163 lines
7.4 KiB
C++
163 lines
7.4 KiB
C++
/* ----------------------------------------------------------------------------
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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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* See LICENSE for the license information
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* -------------------------------------------------------------------------- */
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/**
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* @file LocalizationExample.cpp
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* @brief Simple robot localization example, with three "GPS-like" measurements
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* @author Frank Dellaert
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*/
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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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// We will use Pose2 variables (x, y, theta) to represent the robot positions
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#include <gtsam/geometry/Pose2.h>
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// We will use simple integer Keys to refer to the robot poses.
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#include <gtsam/inference/Key.h>
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// As in OdometryExample.cpp, we use a BetweenFactor to model odometry measurements.
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#include <gtsam/slam/BetweenFactor.h>
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// We add all facors to a Nonlinear Factor Graph, as our factors are nonlinear.
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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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using namespace std;
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using namespace gtsam;
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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 NoiseModelFactorN.
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#include <gtsam/nonlinear/NonlinearFactor.h>
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class UnaryFactor: public NoiseModelFactorN<Pose2> {
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// The factor will hold a measurement consisting of an (X,Y) location
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// We could this with a Point2 but here we just use two doubles
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double mx_, my_;
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public:
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// Provide access to Matrix& version of evaluateError:
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using NoiseModelFactor1<Pose2>::evaluateError;
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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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NoiseModelFactorN<Pose2>(model, j), mx_(x), my_(y) {}
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~UnaryFactor() override {}
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// Using the NoiseModelFactorN base class there are two functions 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& q, OptionalMatrixType H) const override {
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// The measurement function for a GPS-like measurement h(q) which predicts the measurement (m) is h(q) = q, q = [qx qy qtheta]
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// The error is then simply calculated as E(q) = h(q) - m:
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// error_x = q.x - mx
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// error_y = q.y - my
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// Node's orientation reflects in the Jacobian, in tangent space this is equal to the right-hand rule rotation matrix
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// H = [ cos(q.theta) -sin(q.theta) 0 ]
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// [ sin(q.theta) cos(q.theta) 0 ]
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const Rot2& R = q.rotation();
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if (H) (*H) = (gtsam::Matrix(2, 3) << R.c(), -R.s(), 0.0, R.s(), R.c(), 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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// 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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gtsam::NonlinearFactor::shared_ptr clone() const override {
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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, we encourage you the use of unit testing your custom factors,
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// (as all GTSAM factors are), in which you would need an equals and print, to satisfy the
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// GTSAM_CONCEPT_TESTABLE_INST(T) defined in Testable.h, but these are not needed below.
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}; // UnaryFactor
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int main(int argc, char** argv) {
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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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// 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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auto odometryNoise = noiseModel::Diagonal::Sigmas(Vector3(0.2, 0.2, 0.1));
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// Create odometry (Between) factors between consecutive poses
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graph.emplace_shared<BetweenFactor<Pose2> >(1, 2, Pose2(2.0, 0.0, 0.0), odometryNoise);
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graph.emplace_shared<BetweenFactor<Pose2> >(2, 3, Pose2(2.0, 0.0, 0.0), odometryNoise);
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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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auto unaryNoise =
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noiseModel::Diagonal::Sigmas(Vector2(0.1, 0.1)); // 10cm std on x,y
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graph.emplace_shared<UnaryFactor>(1, 0.0, 0.0, unaryNoise);
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graph.emplace_shared<UnaryFactor>(2, 2.0, 0.0, unaryNoise);
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graph.emplace_shared<UnaryFactor>(3, 4.0, 0.0, unaryNoise);
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graph.print("\nFactor Graph:\n"); // print
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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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// 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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// 5. Calculate and print marginal covariances for all variables
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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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return 0;
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}
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