gtsam/examples/PlanarSLAMExample.cpp

/* ----------------------------------------------------------------------------

 * 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

 * -------------------------------------------------------------------------- */

/**
 * @file PlanarSLAMExample.cpp
 * @brief Simple robotics example using odometry measurements and bearing-range (laser) measurements
 * @author Alex Cunningham
 */

/**
 * A simple 2D planar slam example with landmarks
 *  - The robot and landmarks are on a 2 meter grid
 *  - Robot poses are facing along the X axis (horizontal, to the right in 2D)
 *  - The robot moves 2 meters each step
 *  - We have full odometry between poses
 *  - We have bearing and range information for measurements
 *  - Landmarks are 2 meters away from the robot trajectory
 */

// As this is a planar SLAM example, we will use Pose2 variables (x, y, theta) to represent
// the robot positions and Point2 variables (x, y) to represent the landmark coordinates.
#include <gtsam/geometry/Pose2.h>
#include <gtsam/geometry/Point2.h>

// Each variable in the system (poses and landmarks) must be identified with a unique key.
// We can either use simple integer keys (1, 2, 3, ...) or symbols (X1, X2, L1).
// Here we will use Symbols
#include <gtsam/inference/Symbol.h>

// In GTSAM, measurement functions are represented as 'factors'. Several common factors
// have been provided with the library for solving robotics/SLAM/Bundle Adjustment problems.
// Here we will use a RangeBearing factor for the range-bearing measurements to identified
// landmarks, and Between factors for the relative motion described by odometry measurements.
// Also, we will initialize the robot at the origin using a Prior factor.
#include <gtsam/slam/PriorFactor.h>
#include <gtsam/slam/BetweenFactor.h>
#include <gtsam/slam/BearingRangeFactor.h>

// When the factors are created, we will add them to a Factor Graph. As the factors we are using
// are nonlinear factors, we will need a Nonlinear Factor Graph.
#include <gtsam/nonlinear/NonlinearFactorGraph.h>

// Finally, once all of the factors have been added to our factor graph, we will want to
// solve/optimize to graph to find the best (Maximum A Posteriori) set of variable values.
// GTSAM includes several nonlinear optimizers to perform this step. Here we will use the
// common Levenberg-Marquardt solver
#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>

// Once the optimized values have been calculated, we can also calculate the marginal covariance
// of desired variables
#include <gtsam/nonlinear/Marginals.h>

// The nonlinear solvers within GTSAM are iterative solvers, meaning they linearize the
// nonlinear functions around an initial linearization point, then solve the linear system
// to update the linearization point. This happens repeatedly until the solver converges
// to a consistent set of variable values. This requires us to specify an initial guess
// for each variable, held in a Values container.
#include <gtsam/nonlinear/Values.h>


using namespace std;
using namespace gtsam;

int main(int argc, char** argv) {

  // Create a factor graph
  NonlinearFactorGraph graph;

  // Create the keys we need for this simple example
  static Symbol x1('x',1), x2('x',2), x3('x',3);
  static Symbol l1('l',1), l2('l',2);

  // Add a prior on pose x1 at the origin. A prior factor consists of a mean and a noise model (covariance matrix)
  Pose2 prior(0.0, 0.0, 0.0); // prior mean is at origin
  noiseModel::Diagonal::shared_ptr priorNoise = noiseModel::Diagonal::Sigmas((Vector(3) << 0.3, 0.3, 0.1).finished()); // 30cm std on x,y, 0.1 rad on theta
  graph.add(PriorFactor<Pose2>(x1, prior, priorNoise)); // add directly to graph

  // Add two odometry factors
  Pose2 odometry(2.0, 0.0, 0.0); // create a measurement for both factors (the same in this case)
  noiseModel::Diagonal::shared_ptr odometryNoise = noiseModel::Diagonal::Sigmas((Vector(3) << 0.2, 0.2, 0.1).finished()); // 20cm std on x,y, 0.1 rad on theta
  graph.add(BetweenFactor<Pose2>(x1, x2, odometry, odometryNoise));
  graph.add(BetweenFactor<Pose2>(x2, x3, odometry, odometryNoise));

  // Add Range-Bearing measurements to two different landmarks
  // create a noise model for the landmark measurements
  noiseModel::Diagonal::shared_ptr measurementNoise = noiseModel::Diagonal::Sigmas((Vector(2) << 0.1, 0.2).finished()); // 0.1 rad std on bearing, 20cm on range
  // create the measurement values - indices are (pose id, landmark id)
  Rot2 bearing11 = Rot2::fromDegrees(45),
       bearing21 = Rot2::fromDegrees(90),
       bearing32 = Rot2::fromDegrees(90);
  double range11 = std::sqrt(4.0+4.0),
         range21 = 2.0,
         range32 = 2.0;

  // Add Bearing-Range factors
  graph.add(BearingRangeFactor<Pose2, Point2>(x1, l1, bearing11, range11, measurementNoise));
  graph.add(BearingRangeFactor<Pose2, Point2>(x2, l1, bearing21, range21, measurementNoise));
  graph.add(BearingRangeFactor<Pose2, Point2>(x3, l2, bearing32, range32, measurementNoise));

  // Print
  graph.print("Factor Graph:\n");

  // Create (deliberately inaccurate) initial estimate
  Values initialEstimate;
  initialEstimate.insert(x1, Pose2(0.5, 0.0, 0.2));
  initialEstimate.insert(x2, Pose2(2.3, 0.1,-0.2));
  initialEstimate.insert(x3, Pose2(4.1, 0.1, 0.1));
  initialEstimate.insert(l1, Point2(1.8, 2.1));
  initialEstimate.insert(l2, Point2(4.1, 1.8));

  // Print
  initialEstimate.print("Initial Estimate:\n");

  // Optimize using Levenberg-Marquardt optimization. The optimizer
  // accepts an optional set of configuration parameters, controlling
  // things like convergence criteria, the type of linear system solver
  // to use, and the amount of information displayed during optimization.
  // Here we will use the default set of parameters.  See the
  // documentation for the full set of parameters.
  LevenbergMarquardtOptimizer optimizer(graph, initialEstimate);
  Values result = optimizer.optimize();
  result.print("Final Result:\n");

  // Calculate and print marginal covariances for all variables
  Marginals marginals(graph, result);
  print(marginals.marginalCovariance(x1), "x1 covariance");
  print(marginals.marginalCovariance(x2), "x2 covariance");
  print(marginals.marginalCovariance(x3), "x3 covariance");
  print(marginals.marginalCovariance(l1), "l1 covariance");
  print(marginals.marginalCovariance(l2), "l2 covariance");

  return 0;
}