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Plot marginals, sample

release/4.3a0
Frank Dellaert 2012-06-05 13:29:26 +00:00
parent 10d6157d1d
commit 7b48e56d56
4 changed files with 145 additions and 36 deletions
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85
examples/matlab/PlanarSLAMExample.m
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@ -20,56 +20,75 @@
% - Landmarks are 2 meters away from the robot trajectory
%% Create keys for variables
x1 = symbol('x',1); x2 = symbol('x',2); x3 = symbol('x',3);
l1 = symbol('l',1); l2 = symbol('l',2);
i1 = symbol('x',1); i2 = symbol('x',2); i3 = symbol('x',3);
j1 = symbol('l',1); j2 = symbol('l',2);
%% Create graph container and add factors to it
graph = planarSLAMGraph;
%% Add prior
% gaussian for prior
priorNoise = gtsamSharedNoiseModel_Sigmas([0.3; 0.3; 0.1]);
priorMean = gtsamPose2(0.0, 0.0, 0.0); % prior at origin
graph.addPrior(x1, priorMean, priorNoise); % add directly to graph
priorNoise = gtsamSharedNoiseModel_Sigmas([0.3; 0.3; 0.1]);
graph.addPrior(i1, priorMean, priorNoise); % add directly to graph
%% Add odometry
% general noisemodel for odometry
odometry = gtsamPose2(2.0, 0.0, 0.0);
odometryNoise = gtsamSharedNoiseModel_Sigmas([0.2; 0.2; 0.1]);
odometry = gtsamPose2(2.0, 0.0, 0.0); % create a measurement for both factors (the same in this case)
graph.addOdometry(x1, x2, odometry, odometryNoise);
graph.addOdometry(x2, x3, odometry, odometryNoise);
graph.addOdometry(i1, i2, odometry, odometryNoise);
graph.addOdometry(i2, i3, odometry, odometryNoise);
%% Add measurements
% general noisemodel for measurements
meas_model = gtsamSharedNoiseModel_Sigmas([0.1; 0.2]);
% create the measurement values - indices are (pose id, landmark id)
%% Add bearing/range measurement factors
degrees = pi/180;
bearing11 = gtsamRot2(45*degrees);
bearing21 = gtsamRot2(90*degrees);
bearing32 = gtsamRot2(90*degrees);
range11 = sqrt(4+4);
range21 = 2.0;
range32 = 2.0;
% % create bearing/range factors and add them
graph.addBearingRange(x1, l1, bearing11, range11, meas_model);
graph.addBearingRange(x2, l1, bearing21, range21, meas_model);
graph.addBearingRange(x3, l2, bearing32, range32, meas_model);
noiseModel = gtsamSharedNoiseModel_Sigmas([0.1; 0.2]);
if 1
graph.addBearingRange(i1, j1, gtsamRot2(45*degrees), sqrt(4+4), noiseModel);
graph.addBearingRange(i2, j1, gtsamRot2(90*degrees), 2, noiseModel);
else
bearingModel = gtsamSharedNoiseModel_Sigmas(0.1);
graph.addBearing(i1, j1, gtsamRot2(45*degrees), bearingModel);
graph.addBearing(i2, j1, gtsamRot2(90*degrees), bearingModel);
end
graph.addBearingRange(i3, j2, gtsamRot2(90*degrees), 2, noiseModel);
% print
graph.print('full graph');
graph.print(sprintf('\nFull graph:\n'));
%% Initialize to noisy points
initialEstimate = planarSLAMValues;
initialEstimate.insertPose(x1, gtsamPose2(0.5, 0.0, 0.2));
initialEstimate.insertPose(x2, gtsamPose2(2.3, 0.1,-0.2));
initialEstimate.insertPose(x3, gtsamPose2(4.1, 0.1, 0.1));
initialEstimate.insertPoint(l1, gtsamPoint2(1.8, 2.1));
initialEstimate.insertPoint(l2, gtsamPoint2(4.1, 1.8));
initialEstimate.insertPose(i1, gtsamPose2(0.5, 0.0, 0.2));
initialEstimate.insertPose(i2, gtsamPose2(2.3, 0.1,-0.2));
initialEstimate.insertPose(i3, gtsamPose2(4.1, 0.1, 0.1));
initialEstimate.insertPoint(j1, gtsamPoint2(1.8, 2.1));
initialEstimate.insertPoint(j2, gtsamPoint2(4.1, 1.8));
initialEstimate.print('initial estimate');
initialEstimate.print(sprintf('\nInitial estimate:\n'));
%% Optimize using Levenberg-Marquardt optimization with an ordering from colamd
result = graph.optimize(initialEstimate);
result.print('final result');
result.print(sprintf('\nFinal result:\n'));
%% Plot Covariance Ellipses
figure(1);clf;hold on
marginals = graph.marginals(result);
for i=1:3
key = symbol('x',i);
pose{i} = result.pose(key);
P{i}=marginals.marginalCovariance(key);
if i>1
plot([pose{i-1}.x;pose{i}.x],[pose{i-1}.y;pose{i}.y],'r-');
end
end
for i=1:3
plotPose2(pose{i},'g',P{i})
end
for j=1:2
key = symbol('l',j);
point{j} = result.point(key);
Q{j}=marginals.marginalCovariance(key);
plotPoint2(point{j},'b',Q{j})
end
plot([pose{1}.x;point{1}.x],[pose{1}.y;point{1}.y],'c-');
plot([pose{2}.x;point{1}.x],[pose{2}.y;point{1}.y],'c-');
plot([pose{3}.x;point{2}.x],[pose{3}.y;point{2}.y],'c-');
axis equal

