Merged in feature/gtsam-tutorial (pull request #262)
Updated gtsam.lyx Approved-by: Frank Dellaert <dellaert@cc.gatech.edu>release/4.3a0
Yao Chen
Frank Dellaert
commit
05d973ac70
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@ -0,0 +1,7 @@
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// add unary measurement factors, like GPS, on all three poses
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noiseModel::Diagonal::shared_ptr unaryNoise =
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noiseModel::Diagonal::Sigmas(Vector2(0.1, 0.1)); // 10cm std on x,y
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graph.add(boost::make_shared<UnaryFactor>(1, 0.0, 0.0, unaryNoise));
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graph.add(boost::make_shared<UnaryFactor>(2, 2.0, 0.0, unaryNoise));
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graph.add(boost::make_shared<UnaryFactor>(3, 4.0, 0.0, unaryNoise));
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class UnaryFactor: public NoiseModelFactor1<Pose2> {
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double mx_, my_; ///< X and Y measurements
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public:
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UnaryFactor(Key j, double x, double y, const SharedNoiseModel& model):
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NoiseModelFactor1<Pose2>(model, j), mx_(x), my_(y) {}
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Vector evaluateError(const Pose2& q,
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boost::optional<Matrix&> H = boost::none) const
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{
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if (H) (*H) = (Matrix(2,3)<< 1.0,0.0,0.0, 0.0,1.0,0.0).finished();
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return (Vector(2) << q.x() - mx_, q.y() - my_).finished();
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}
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};
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@ -0,0 +1,18 @@
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Final Result:
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Values with 3 values:
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Value 1: (-1.5e-14, 1.3e-15, -1.4e-16)
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Value 2: (2, 3.1e-16, -8.5e-17)
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Value 3: (4, -6e-16, -8.2e-17)
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x1 covariance:
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0.0083 4.3e-19 -1.1e-18
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4.3e-19 0.0094 -0.0031
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-1.1e-18 -0.0031 0.0082
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x2 covariance:
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0.0071 2.5e-19 -3.4e-19
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2.5e-19 0.0078 -0.0011
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-3.4e-19 -0.0011 0.0082
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x3 covariance:
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0.0083 4.4e-19 1.2e-18
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4.4e-19 0.0094 0.0031
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1.2e-18 0.0031 0.018
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// Create an empty nonlinear factor graph
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NonlinearFactorGraph graph;
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// Add a Gaussian prior on pose x_1
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Pose2 priorMean(0.0, 0.0, 0.0);
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noiseModel::Diagonal::shared_ptr priorNoise =
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noiseModel::Diagonal::Sigmas(Vector3(0.3, 0.3, 0.1));
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graph.add(PriorFactor<Pose2>(1, priorMean, priorNoise));
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// Add two odometry factors
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Pose2 odometry(2.0, 0.0, 0.0);
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noiseModel::Diagonal::shared_ptr odometryNoise =
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noiseModel::Diagonal::Sigmas(Vector3(0.2, 0.2, 0.1));
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graph.add(BetweenFactor<Pose2>(1, 2, odometry, odometryNoise));
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graph.add(BetweenFactor<Pose2>(2, 3, odometry, odometryNoise));
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// Query the marginals
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cout.precision(2);
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Marginals marginals(graph, result);
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cout << "x1 covariance:\n" << marginals.marginalCovariance(1) << endl;
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cout << "x2 covariance:\n" << marginals.marginalCovariance(2) << endl;
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cout << "x3 covariance:\n" << marginals.marginalCovariance(3) << endl;
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@ -0,0 +1,9 @@
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// create (deliberatly inaccurate) initial estimate
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Values initial;
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initial.insert(1, Pose2(0.5, 0.0, 0.2));
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initial.insert(2, Pose2(2.3, 0.1, -0.2));
