88 lines
2.9 KiB
Matlab
88 lines
2.9 KiB
Matlab
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% GTSAM Copyright 2010, Georgia Tech Research Corporation,
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% Atlanta, Georgia 30332-0415
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% All Rights Reserved
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% Authors: Frank Dellaert, et al. (see THANKS for the full author list)
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%
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% See LICENSE for the license information
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%
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% @brief Simple robotics example using the pre-built planar SLAM domain
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% @author Alex Cunningham
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% @author Frank Dellaert
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% Assumptions
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% - All values are axis aligned
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% - Robot poses are facing along the X axis (horizontal, to the right in images)
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% - We have bearing and range information for measurements
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% - We have full odometry for measurements
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% - The robot and landmarks are on a grid, moving 2 meters each step
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% - Landmarks are 2 meters away from the robot trajectory
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%% Create keys for variables
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x1 = 1; x2 = 2; x3 = 3;
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l1 = 1; l2 = 2;
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%% Create graph container and add factors to it
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graph = planarSLAMGraph;
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%% Add prior
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% gaussian for prior
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prior_model = SharedNoiseModel_sharedSigmas([0.3; 0.3; 0.1]);
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prior_measurement = Pose2(0.0, 0.0, 0.0); % prior at origin
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graph.addPrior(x1, prior_measurement, prior_model); % add directly to graph
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%% Add odometry
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% general noisemodel for odometry
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odom_model = SharedNoiseModel_sharedSigmas([0.2; 0.2; 0.1]);
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odom_measurement = Pose2(2.0, 0.0, 0.0); % create a measurement for both factors (the same in this case)
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graph.addOdometry(x1, x2, odom_measurement, odom_model);
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graph.addOdometry(x2, x3, odom_measurement, odom_model);
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%% Add measurements
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% general noisemodel for measurements
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meas_model = SharedNoiseModel_sharedSigmas([0.1; 0.2]);
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% create the measurement values - indices are (pose id, landmark id)
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degrees = pi/180;
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bearing11 = Rot2(45*degrees);
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bearing21 = Rot2(90*degrees);
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bearing32 = Rot2(90*degrees);
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range11 = sqrt(4+4);
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range21 = 2.0;
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range32 = 2.0;
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% create bearing/range factors and add them
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graph.addBearingRange(x1, l1, bearing11, range11, meas_model);
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graph.addBearingRange(x2, l1, bearing21, range21, meas_model);
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graph.addBearingRange(x3, l2, bearing32, range32, meas_model);
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% print
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graph.print('full graph');
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%% Initialize to noisy points
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initialEstimate = planarSLAMValues;
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initialEstimate.insertPose(x1, Pose2(0.5, 0.0, 0.2));
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initialEstimate.insertPose(x2, Pose2(2.3, 0.1,-0.2));
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initialEstimate.insertPose(x3, Pose2(4.1, 0.1, 0.1));
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initialEstimate.insertPoint(l1, Point2(1.8, 2.1));
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initialEstimate.insertPoint(l2, Point2(4.1, 1.8));
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initialEstimate.print('initial estimate');
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%% Optimize using Levenberg-Marquardt optimization with an ordering from colamd
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result = graph.optimize(initialEstimate);
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result.print('final result');
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%% Get the corresponding dense matrix
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ord = graph.orderingCOLAMD(result);
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gfg = graph.linearize(result,ord);
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denseAb = gfg.denseJacobian;
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%% Get sparse matrix A and RHS b
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IJS = gfg.sparseJacobian_();
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Ab=sparse(IJS(1,:),IJS(2,:),IJS(3,:));
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A = Ab(:,1:end-1);
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b = full(Ab(:,end));
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spy(A);
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