demo_DMP_GMR03.m 5.82 KB
 Sylvain Calinon committed Sep 11, 2015 1 function demo_DMP_GMR03  Sylvain Calinon committed Sep 16, 2015 2 3 4 5 6 7 8 9 10 11 12 % Enhanced dynamic movement primitive (DMP) model trained with EM by using a Gaussian mixture % model (GMM) representation, with full covariance matrices coordinating the different variables % in the feature space. After learning (i.e., autonomous organization of the basis functions % (position and spread), Gaussian mixture regression (GMR) is used to regenerate the path of % a spring-damper system, resulting in a nonlinear force profile. % % 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. %  Sylvain Calinon committed Jan 11, 2016 13 % @article{Calinon16JIST,  Sylvain Calinon committed Sep 16, 2015 14 15 16 % author="Calinon, S.", % title="A Tutorial on Task-Parameterized Movement Learning and Retrieval", % journal="Intelligent Service Robotics",  Sylvain Calinon committed Jan 11, 2016 17 18 19 20 21 22 % publisher="Springer Berlin Heidelberg", % doi="10.1007/s11370-015-0187-9", % year="2016", % volume="9", % number="1", % pages="1--29"  Sylvain Calinon committed Sep 16, 2015 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 % } % % 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 .  Sylvain Calinon committed Sep 11, 2015 41 42 43  addpath('./m_fcts/');  Sylvain Calinon committed Sep 16, 2015 44   Sylvain Calinon committed Sep 11, 2015 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 %% Parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% model.nbStates = 5; %Number of states in the GMM model.nbVar = 3; %Number of variables [s,F1,F2] (decay term and perturbing force) model.nbVarPos = model.nbVar-1; %Dimension of spatial variables model.kP = 50; %Stiffness gain model.kV = (2*model.kP)^.5; %Damping gain (with ideal underdamped damping ratio) model.alpha = 1.0; %Decay factor model.dt = 0.01; %Duration of time step nbData = 200; %Length of each trajectory nbSamples = 4; %Number of demonstrations L = [eye(model.nbVarPos)*model.kP, eye(model.nbVarPos)*model.kV]; %Feedback term %Create transformation matrix to compute r(1).currTar = x + dx*kV/kP + ddx/kP, see Eq. (4.0.2) in doc/TechnicalReport.pdf K1d = [1, model.kV/model.kP, 1/model.kP]; K = kron(K1d,eye(model.nbVarPos));  Sylvain Calinon committed Sep 20, 2015 62 %% Load handwriting data  Sylvain Calinon committed Sep 11, 2015 63 64 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% demos=[];  Sylvain Calinon committed Sep 20, 2015 65 load('data/2Dletters/G.mat');  Sylvain Calinon committed Sep 11, 2015 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 sIn(1) = 1; %Initialization of decay term for t=2:nbData sIn(t) = sIn(t-1) - model.alpha * sIn(t-1) * model.dt; %Update of decay term (ds/dt=-alpha s) end Data=[]; DataDMP=[]; for n=1:nbSamples %Demonstration data as [x;dx;ddx] s(n).Data = spline(1:size(demos{n}.pos,2), demos{n}.pos, linspace(1,size(demos{n}.pos,2),nbData)); %Resampling s(n).Data = [s(n).Data; gradient(s(n).Data)/model.dt]; %Velocity computation s(n).Data = [s(n).Data; gradient(s(n).Data(end-model.nbVarPos+1:end,:))/model.dt]; %Acceleration computation DataDMP = [DataDMP [sIn; K*s(n).Data]]; %Training data as [s;r(1).currTar] Data = [Data s(n).Data]; %Original data as [x;dx;ddx] end %% Learning and reproduction %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %model = init_GMM_timeBased(DataDMP, model); %model = init_GMM_logBased(DataDMP, model); %Log-spread in s <-> equal spread in t model = init_GMM_kmeans(DataDMP, model); model = EM_GMM(DataDMP, model); %Spring-damper attractor path retrieval r(1).currTar = GMR(model, sIn, 1, 2:model.nbVar); %Motion retrieval with DMP x = Data(1:model.nbVarPos,1); dx = zeros(model.nbVarPos,1); for t=1:nbData %Compute acceleration, velocity and position ddx = L * [r(1).currTar(:,t)-x; -dx]; %Spring-damper system dx = dx + ddx * model.dt; x = x + dx * model.dt; r(1).Data(:,t) = x; end %% Plots %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure('position',[10,10,1300,450],'color',[1 1 1]); xx = round(linspace(1,64,model.nbStates)); clrmap = colormap('jet')*0.5; clrmap = min(clrmap(xx,:),.9); %Activation of the basis functions for i=1:model.nbStates h(i,:) = model.Priors(i) * gaussPDF(sIn, model.Mu(1,i), model.Sigma(1,1,i)); end h = h ./ repmat(sum(h,1)+realmin, model.nbStates, 1); %Spatial plot subplot(2,4,[1,5]); hold on; axis off; plot(Data(1,:),Data(2,:),'.','markersize',8,'color',[.7 .7 .7]); plot(r(1).Data(1,:),r(1).Data(2,:),'-','linewidth',3,'color',[.8 0 0]); axis equal; %Timeline plot of the nonlinear perturbing force subplot(2,4,[2:4]); hold on; for n=1:nbSamples plot(sIn, DataDMP(2,(n-1)*nbData+1:n*nbData), '-','linewidth',2,'color',[.7 .7 .7]); end for i=1:model.nbStates plotGMM(model.Mu(1:2,i), model.Sigma(1:2,1:2,i), clrmap(i,:), .7); end plot(sIn, r(1).currTar(1,:), '-','linewidth',2,'color',[.8 0 0]); axis([0 1 min(DataDMP(2,:)) max(DataDMP(2,:))]); ylabel('$\hat{x}_1$','fontsize',16,'interpreter','latex'); view(180,-90); %Timeline plot of the basis functions activation subplot(2,4,[6:8]); hold on; for i=1:model.nbStates patch([sIn(1), sIn, sIn(end)], [0, h(i,:), 0], min(clrmap(i,:)+0.5,1), 'EdgeColor', 'none', 'facealpha', .4); plot(sIn, h(i,:), 'linewidth', 2, 'color', min(clrmap(i,:)+0.2,1)); end axis([0 1 0 1]); xlabel('$s$','fontsize',16,'interpreter','latex'); ylabel('$h$','fontsize',16,'interpreter','latex'); view(180,-90); %print('-dpng','graphs/demo_DMP_GMR03.png'); pause; close all;