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initial.insert(3, Pose2(4.1, 0.1, 0.1));
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// optimize using Levenberg-Marquardt optimization
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Values result = LevenbergMarquardtOptimizer(graph, initial).optimize();
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Factor Graph:
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size: 3
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factor 0: PriorFactor on 1
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prior mean: (0, 0, 0)
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noise model: diagonal sigmas [0.3; 0.3; 0.1];
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factor 1: BetweenFactor(1,2)
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measured: (2, 0, 0)
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noise model: diagonal sigmas [0.2; 0.2; 0.1];
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factor 2: BetweenFactor(2,3)
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measured: (2, 0, 0)
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noise model: diagonal sigmas [0.2; 0.2; 0.1];
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Initial Estimate:
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Values with 3 values:
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Value 1: (0.5, 0, 0.2)
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Value 2: (2.3, 0.1, -0.2)
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Value 3: (4.1, 0.1, 0.1)
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Final Result:
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Values with 3 values:
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Value 1: (-1.8e-16, 8.7e-18, -9.1e-19)
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Value 2: (2, 7.4e-18, -2.5e-18)
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Value 3: (4, -1.8e-18, -3.1e-18)
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@ -0,0 +1,12 @@
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x1 covariance:
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0.09 1.1e-47 5.7e-33
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1.1e-47 0.09 1.9e-17
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5.7e-33 1.9e-17 0.01
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x2 covariance:
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0.13 4.7e-18 2.4e-18
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4.7e-18 0.17 0.02
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2.4e-18 0.02 0.02
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x3 covariance:
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0.17 2.7e-17 8.4e-18
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2.7e-17 0.37 0.06
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8.4e-18 0.06 0.03
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% Create graph container and add factors to it
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graph = NonlinearFactorGraph;
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% Create keys for variables
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i1 = symbol('x',1); i2 = symbol('x',2); i3 = symbol('x',3);
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j1 = symbol('l',1); j2 = symbol('l',2);
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% Add prior
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priorMean = Pose2(0.0, 0.0, 0.0); % prior at origin
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priorNoise = noiseModel.Diagonal.Sigmas([0.3; 0.3; 0.1]);
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% add directly to graph
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graph.add(PriorFactorPose2(i1, priorMean, priorNoise));
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% Add odometry
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odometry = Pose2(2.0, 0.0, 0.0);
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odometryNoise = noiseModel.Diagonal.Sigmas([0.2; 0.2; 0.1]);
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graph.add(BetweenFactorPose2(i1, i2, odometry, odometryNoise));
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graph.add(BetweenFactorPose2(i2, i3, odometry, odometryNoise));
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% Add bearing/range measurement factors
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degrees = pi/180;
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brNoise = noiseModel.Diagonal.Sigmas([0.1; 0.2]);
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graph.add(BearingRangeFactor2D(i1, j1, Rot2(45*degrees), sqrt(8), brNoise));
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graph.add(BearingRangeFactor2D(i2, j1, Rot2(90*degrees), 2, brNoise));
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graph.add(BearingRangeFactor2D(i3, j2, Rot2(90*degrees), 2, brNoise));
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>> result
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Values with 5 values:
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l1: (2, 2)
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l2: (4, 2)
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x1: (-1.8e-16, 5.1e-17, -1.5e-17)
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x2: (2, -5.8e-16, -4.6e-16)
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x3: (4, -3.1e-15, -4.6e-16)
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@ -0,0 +1,15 @@
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%% Initialize graph, initial estimate, and odometry noise
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datafile = findExampleDataFile('w100.graph');
