demo_testLQR02.m 2.52 KB
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function demo_testLQR02
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% Test of the linear quadratic regulation (evaluation of the damping ratio found by the system)
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%
% Author:	Sylvain Calinon, 2014
%         http://programming-by-demonstration.org/SylvainCalinon
%
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% 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:
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%
% @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.nbVar = 2; %Dimension of the datapoints in the dataset (here: t,x1)
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model.dt = 0.01; %Time step
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nbData = 1000; %Number of datapoints
nbRepros = 1; %Number of reproductions with new situations randomly generated
rFactor = 1E-1; %Weighting term for the minimization of control commands in LQR

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%% Reproduction with LQR
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('Reproductions with LQR...');
DataIn = [1:nbData] * model.dt;
a.currTar = ones(1,nbData);
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a.currSigma = ones(1,1,nbData); %-> LQR with cost X'X + u'u
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for n=1:nbRepros
	%r(n) = reproduction_LQR_finiteHorizon(DataIn, model, a, 0, rFactor);
	r(n) = reproduction_LQR_infiniteHorizon(DataIn, model, a, 0, rFactor);
end

%% Plots
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure('position',[20,50,1300,500]);
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hold on; box on;
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%Plot target
plot(r(1).Data(1,:), a.currTar, 'r-', 'linewidth', 2);
for n=1:nbRepros
	%Plot trajectories
	plot(r(n).Data(1,:), r(n).Data(2,:), 'k-', 'linewidth', 2);
end
xlabel('t'); ylabel('x_1');

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figure;
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%Plot norm of control commands
subplot(1,3,1); hold on;
for n=1:nbRepros
	plot(DataIn, r(n).ddxNorm, 'k-', 'linewidth', 2);
end
xlabel('t'); ylabel('|ddx|');
%Plot stiffness
subplot(1,3,2); hold on;
for n=1:nbRepros
	plot(DataIn, r(n).kpDet, 'k-', 'linewidth', 2);
end
xlabel('t'); ylabel('kp');
%Plot stiffness/damping ratio (equals to optimal control ratio 1/2^.5)
subplot(1,3,3); hold on;
for n=1:nbRepros
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	%Ideal damping ratio of 1/2^.5 = 0.7071, corresponding to r(n).kvDet(1) = (2*r(n).kpDet(1))^.5
	dampingRatio = r(n).kvDet(:) ./ (2*r(n).kpDet(:).^.5);
	plot(DataIn, dampingRatio, 'k-', 'linewidth', 2);
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end
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xlabel('t'); ylabel('kv / 2 kp^{0.5}');
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pause;
close all;
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