Removed SLAM namespaces from Localization Example
Stephen Williams
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@ -15,87 +15,166 @@
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* @author Frank Dellaert
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*/
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// pull in the 2D PoseSLAM domain with all typedefs and helper functions defined
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#include <gtsam/slam/pose2SLAM.h>
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/**
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* A simple 2D pose slam example with "GPS" measurements
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* - The robot moves forward 2 meter each iteration
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* - The robot initially faces along the X axis (horizontal, to the right in 2D)
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* - We have full odometry between pose
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* - We have "GPS-like" measurements implemented with a custom factor
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*/
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// include this for marginals
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// As this is a planar SLAM example, we will use Pose2 variables (x, y, theta) to represent
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// the robot positions
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#include <gtsam/geometry/Pose2.h>
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// Each variable in the system (poses) must be identified with a unique key.
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// We can either use simple integer keys (1, 2, 3, ...) or symbols (X1, X2, L1).
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// Here we will use simple integer keys
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#include <gtsam/nonlinear/Key.h>
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// In GTSAM, measurement functions are represented as 'factors'. Several common factors
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// have been provided with the library for solving robotics/SLAM/Bundle Adjustment problems.
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// Here we will use Between factors for the relative motion described by odometry measurements.
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// Because we have global measurements in the form of "GPS-like" measurements, we don't
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// actually need to provide an initial position prior in this example. We will create our
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// custom factor shortly.
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#include <gtsam/slam/BetweenFactor.h>
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// When the factors are created, we will add them to a Factor Graph. As the factors we are using
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// are nonlinear factors, we will need a Nonlinear Factor Graph.
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#include <gtsam/nonlinear/NonlinearFactorGraph.h>
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// The nonlinear solvers within GTSAM are iterative solvers, meaning they linearize the
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// nonlinear functions around an initial linearization point, then solve the linear system
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// to update the linearization point. This happens repeatedly until the solver converges
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// to a consistent set of variable values. This requires us to specify an initial guess
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// for each variable, held in a Values container.
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#include <gtsam/nonlinear/Values.h>
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// Finally, once all of the factors have been added to our factor graph, we will want to
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// solve/optimize to graph to find the best (Maximum A Posteriori) set of variable values.
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// GTSAM includes several nonlinear optimizers to perform this step. Here we will use the
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// standard Levenberg-Marquardt solver
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#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
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// Once the optimized values have been calculated, we can also calculate the marginal covariance
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// of desired variables
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#include <gtsam/nonlinear/Marginals.h>
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#include <iomanip>
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#include <iostream>
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using namespace std;
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using namespace gtsam;
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using namespace gtsam::noiseModel;
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/**
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* UnaryFactor
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* Example on how to create a GPS-like factor on position alone.
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*/
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// Before we begin the example, we must create a custom unary factor to implement a
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// "GPS-like" functionality. Because standard GPS measurements provide information
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// only on the position, and not on the orientation, we cannot use a simple prior to
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// properly model this measurement.
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//
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// The factor will be a unary factor, affect only a single system variable. It will
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// also use a standard Gaussian noise model. Hence, we will derive our new factor from
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// the NoiseModelFactor1.
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#include <gtsam/nonlinear/NonlinearFactor.h>
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class UnaryFactor: public NoiseModelFactor1<Pose2> {
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double mx_, my_; ///< X and Y measurements
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// The factor will hold a measurement consisting of an (X,Y) location
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Point2 measurement_;
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public:
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/// shorthand for a smart pointer to a factor
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typedef boost::shared_ptr<UnaryFactor> shared_ptr;
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// The constructor requires the variable key, the (X, Y) measurement value, and the noise model
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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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NoiseModelFactor1<Pose2>(model, j), measurement_(x, y) {}
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virtual ~UnaryFactor() {}
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Vector evaluateError(const Pose2& q,
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boost::optional<Matrix&> H = boost::none) const
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// By using the NoiseModelFactor base classes, the only two function that must be overridden.
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// The first is the 'evaluateError' function. This function implements the desired measurement
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// function, returning a vector of errors when evaluated at the provided variable value. It
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// must also calculate the Jacobians for this measurement function, if requested.
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Vector evaluateError(const Pose2& pose, 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);
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return Vector_(2, q.x() - mx_, q.y() - my_);
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// The measurement function for a GPS-like measurement is simple:
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// error_x = pose.x - measurement.x
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// error_y = pose.y - measurement.y
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// Consequently, the Jacobians are:
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// [ derror_x/dx derror_x/dy derror_x/dtheta ] = [1 0 0]
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// [ derror_y/dx derror_y/dy derror_y/dtheta ] = [0 1 0]
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if (H)
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(*H) = Matrix_(2,3, 1.0,0.0,0.0, 0.0,1.0,0.0);
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return Vector_(2, pose.x() - measurement_.x(), pose.y() - measurement_.y());
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}
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// The second is a 'clone' function that allows the factor to be copied. Under most
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// circumstances, the following code that employs the default copy constructor should
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// work fine.
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virtual gtsam::NonlinearFactor::shared_ptr clone() const {
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return boost::static_pointer_cast<gtsam::NonlinearFactor>(
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gtsam::NonlinearFactor::shared_ptr(new UnaryFactor(*this))); }
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// Additionally, custom factors should really provide specific implementations of
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// 'equals' to ensure proper operation will all GTSAM functionality, and a custom
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// 'print' function, if desired.