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model = noiseModel.Diagonal.Sigmas([0.05; 0.05; 5*pi/180]);
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[graph,initial] = load2D(datafile, model);
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%% Add a Gaussian prior on pose x_0
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priorMean = Pose2(0, 0, 0);
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priorNoise = noiseModel.Diagonal.Sigmas([0.01; 0.01; 0.01]);
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graph.add(PriorFactorPose2(0, priorMean, priorNoise));
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%% Optimize using Levenberg-Marquardt optimization and get marginals
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optimizer = LevenbergMarquardtOptimizer(graph, initial);
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result = optimizer.optimizeSafely;
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marginals = Marginals(graph, result);
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NonlinearFactorGraph graph;
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noiseModel::Diagonal::shared_ptr priorNoise =
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noiseModel::Diagonal::Sigmas(Vector3(0.3, 0.3, 0.1));
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graph.add(PriorFactor<Pose2>(1, Pose2(0, 0, 0), priorNoise));
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// Add odometry factors
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noiseModel::Diagonal::shared_ptr model =
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noiseModel::Diagonal::Sigmas(Vector3(0.2, 0.2, 0.1));
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graph.add(BetweenFactor<Pose2>(1, 2, Pose2(2, 0, 0 ), model));
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graph.add(BetweenFactor<Pose2>(2, 3, Pose2(2, 0, M_PI_2), model));
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graph.add(BetweenFactor<Pose2>(3, 4, Pose2(2, 0, M_PI_2), model));
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graph.add(BetweenFactor<Pose2>(4, 5, Pose2(2, 0, M_PI_2), model));
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// Add the loop closure constraint
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graph.add(BetweenFactor<Pose2>(5, 2, Pose2(2, 0, M_PI_2), model));
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graph = NonlinearFactorGraph;
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priorNoise = noiseModel.Diagonal.Sigmas([0.3; 0.3; 0.1]);
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graph.add(PriorFactorPose2(1, Pose2(0, 0, 0), priorNoise));
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%% Add odometry factors
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model = noiseModel.Diagonal.Sigmas([0.2; 0.2; 0.1]);
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graph.add(BetweenFactorPose2(1, 2, Pose2(2, 0, 0 ), model));
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graph.add(BetweenFactorPose2(2, 3, Pose2(2, 0, pi/2), model));
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graph.add(BetweenFactorPose2(3, 4, Pose2(2, 0, pi/2), model));
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graph.add(BetweenFactorPose2(4, 5, Pose2(2, 0, pi/2), model));
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%% Add pose constraint
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graph.add(BetweenFactorPose2(5, 2, Pose2(2, 0, pi/2), model));
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%% Initialize graph, initial estimate, and odometry noise
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datafile = findExampleDataFile('sphere2500.txt');
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model = noiseModel.Diagonal.Sigmas([5*pi/180; 5*pi/180; 5*pi/180; 0.05; 0.05; 0.05]);
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[graph,initial] = load3D(datafile, model, true, 2500);
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plot3DTrajectory(initial, 'g-', false); % Plot Initial Estimate
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%% Read again, now with all constraints, and optimize
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graph = load3D(datafile, model, false, 2500);
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graph.add(NonlinearEqualityPose3(0, initial.atPose3(0)));
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optimizer = LevenbergMarquardtOptimizer(graph, initial);
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result = optimizer.optimizeSafely();
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plot3DTrajectory(result, 'r-', false); axis equal;
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%% Add factors for all measurements
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noise = noiseModel.Isotropic.Sigma(2, measurementNoiseSigma);
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for i = 1:length(Z),
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for k = 1:length(Z{i})
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j = J{i}{k};
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G.add(GenericProjectionFactorCal3_S2(
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Z{i}{k}, noise, symbol('x', i), symbol('p', j), K));
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end
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end
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int relinearizeInterval = 3;
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NonlinearISAM isam(relinearizeInterval);
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// ... first frame initialization omitted ...
