564 lines
20 KiB
C++
564 lines
20 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 testPose2SLAM.cpp
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* @author Frank Dellaert, Viorela Ila
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**/
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// Magically casts strings like "x3" to a Symbol('x',3) key, see Key.h
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#define GTSAM_MAGIC_KEY
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#include <gtsam/slam/pose2SLAM.h>
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#include <gtsam/nonlinear/NonlinearOptimizer.h>
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#include <gtsam/inference/FactorGraph.h>
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#include <gtsam/base/numericalDerivative.h>
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using namespace gtsam;
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#include <CppUnitLite/TestHarness.h>
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#include <boost/shared_ptr.hpp>
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#include <boost/assign/std/list.hpp>
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using namespace boost;
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using namespace boost::assign;
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#include <iostream>
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using namespace std;
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typedef pose2SLAM::Odometry Pose2Factor;
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// common measurement covariance
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static double sx=0.5, sy=0.5,st=0.1;
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static noiseModel::Gaussian::shared_ptr covariance(
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noiseModel::Gaussian::Covariance(Matrix_(3, 3,
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sx*sx, 0.0, 0.0,
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0.0, sy*sy, 0.0,
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0.0, 0.0, st*st
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)));
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//static noiseModel::Gaussian::shared_ptr I3(noiseModel::Unit::Create(3));
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/* ************************************************************************* */
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// Test constraint, small displacement
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Vector f1(const Pose2& pose1, const Pose2& pose2) {
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Pose2 z(2.1130913087, 0.468461064817, 0.436332312999);
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Pose2Factor constraint(1, 2, z, covariance);
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return constraint.evaluateError(pose1, pose2);
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}
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TEST( Pose2SLAM, constraint1 )
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{
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// create a factor between unknown poses p1 and p2
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Pose2 pose1, pose2(2.1130913087, 0.468461064817, 0.436332312999);
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Pose2Factor constraint(1, 2, pose2, covariance);
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Matrix H1, H2;
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Vector actual = constraint.evaluateError(pose1, pose2, H1, H2);
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Matrix numericalH1 = numericalDerivative21(&f1 , pose1, pose2);
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EXPECT(assert_equal(numericalH1,H1,5e-3));
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Matrix numericalH2 = numericalDerivative22(&f1 , pose1, pose2);
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EXPECT(assert_equal(numericalH2,H2));
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}
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/* ************************************************************************* */
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// Test constraint, large displacement
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Vector f2(const Pose2& pose1, const Pose2& pose2) {
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Pose2 z(2,2,M_PI_2);
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Pose2Factor constraint(1, 2, z, covariance);
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return constraint.evaluateError(pose1, pose2);
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}
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TEST( Pose2SLAM, constraint2 )
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{
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// create a factor between unknown poses p1 and p2
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Pose2 pose1, pose2(2,2,M_PI_2);
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Pose2Factor constraint(1, 2, pose2, covariance);
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Matrix H1, H2;
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Vector actual = constraint.evaluateError(pose1, pose2, H1, H2);
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Matrix numericalH1 = numericalDerivative21(&f2 , pose1, pose2);
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EXPECT(assert_equal(numericalH1,H1,5e-3));
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Matrix numericalH2 = numericalDerivative22(&f2 , pose1, pose2);
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EXPECT(assert_equal(numericalH2,H2));
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}
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/* ************************************************************************* */
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TEST( Pose2SLAM, constructor )
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{
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// create a factor between unknown poses p1 and p2
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Pose2 measured(2,2,M_PI_2);
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pose2SLAM::Graph graph;
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graph.addOdometry(1,2,measured, covariance);
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// get the size of the graph
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size_t actual = graph.size();
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// verify
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size_t expected = 1;
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CHECK(actual == expected);
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}
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/* ************************************************************************* */