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virtual bool equals(const NonlinearFactor& expected, double tol=1e-9) const {
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const UnaryFactor* e = dynamic_cast<const UnaryFactor*> (&expected);
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return e != NULL && NoiseModelFactor1::equals(*e, tol) && this->measurement_.equals(e->measurement_, tol);
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}
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virtual void print(const std::string& s, const KeyFormatter& keyFormatter = DefaultKeyFormatter) const {
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std::cout << s << "UnaryFactor(" << keyFormatter(this->key()) << ")\n";
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measurement_.print(" measurement: ");
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this->noiseModel_->print(" noise model: ");
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}
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};
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/**
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* Example of a more complex 2D localization example
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* - Robot poses are facing along the X axis (horizontal, to the right in 2D)
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* - The robot moves 2 meters each step
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* - We have full odometry between poses
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* - We have unary measurement factors at eacht time step
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*/
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int main(int argc, char** argv) {
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// create the graph (defined in pose2SLAM.h, derived from NonlinearFactorGraph)
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pose2SLAM::Graph graph;
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// 1. Create a factor graph container and add factors to it
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NonlinearFactorGraph graph;
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// add two odometry factors
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Pose2 odometry(2.0, 0.0, 0.0); // create a measurement for both factors (the same in this case)
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SharedDiagonal odometryNoise = Diagonal::Sigmas(Vector_(3, 0.2, 0.2, 0.1)); // 20cm std on x,y, 0.1 rad on theta
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graph.addRelativePose(1, 2, odometry, odometryNoise);
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graph.addRelativePose(2, 3, odometry, odometryNoise);
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// 2a. Add odometry factors
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// For simplicity, we will use the same noise model for each odometry factor
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noiseModel::Diagonal::shared_ptr odometryNoise = noiseModel::Diagonal::Sigmas(Vector_(3, 0.2, 0.2, 0.1));
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// Create odometry (Between) factors between consecutive poses
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graph.add(BetweenFactor<Pose2>(1, 2, Pose2(2.0, 0.0, 0.0), odometryNoise));
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graph.add(BetweenFactor<Pose2>(2, 3, Pose2(2.0, 0.0, 0.0), odometryNoise));
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// add unary measurement factors, like GPS, on all three poses
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SharedDiagonal noiseModel = Diagonal::Sigmas(Vector_(2, 0.1, 0.1)); // 10cm std on x,y
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graph.push_back(boost::make_shared<UnaryFactor>(1, 0, 0, noiseModel));
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graph.push_back(boost::make_shared<UnaryFactor>(2, 2, 0, noiseModel));
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graph.push_back(boost::make_shared<UnaryFactor>(3, 4, 0, noiseModel));
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// 2b. Add "GPS-like" measurements
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// We will use our custom UnaryFactor for this.
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noiseModel::Diagonal::shared_ptr unaryNoise = noiseModel::Diagonal::Sigmas(Vector_(2, 0.1, 0.1)); // 10cm std on x,y
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graph.add(UnaryFactor(1, 0.0, 0.0, unaryNoise));
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graph.add(UnaryFactor(3, 4.0, 0.0, unaryNoise));
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graph.print("\nFactor Graph:\n"); // print
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// print
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graph.print("\nFactor graph:\n");
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// 3. Create the data structure to hold the initialEstimate estimate to the solution
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// For illustrative purposes, these have been deliberately set to incorrect values
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Values initialEstimate;
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initialEstimate.insert(1, Pose2(0.5, 0.0, 0.2));
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initialEstimate.insert(2, Pose2(2.3, 0.1, -0.2));
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initialEstimate.insert(3, Pose2(4.1, 0.1, 0.1));
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initialEstimate.print("\nInitial Estimate:\n"); // print
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// create (deliberatly inaccurate) initial estimate
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pose2SLAM::Values initialEstimate;
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initialEstimate.insertPose(1, Pose2(0.5, 0.0, 0.2));
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initialEstimate.insertPose(2, Pose2(2.3, 0.1,-0.2));
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initialEstimate.insertPose(3, Pose2(4.1, 0.1, 0.1));
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initialEstimate.print("\nInitial estimate:\n ");
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// 4. Optimize using Levenberg-Marquardt optimization. The optimizer
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// accepts an optional set of configuration parameters, controlling
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// things like convergence criteria, the type of linear system solver
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// to use, and the amount of information displayed during optimization.
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// Here we will use the default set of parameters. See the
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// documentation for the full set of parameters.
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LevenbergMarquardtOptimizer optimizer(graph, initialEstimate);
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Values result = optimizer.optimize();
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result.print("Final Result:\n");
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// use an explicit Optimizer object
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LevenbergMarquardtOptimizer optimizer(graph, initialEstimate);
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pose2SLAM::Values result = optimizer.optimize();
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result.print("\nFinal result:\n ");
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// 5. Calculate and print marginal covariances for all variables
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Marginals marginals(graph, result);
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cout << "Pose 1 covariance:\n" << marginals.marginalCovariance(1) << endl;
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cout << "Pose 2 covariance:\n" << marginals.marginalCovariance(2) << endl;
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cout << "Pose 3 covariance:\n" << marginals.marginalCovariance(3) << endl;
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// Query the marginals
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Marginals marginals(graph, result);
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cout.precision(2);
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cout << "\nP1:\n" << marginals.marginalCovariance(1) << endl;
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cout << "\nP2:\n" << marginals.marginalCovariance(2) << endl;
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cout << "\nP3:\n" << marginals.marginalCovariance(3) << endl;
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return 0;
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return 0;
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}
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