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// Loop over the different poses, adding the observations to iSAM
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for (size_t i = 1; i < poses.size(); ++i) {
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// Add factors for each landmark observation
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NonlinearFactorGraph graph;
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for (size_t j = 0; j < points.size(); ++j) {
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graph.add(
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GenericProjectionFactor<Pose3, Point3, Cal3_S2>
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(z[i][j], noise,Symbol('x', i), Symbol('l', j), K)
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);
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}
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// Add an initial guess for the current pose
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Values initialEstimate;
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initialEstimate.insert(Symbol('x', i), initial_x[i]);
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// Update iSAM with the new factors
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isam.update(graph, initialEstimate);
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}
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>> graph.error(initialEstimate)
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ans =
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20.1086
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>> graph.error(result)
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ans =
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8.2631e-18
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@ -0,0 +1,23 @@
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>> priorNoise
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diagonal sigmas [0.3; 0.3; 0.1];
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>> graph
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size: 6
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factor 0: PriorFactor on 1
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prior mean: (0, 0, 0)
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noise model: diagonal sigmas [0.3; 0.3; 0.1];
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factor 1: BetweenFactor(1,2)
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measured: (2, 0, 0)
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noise model: diagonal sigmas [0.2; 0.2; 0.1];
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factor 2: BetweenFactor(2,3)
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measured: (2, 0, 1.6)
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noise model: diagonal sigmas [0.2; 0.2; 0.1];
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factor 3: BetweenFactor(3,4)
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measured: (2, 0, 1.6)
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noise model: diagonal sigmas [0.2; 0.2; 0.1];
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factor 4: BetweenFactor(4,5)
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measured: (2, 0, 1.6)
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noise model: diagonal sigmas [0.2; 0.2; 0.1];
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factor 5: BetweenFactor(5,2)
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measured: (2, 0, 1.6)
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noise model: diagonal sigmas [0.2; 0.2; 0.1];
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@ -0,0 +1,7 @@
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>> whos
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Name Size Bytes Class
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graph 1x1 112 gtsam.NonlinearFactorGraph
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priorNoise 1x1 112 gtsam.noiseModel.Diagonal
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model 1x1 112 gtsam.noiseModel.Diagonal
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initialEstimate 1x1 112 gtsam.Values
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optimizer 1x1 112 gtsam.LevenbergMarquardtOptimizer
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@ -0,0 +1,124 @@
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\global\long\def\Vector#1{{\bf #1}}
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\global\long\def\Matrix#1{{\bf #1}}
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\global\long\def\eq#1{equation (\ref{eq:=0000231})}