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TEST( Pose2SLAM, linearization )
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{
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// create a factor between unknown poses p1 and p2
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Pose2 measured(2,2,M_PI_2);
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Pose2Factor constraint(1,2,measured, covariance);
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pose2SLAM::Graph graph;
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graph.addOdometry(1,2,measured, covariance);
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// Choose a linearization point
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Pose2 p1(1.1,2,M_PI_2); // robot at (1.1,2) looking towards y (ground truth is at 1,2, see testPose2)
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Pose2 p2(-1,4.1,M_PI); // robot at (-1,4) looking at negative (ground truth is at 4.1,2)
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pose2SLAM::Values config;
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config.insert(pose2SLAM::PoseKey(1),p1);
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config.insert(pose2SLAM::PoseKey(2),p2);
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// Linearize
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Ordering ordering(*config.orderingArbitrary());
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boost::shared_ptr<FactorGraph<GaussianFactor> > lfg_linearized = graph.linearize(config, ordering);
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//lfg_linearized->print("lfg_actual");
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// the expected linear factor
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FactorGraph<GaussianFactor> lfg_expected;
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Matrix A1 = Matrix_(3,3,
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0.0,-2.0, -4.2,
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2.0, 0.0, -4.2,
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0.0, 0.0,-10.0);
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Matrix A2 = Matrix_(3,3,
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2.0, 0.0, 0.0,
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0.0, 2.0, 0.0,
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0.0, 0.0, 10.0);
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Vector b = Vector_(3,-0.1/sx,0.1/sy,0.0);
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SharedDiagonal probModel1 = noiseModel::Unit::Create(3);
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lfg_expected.push_back(JacobianFactor::shared_ptr(new JacobianFactor(ordering["x1"], A1, ordering["x2"], A2, b, probModel1)));
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CHECK(assert_equal(lfg_expected, *lfg_linearized));
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}
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/* ************************************************************************* */
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TEST(Pose2Graph, optimize) {
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// create a Pose graph with one equality constraint and one measurement
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shared_ptr<pose2SLAM::Graph> fg(new pose2SLAM::Graph);
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fg->addPoseConstraint(0, Pose2(0,0,0));
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fg->addOdometry(0, 1, Pose2(1,2,M_PI_2), covariance);
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// Create initial config
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boost::shared_ptr<Values> initial(new Values());
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initial->insert(pose2SLAM::PoseKey(0), Pose2(0,0,0));
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initial->insert(pose2SLAM::PoseKey(1), Pose2(0,0,0));
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// Choose an ordering and optimize
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shared_ptr<Ordering> ordering(new Ordering);
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*ordering += "x0","x1";
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typedef NonlinearOptimizer<pose2SLAM::Graph> Optimizer;
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NonlinearOptimizationParameters::shared_ptr params = NonlinearOptimizationParameters::newDrecreaseThresholds(1e-15, 1e-15);
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Optimizer optimizer0(fg, initial, ordering, params);
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Optimizer optimizer = optimizer0.levenbergMarquardt();
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// Check with expected config
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Values expected;
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expected.insert(pose2SLAM::PoseKey(0), Pose2(0,0,0));
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expected.insert(pose2SLAM::PoseKey(1), Pose2(1,2,M_PI_2));
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CHECK(assert_equal(expected, *optimizer.values()));
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}
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/* ************************************************************************* */
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// test optimization with 3 poses
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TEST(Pose2Graph, optimizeThreePoses) {
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// Create a hexagon of poses
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Values hexagon = pose2SLAM::circle(3,1.0);
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Pose2 p0 = hexagon[pose2SLAM::PoseKey(0)], p1 = hexagon[pose2SLAM::PoseKey(1)];
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// create a Pose graph with one equality constraint and one measurement
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shared_ptr<pose2SLAM::Graph> fg(new pose2SLAM::Graph);
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fg->addPoseConstraint(0, p0);
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Pose2 delta = p0.between(p1);
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fg->addOdometry(0, 1, delta, covariance);
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fg->addOdometry(1, 2, delta, covariance);
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fg->addOdometry(2, 0, delta, covariance);
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// Create initial config
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boost::shared_ptr<Values> initial(new Values());
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initial->insert(pose2SLAM::PoseKey(0), p0);
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initial->insert(pose2SLAM::PoseKey(1), hexagon[pose2SLAM::PoseKey(1)].retract(Vector_(3,-0.1, 0.1,-0.1)));
