Commit 191b8988 authored by Sylvain Calinon's avatar Sylvain Calinon

Division of demo01.m into 3 distinct examples

parent 6e3eeead
......@@ -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
......
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;
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;
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;
......
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