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\global\long\def\eye#1{\Vector{I_{#1}}}
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\global\long\def\leftsparrow#1{\stackrel{#1}{\leftarrow}}
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\global\long\def\rightsparrow#1{\stackrel{#1}{\rightarrow}}
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\global\long\def\chain{\mathcal{M}}
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\global\long\def\define{\stackrel{\Delta}{=}}
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\global\long\def\argmin#1{\mathop{\textrm{argmin \,}}_{#1}}
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\global\long\def\Norm#1{\Vert#1\Vert}
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\global\long\def\SqrNorm#1{\Vert#1\Vert^{2}}
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\global\long\def\Ltwo#1{\mathcal{L}^{2}\left(#1\right)}
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\global\long\def\Normal#1#2#3{\mathcal{N}(#1;#2,#3)}
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\global\long\def\LogNormal#1#2#3{ (#1-#2)^{T} #3^{-1} (#1-#2) }
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\global\long\def\SqrMah#1#2#3{\Vert{#1}-{#2}\Vert_{#3}^{2}}
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\global\long\def\SqrZMah#1#2{\Vert{#1}\Vert_{#2}^{2}}
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\global\long\def\Info#1#2#3{\mathcal{N}^{-1}(#1;#2,#3)}
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\providecommand{\half}{\frac{1}{2}}
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\global\long\def\Mah#1#2#3{\Vert{#1}-{#2}\Vert_{#3}}
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\global\long\def\MahDeriv#1#2#3#4{\biggl(\deriv{#2}{#4}\biggr)^{T} #3^{-1} (#1-#2)}
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\global\long\def\argmin#1{\mathop{\textrm{argmin \,}}_{#1}}
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\global\long\def\argmax#1{\mathop{\textrm{argmax \,}}_{#1}}
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\global\long\def\deriv#1#2{\frac{\partial#1}{\partial#2}}
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\global\long\def\at#1#2{#1\biggr\rvert_{#2}}
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\global\long\def\Jac#1#2#3{ \at{\deriv{#1}{#2}} {#3} }
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\global\long\def\Rone{\mathbb{R}}
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\global\long\def\Pone{\mathbb{P}}
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\global\long\def\Rtwo{\mathbb{R}^{2}}
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\global\long\def\Ptwo{\mathbb{P}^{2}}
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\global\long\def\Stwo{\mathbb{S}^{2}}
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\global\long\def\Complex{\mathbb{C}}
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\global\long\def\Z{\mathbb{Z}}
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\global\long\def\Rplus{\mathbb{R}^{+}}
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\global\long\def\SOtwo{SO(2)}
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\global\long\def\sotwo{\mathfrak{so(2)}}
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\global\long\def\skew#1{[#1]_{+}}
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\global\long\def\SEtwo{SE(2)}
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\global\long\def\setwo{\mathfrak{se(2)}}
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\global\long\def\Skew#1{[#1]_{\times}}
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\global\long\def\Rthree{\mathbb{R}^{3}}
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\global\long\def\Pthree{\mathbb{P}^{3}}
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\global\long\def\SOthree{SO(3)}
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\global\long\def\sothree{\mathfrak{so(3)}}
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\global\long\def\Rsix{\mathbb{R}^{6}}
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\global\long\def\SEthree{SE(3)}
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\global\long\def\sethree{\mathfrak{se(3)}}
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\global\long\def\Rn{\mathbb{R}^{n}}
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\global\long\def\Afftwo{Aff(2)}
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\global\long\def\afftwo{\mathfrak{aff(2)}}
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\global\long\def\SLthree{SL(3)}
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\global\long\def\slthree{\mathfrak{sl(3)}}
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\global\long\def\stirling#1#2{\genfrac{\{}{\}}{0pt}{}{#1}{#2}}