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initial->insert(pose2SLAM::PoseKey(2), hexagon[pose2SLAM::PoseKey(2)].retract(Vector_(3, 0.1,-0.1, 0.1)));
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// Choose an ordering
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shared_ptr<Ordering> ordering(new Ordering);
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*ordering += "x0","x1","x2";
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// optimize
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NonlinearOptimizationParameters::shared_ptr params = NonlinearOptimizationParameters::newDrecreaseThresholds(1e-15, 1e-15);
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pose2SLAM::Optimizer optimizer0(fg, initial, ordering, params);
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pose2SLAM::Optimizer optimizer = optimizer0.levenbergMarquardt();
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Values actual = *optimizer.values();
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// Check with ground truth
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CHECK(assert_equal(hexagon, actual));
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}
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/* ************************************************************************* */
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// test optimization with 6 poses arranged in a hexagon and a loop closure
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TEST_UNSAFE(Pose2SLAM, optimizeCircle) {
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// Create a hexagon of poses
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Values hexagon = pose2SLAM::circle(6,1.0);
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Pose2 p0 = hexagon[pose2SLAM::PoseKey(0)], p1 = hexagon[pose2SLAM::PoseKey(1)];
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// create a Pose graph with one equality constraint and one measurement
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shared_ptr<pose2SLAM::Graph> fg(new pose2SLAM::Graph);
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fg->addPoseConstraint(0, p0);
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Pose2 delta = p0.between(p1);
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fg->addOdometry(0, 1, delta, covariance);
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fg->addOdometry(1,2, delta, covariance);
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fg->addOdometry(2,3, delta, covariance);
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fg->addOdometry(3,4, delta, covariance);
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fg->addOdometry(4,5, delta, covariance);
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fg->addOdometry(5, 0, delta, covariance);
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// Create initial config
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boost::shared_ptr<Values> initial(new Values());
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initial->insert(pose2SLAM::PoseKey(0), p0);
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initial->insert(pose2SLAM::PoseKey(1), hexagon[pose2SLAM::PoseKey(1)].retract(Vector_(3,-0.1, 0.1,-0.1)));
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initial->insert(pose2SLAM::PoseKey(2), hexagon[pose2SLAM::PoseKey(2)].retract(Vector_(3, 0.1,-0.1, 0.1)));
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initial->insert(pose2SLAM::PoseKey(3), hexagon[pose2SLAM::PoseKey(3)].retract(Vector_(3,-0.1, 0.1,-0.1)));
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initial->insert(pose2SLAM::PoseKey(4), hexagon[pose2SLAM::PoseKey(4)].retract(Vector_(3, 0.1,-0.1, 0.1)));
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initial->insert(pose2SLAM::PoseKey(5), hexagon[pose2SLAM::PoseKey(5)].retract(Vector_(3,-0.1, 0.1,-0.1)));
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// Choose an ordering
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shared_ptr<Ordering> ordering(new Ordering);
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*ordering += "x0","x1","x2","x3","x4","x5";
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// optimize
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NonlinearOptimizationParameters::shared_ptr params = NonlinearOptimizationParameters::newDrecreaseThresholds(1e-15, 1e-15);
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pose2SLAM::Optimizer optimizer0(fg, initial, ordering, params);
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pose2SLAM::Optimizer optimizer = optimizer0.levenbergMarquardt();
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Values actual = *optimizer.values();
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// Check with ground truth
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CHECK(assert_equal(hexagon, actual));
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// Check loop closure
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CHECK(assert_equal(delta,actual[pose2SLAM::PoseKey(5)].between(actual[pose2SLAM::PoseKey(0)])));
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// Pose2SLAMOptimizer myOptimizer("3");
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// Matrix A1 = myOptimizer.a1();
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// LONGS_EQUAL(3, A1.rows());
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// LONGS_EQUAL(17, A1.cols()); // 7 + 7 + 3
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//
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// Matrix A2 = myOptimizer.a2();
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// LONGS_EQUAL(3, A1.rows());
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// LONGS_EQUAL(7, A2.cols()); // 7
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//
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// Vector b1 = myOptimizer.b1();
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// LONGS_EQUAL(9, b1.size()); // 3 + 3 + 3
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//
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// Vector b2 = myOptimizer.b2();
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// LONGS_EQUAL(3, b2.size()); // 3
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//
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// // Here, call matlab to
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// // A=[A1;A2], b=[b1;b2]
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// // R=qr(A1)
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// // call pcg on A,b, with preconditioner R -> get x
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//
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// Vector x = myOptimizer.optimize();
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// LONGS_EQUAL(9, x.size()); // 3 + 3 + 3
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//
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// myOptimizer.update(x);
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//
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// Values expected;