79
examples/matlab/PlanarSLAMExample_sampling.m Normal file
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@ -0,0 +1,79 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% GTSAM Copyright 2010, Georgia Tech Research Corporation,
% Atlanta, Georgia 30332-0415
% All Rights Reserved
% Authors: Frank Dellaert, et al. (see THANKS for the full author list)
%
% See LICENSE for the license information
%
% @brief Simple robotics example using the pre-built planar SLAM domain
% @author Alex Cunningham
% @author Frank Dellaert
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Create the same factor graph as in PlanarSLAMExample
i1 = symbol('x',1); i2 = symbol('x',2); i3 = symbol('x',3);
graph = planarSLAMGraph;
priorMean = gtsamPose2(0.0, 0.0, 0.0); % prior at origin
priorNoise = gtsamSharedNoiseModel_Sigmas([0.3; 0.3; 0.1]);
graph.addPrior(i1, priorMean, priorNoise); % add directly to graph
odometry = gtsamPose2(2.0, 0.0, 0.0);
odometryNoise = gtsamSharedNoiseModel_Sigmas([0.2; 0.2; 0.1]);
graph.addOdometry(i1, i2, odometry, odometryNoise);
graph.addOdometry(i2, i3, odometry, odometryNoise);
%% Except, for measurements we offer a choice
j1 = symbol('l',1); j2 = symbol('l',2);
degrees = pi/180;
noiseModel = gtsamSharedNoiseModel_Sigmas([0.1; 0.2]);
if 1
graph.addBearingRange(i1, j1, gtsamRot2(45*degrees), sqrt(4+4), noiseModel);
graph.addBearingRange(i2, j1, gtsamRot2(90*degrees), 2, noiseModel);
else
bearingModel = gtsamSharedNoiseModel_Sigmas(0.1);
graph.addBearing(i1, j1, gtsamRot2(45*degrees), bearingModel);
graph.addBearing(i2, j1, gtsamRot2(90*degrees), bearingModel);
end
graph.addBearingRange(i3, j2, gtsamRot2(90*degrees), 2, noiseModel);
%% Initialize MCMC sampler with ground truth
sample = planarSLAMValues;
sample.insertPose(i1, gtsamPose2(0,0,0));
sample.insertPose(i2, gtsamPose2(2,0,0));
sample.insertPose(i3, gtsamPose2(4,0,0));
sample.insertPoint(j1, gtsamPoint2(2,2));
sample.insertPoint(j2, gtsamPoint2(4,2));
%% Calculate and plot Covariance Ellipses
figure(1);clf;hold on
marginals = graph.marginals(sample);
for i=1:3
key = symbol('x',i);
pose{i} = sample.pose(key);
P{i}=marginals.marginalCovariance(key);
if i>1
plot([pose{i-1}.x;pose{i}.x],[pose{i-1}.y;pose{i}.y],'r-');
end
end
for i=1:3
plotPose2(pose{i},'g',P{i})
end
for j=1:2
key = symbol('l',j);
point{j} = sample.point(key);
Q{j}=marginals.marginalCovariance(key);
S{j}=chol(Q{j}); % for sampling
plotPoint2(point{j},'b',Q{j})
end
plot([pose{1}.x;point{1}.x],[pose{1}.y;point{1}.y],'c-');
plot([pose{2}.x;point{1}.x],[pose{2}.y;point{1}.y],'c-');
plot([pose{3}.x;point{2}.x],[pose{3}.y;point{2}.y],'c-');
axis equal
%% Do Sampling on point 2
N=1000;
for s=1:N
delta = S{2}*randn(2,1);
proposedPoint = gtsamPoint2(point{2}.x+delta(1),point{2}.y+delta(2));
plotPoint2(proposedPoint,'k.')
end

11
examples/matlab/plotPoint2.m Normal file
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function plotPoint2(p,color,P)
% plotPose2: show a Pose2, possibly with covariance matrix
if size(color,2)==1
plot(p.x,p.y,[color '*']);
else
plot(p.x,p.y,color);
end
if nargin>2
pPp = P(1:2,1:2); % covariance matrix in pose coordinate frame
covarianceEllipse([p.x;p.y],pPp,color(1));
end

2
examples/matlab/plotPose2.m
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@ -1,6 +1,6 @@
function plotPose2(p,color,P)
% plotPose2: show a Pose2, possibly with covariance matrix
plot(p.x,p.y,[color '.']);
plot(p.x,p.y,[color '*']);
c = cos(p.theta);
s = sin(p.theta);
quiver(p.x,p.y,c,s,0.1,color);