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|
||||
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|
||||
|
||||
|
||||
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|
||||
|
||||
|
|
@ -0,0 +1,133 @@
|
|||
@String { ICCV = {Intl. Conf. on Computer Vision (ICCV)} }
|
||||
@String { IROS = {IEEE/RSJ Intl. Conf. on Intelligent Robots and Systems (IROS)} }
|
||||
@String { CVPR = {IEEE Conf. on Computer Vision and Pattern Recognition (CVPR)} }
|
||||
@String { IJRR = {Intl. J. of Robotics Research} }
|
||||
@String { RAS = {Robotics and Autonomous Systems} }
|
||||
@String { TRO = {{IEEE} Trans. Robotics} }
|
||||
@String { IT = {{IEEE} Trans. Inform. Theory} }
|
||||
@String { ISRR = {Proc. of the Intl. Symp. of Robotics Research (ISRR)} }
|
||||
|
||||
@inproceedings{Davison03iccv,
|
||||
title = {Real-Time Simultaneous Localisation and Mapping with a Single Camera},
|
||||
author = {A.J. Davison},
|
||||
booktitle = ICCV,
|
||||
year = {2003},
|
||||
month = {Oct},
|
||||
pages = {1403-1410}
|
||||
}
|
||||
|
||||
@inproceedings{Dellaert10iros,
|
||||
title = {Subgraph-preconditioned Conjugate Gradient for Large Scale SLAM},
|
||||
author = {F. Dellaert and J. Carlson and V. Ila and K. Ni and C.E. Thorpe},
|
||||
booktitle = IROS,
|
||||
year = {2010},
|
||||
}
|
||||
|
||||
@inproceedings{Dellaert99b,
|
||||
title = {Using the Condensation Algorithm for Robust, Vision-based Mobile Robot Localization},
|
||||
author = {F. Dellaert and D. Fox and W. Burgard and S. Thrun},
|
||||
booktitle = CVPR,
|
||||
year = {1999}
|
||||
}
|
||||
|
||||
@article{Dellaert06ijrr,
|
||||
title = {Square {Root} {SAM}: Simultaneous Localization and Mapping via Square Root Information Smoothing},
|
||||
author = {F. Dellaert and M. Kaess},
|
||||
journal = IJRR,
|
||||
year = {2006},
|
||||
month = {Dec},
|
||||
number = {12},
|
||||
pages = {1181--1203},
|
||||
volume = {25},
|
||||
}
|
||||
|
||||
@article{DurrantWhyte06ram,
|
||||
title = {Simultaneous Localisation and Mapping ({SLAM}): Part {I} The Essential Algorithms},
|
||||
author = {H.F. Durrant-Whyte and T. Bailey},
|
||||
journal = {Robotics \& Automation Magazine},
|
||||
year = {2006},
|
||||
month = {Jun},
|
||||
}
|
||||
|
||||
@inproceedings{Jian11iccv,
|
||||
title = {Generalized Subgraph Preconditioners for Large-Scale Bundle Adjustment},
|
||||
author = {Y.-D. Jian and D. Balcan and F. Dellaert},
|
||||
booktitle = ICCV,
|
||||
year = {2011},
|
||||
}
|
||||
|
||||
@article{Kaess09ras,
|
||||
title = {Covariance Recovery from a Square Root Information Matrix for Data Association},
|
||||
author = {M. Kaess and F. Dellaert},
|
||||
journal = RAS,
|
||||
year = {2009},
|
||||
}
|
||||
|
||||
@article{Kaess12ijrr,
|
||||
title = {{iSAM2}: Incremental Smoothing and Mapping Using the {B}ayes Tree},
|
||||
author = {M. Kaess and H. Johannsson and R. Roberts and V. Ila and J. Leonard and F. Dellaert},
|
||||
journal = IJRR,
|
||||
year = {2012},
|
||||
month = {Feb},
|
||||
pages = {217--236},
|
||||
volume = {31},
|
||||
issue = {2},
|
||||
}
|
||||
|
||||
@article{Kaess08tro,
|
||||
title = {{iSAM}: Incremental Smoothing and Mapping},
|
||||
author = {M. Kaess and A. Ranganathan and F. Dellaert},
|
||||
journal = TRO,
|
||||
year = {2008},
|
||||
month = {Dec},
|
||||
number = {6},
|
||||
pages = {1365-1378},
|
||||
volume = {24},
|
||||
}
|
||||
|
||||
@book{Koller09book,
|
||||
title = {Probabilistic Graphical Models: Principles and Techniques},
|
||||
author = {D. Koller and N. Friedman},
|
||||
publisher = {The MIT Press},
|
||||
year = {2009}
|
||||
}
|
||||
|
||||
@Article{Kschischang01it,
|
||||
title = {Factor Graphs and the Sum-Product Algorithm},
|
||||
Author = {F.R. Kschischang and B.J. Frey and H-A. Loeliger},
|
||||
Journal = IT,
|
||||
Year = {2001},
|
||||
|
||||
Month = {February},
|
||||
Number = {2},
|
||||
Volume = {47}
|
||||
}
|
||||
|
||||
@article{Loeliger04spm,
|
||||
Title = {An Introduction to Factor Graphs},
|
||||
Author = {H.-A. Loeliger},
|
||||
Journal = {IEEE Signal Processing Magazine},
|
||||
Year = {2004},
|
||||
|
||||
Month = {January},
|
||||
Pages = {28--41}
|
||||
}
|
||||
|
||||
@inproceedings{Nister04cvpr2,
|
||||
title = {Visual Odometry},
|
||||
author = {D. Nist\'er and O. Naroditsky and J. Bergen},
|
||||
booktitle = CVPR,
|
||||
year = {2004},
|
||||
month = {Jun},
|
||||
pages = {652-659},
|
||||
volume = {1}
|
||||
}
|
||||
|
||||
@InProceedings{Smith87b,
|
||||
title = {A stochastic map for uncertain spatial relationships},
|
||||
Author = {R. Smith and M. Self and P. Cheeseman},
|
||||
Booktitle = ISRR,
|
||||
Year = {1988},
|
||||
Pages = {467-474}
|
||||
}
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Reference in New Issue