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// expected.insert(0, Pose2(0.,0.,0.));
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// expected.insert(1, Pose2(1.,0.,0.));
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// expected.insert(2, Pose2(2.,0.,0.));
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//
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// // Check with ground truth
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// CHECK(assert_equal(expected, *myOptimizer.theta()));
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}
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/* ************************************************************************* */
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TEST(Pose2Graph, optimize2) {
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// Pose2SLAMOptimizer myOptimizer("100");
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// Matrix A1 = myOptimizer.a1();
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// Matrix A2 = myOptimizer.a2();
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// cout << "A1: " << A1.rows() << " " << A1.cols() << endl;
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// cout << "A2: " << A2.rows() << " " << A2.cols() << endl;
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//
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// //cout << "error: " << myOptimizer.error() << endl;
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// for(int i = 0; i<10; i++) {
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// myOptimizer.linearize();
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// Vector x = myOptimizer.optimize();
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// myOptimizer.update(x);
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// }
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// //cout << "error: " << myOptimizer.error() << endl;
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// CHECK(myOptimizer.error() < 1.);
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}
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///* ************************************************************************* */
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// SL-NEEDED? TEST(Pose2SLAM, findMinimumSpanningTree) {
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// pose2SLAM::Graph G, T, C;
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// G.addConstraint(1, 2, Pose2(0.,0.,0.), I3);
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// G.addConstraint(1, 3, Pose2(0.,0.,0.), I3);
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// G.addConstraint(2, 3, Pose2(0.,0.,0.), I3);
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//
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// PredecessorMap<pose2SLAM::pose2SLAM::PoseKey> tree =
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// G.findMinimumSpanningTree<pose2SLAM::pose2SLAM::PoseKey, Pose2Factor>();
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// CHECK(tree[1] == 1);
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// CHECK(tree[2] == 1);
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// CHECK(tree[3] == 1);
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//}
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//
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///* ************************************************************************* */
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// SL-NEEDED? TEST(Pose2SLAM, split) {
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// pose2SLAM::Graph G, T, C;
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// G.addConstraint(1, 2, Pose2(0.,0.,0.), I3);
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// G.addConstraint(1, 3, Pose2(0.,0.,0.), I3);
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// G.addConstraint(2, 3, Pose2(0.,0.,0.), I3);
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//
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// PredecessorMap<pose2SLAM::pose2SLAM::PoseKey> tree;
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// tree.insert(1,2);
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// tree.insert(2,2);
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// tree.insert(3,2);
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//
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// G.split<pose2SLAM::pose2SLAM::PoseKey, Pose2Factor>(tree, T, C);
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// LONGS_EQUAL(2, T.size());
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// LONGS_EQUAL(1, C.size());
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//}
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using namespace pose2SLAM;
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/* ************************************************************************* */
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TEST(Pose2Values, pose2Circle )
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{
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// expected is 4 poses tangent to circle with radius 1m
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pose2SLAM::Values expected;
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expected.insert(pose2SLAM::PoseKey(0), Pose2( 1, 0, M_PI_2));
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expected.insert(pose2SLAM::PoseKey(1), Pose2( 0, 1, - M_PI ));
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expected.insert(pose2SLAM::PoseKey(2), Pose2(-1, 0, - M_PI_2));
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expected.insert(pose2SLAM::PoseKey(3), Pose2( 0, -1, 0 ));
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pose2SLAM::Values actual = pose2SLAM::circle(4,1.0);
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CHECK(assert_equal(expected,actual));
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}
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/* ************************************************************************* */
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TEST(Pose2SLAM, expmap )
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{
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// expected is circle shifted to right
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pose2SLAM::Values expected;
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expected.insert(pose2SLAM::PoseKey(0), Pose2( 1.1, 0, M_PI_2));
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expected.insert(pose2SLAM::PoseKey(1), Pose2( 0.1, 1, - M_PI ));
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expected.insert(pose2SLAM::PoseKey(2), Pose2(-0.9, 0, - M_PI_2));
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expected.insert(pose2SLAM::PoseKey(3), Pose2( 0.1, -1, 0 ));
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// Note expmap coordinates are in local coordinates, so shifting to right requires thought !!!
