Tensor GMM learning
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 fprintf('Parameters estimation of tensor GMM with EM:');
@@ -83,12 +60,8 @@ disp('Reproductions with LQR...');
 DataIn = [1:s(1).nbData] * model.dt;
 for n=1:nbSamples
   %Retrieval of attractor path through task-parameterized GMR
-  a(n) = estimateAttractorPath(DataIn, model, s(n));
-  
-  %Reproduction with one of the selected approach
-  %r(n) = reproduction_LQR_finiteHorizon(DataIn, model, a(n), a(n).currTar(:,1), rFactor);
+  a(n) = estimateAttractorPath(DataIn, model, s(n));  
   r(n) = reproduction_LQR_infiniteHorizon(DataIn, model, a(n), a(n).currTar(:,1), rFactor);
-  %r(n) = reproduction_DS(DataIn, model, a(n), a(n).currTar(:,1)); %This function requires to define model.kP and model.kV (see lines 38-39)
 end
 
 
@@ -105,11 +78,7 @@ for n=1:nbRepros
   end
   %Retrieval of attractor path through task-parameterized GMR
   anew(n) = estimateAttractorPath(DataIn, model, rTmp);
-  
-  %Reproduction with one of the selected approach
-  %rnew(n) = reproduction_LQR_finiteHorizon(DataIn, model, anew(n), anew(n).currTar(:,1), rFactor);
   rnew(n) = reproduction_LQR_infiniteHorizon(DataIn, model, anew(n), anew(n).currTar(:,1), rFactor);
-  %rnew(n) = reproduction_DS(DataIn, model, anew(n), anew(n).currTar(:,1)); %The fct requires to define model.kP and model.kV (see lines 38-39)
 end
 
 
@@ -137,7 +106,7 @@ end
 axis(limAxes); axis square; set(gca,'xtick',[],'ytick',[]);
 
 %REPROS
-subplot(1,3,2); hold on; box on; title('Reproductions with LQR');
+subplot(1,3,2); hold on; box on; title('Reproductions with infinite horizon LQR');
 for n=1:nbSamples
   %Plot frames
   for m=1:model.nbFrames
@@ -155,7 +124,7 @@ end
 axis(limAxes); axis square; set(gca,'xtick',[],'ytick',[]);
 
 %NEW REPROS
-subplot(1,3,3); hold on; box on; title('New reproductions with LQR');
+subplot(1,3,3); hold on; box on; title('New reproductions with infinite horizon LQR');
 for n=1:nbRepros
   %Plot frames
   for m=1:model.nbFrames
@@ -172,7 +141,7 @@ for n=1:nbRepros
 end
 axis(limAxes); axis square; set(gca,'xtick',[],'ytick',[]);
 
-print('-dpng','outTest1.png');
+%print('-dpng','outTest1.png');
 
 %Plot additional information 
 figure; 
@@ -197,8 +166,7 @@ plot(r(n).FF(k,:),'b-','linewidth',2);
 legend('ddx feedback','ddx feedforward');
 xlabel('t'); ylabel(['ddx_' num2str(k)]);
 
-print('-dpng','outTest2.png');
-
+%print('-dpng','outTest2.png');
 %pause;
 %close all;