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pose2SLAM::Values circle(pose2SLAM::circle(4,1.0));
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Ordering ordering(*circle.orderingArbitrary());
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VectorValues delta(circle.dims(ordering));
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delta[ordering[pose2SLAM::PoseKey(0)]] = Vector_(3, 0.0,-0.1,0.0);
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delta[ordering[pose2SLAM::PoseKey(1)]] = Vector_(3, -0.1,0.0,0.0);
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delta[ordering[pose2SLAM::PoseKey(2)]] = Vector_(3, 0.0,0.1,0.0);
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delta[ordering[pose2SLAM::PoseKey(3)]] = Vector_(3, 0.1,0.0,0.0);
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pose2SLAM::Values actual = circle.retract(delta, ordering);
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CHECK(assert_equal(expected,actual));
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}
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// Common measurement covariance
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static SharedNoiseModel sigmas = sharedSigmas(Vector_(3,sx,sy,st));
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/* ************************************************************************* */
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// Very simple test establishing Ax-b \approx z-h(x)
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TEST( Pose2Prior, error )
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{
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// Choose a linearization point
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Pose2 p1(1, 0, 0); // robot at (1,0)
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pose2SLAM::Values x0;
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x0.insert(pose2SLAM::PoseKey(1), p1);
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// Create factor
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pose2SLAM::Prior factor(1, p1, sigmas);
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// Actual linearization
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Ordering ordering(*x0.orderingArbitrary());
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boost::shared_ptr<JacobianFactor> linear =
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boost::dynamic_pointer_cast<JacobianFactor>(factor.linearize(x0, ordering));
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// Check error at x0, i.e. delta = zero !
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VectorValues delta(VectorValues::Zero(x0.dims(ordering)));
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delta[ordering["x1"]] = zero(3);
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Vector error_at_zero = Vector_(3,0.0,0.0,0.0);
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CHECK(assert_equal(error_at_zero,factor.whitenedError(x0)));
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CHECK(assert_equal(-error_at_zero,linear->error_vector(delta)));
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// Check error after increasing p2
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VectorValues addition(VectorValues::Zero(x0.dims(ordering)));
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addition[ordering["x1"]] = Vector_(3, 0.1, 0.0, 0.0);
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VectorValues plus = delta + addition;
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pose2SLAM::Values x1 = x0.retract(plus, ordering);
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Vector error_at_plus = Vector_(3,0.1/sx,0.0,0.0); // h(x)-z = 0.1 !
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CHECK(assert_equal(error_at_plus,factor.whitenedError(x1)));
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CHECK(assert_equal(error_at_plus,linear->error_vector(plus)));
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}
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/* ************************************************************************* */
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// common Pose2Prior for tests below
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static gtsam::Pose2 priorVal(2,2,M_PI_2);
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static pose2SLAM::Prior priorFactor(1,priorVal, sigmas);
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/* ************************************************************************* */
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// The error |A*dx-b| approximates (h(x0+dx)-z) = -error_vector
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// Hence i.e., b = approximates z-h(x0) = error_vector(x0)
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LieVector hprior(const Pose2& p1) {
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return LieVector(sigmas->whiten(priorFactor.evaluateError(p1)));
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}
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/* ************************************************************************* */
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TEST( Pose2Prior, linearize )
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{
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// Choose a linearization point at ground truth
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pose2SLAM::Values x0;
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x0.insert(pose2SLAM::PoseKey(1),priorVal);
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// Actual linearization
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Ordering ordering(*x0.orderingArbitrary());
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boost::shared_ptr<JacobianFactor> actual =
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boost::dynamic_pointer_cast<JacobianFactor>(priorFactor.linearize(x0, ordering));
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// Test with numerical derivative
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Matrix numericalH = numericalDerivative11(hprior, priorVal);
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CHECK(assert_equal(numericalH,actual->getA(actual->find(ordering["x1"]))));
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}
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/* ************************************************************************* */
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// Very simple test establishing Ax-b \approx z-h(x)
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TEST( Pose2Factor, error )
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{
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// Choose a linearization point
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Pose2 p1; // robot at origin
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Pose2 p2(1, 0, 0); // robot at (1,0)
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pose2SLAM::Values x0;
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x0.insert(pose2SLAM::PoseKey(1), p1);
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x0.insert(pose2SLAM::PoseKey(2), p2);
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// Create factor
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Pose2 z = p1.between(p2);
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Pose2Factor factor(1, 2, z, covariance);
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// Actual linearization
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Ordering ordering(*x0.orderingArbitrary());
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boost::shared_ptr<JacobianFactor> linear =
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boost::dynamic_pointer_cast<JacobianFactor>(factor.linearize(x0, ordering));
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// Check error at x0, i.e. delta = zero !
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VectorValues delta(x0.dims(ordering));
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delta[ordering["x1"]] = zero(3);
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delta[ordering["x2"]] = zero(3);
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Vector error_at_zero = Vector_(3,0.0,0.0,0.0);
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CHECK(assert_equal(error_at_zero,factor.unwhitenedError(x0)));
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CHECK(assert_equal(-error_at_zero, linear->error_vector(delta)));
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// Check error after increasing p2
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VectorValues plus = delta;
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plus[ordering["x2"]] = Vector_(3, 0.1, 0.0, 0.0);
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pose2SLAM::Values x1 = x0.retract(plus, ordering);
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Vector error_at_plus = Vector_(3,0.1/sx,0.0,0.0); // h(x)-z = 0.1 !
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CHECK(assert_equal(error_at_plus,factor.whitenedError(x1)));
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CHECK(assert_equal(error_at_plus,linear->error_vector(plus)));
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}
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/* ************************************************************************* */
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// common Pose2Factor for tests below
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static Pose2 measured(2,2,M_PI_2);
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static Pose2Factor factor(1,2,measured, covariance);
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/* ************************************************************************* */
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TEST( Pose2Factor, rhs )
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{
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// Choose a linearization point
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Pose2 p1(1.1,2,M_PI_2); // robot at (1.1,2) looking towards y (ground truth is at 1,2, see testPose2)
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Pose2 p2(-1,4.1,M_PI); // robot at (-1,4.1) looking at negative (ground truth is at -1,4)
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pose2SLAM::Values x0;
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x0.insert(pose2SLAM::PoseKey(1),p1);
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x0.insert(pose2SLAM::PoseKey(2),p2);
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// Actual linearization
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Ordering ordering(*x0.orderingArbitrary());
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boost::shared_ptr<JacobianFactor> linear =
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boost::dynamic_pointer_cast<JacobianFactor>(factor.linearize(x0, ordering));
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// Check RHS
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Pose2 hx0 = p1.between(p2);
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CHECK(assert_equal(Pose2(2.1, 2.1, M_PI_2),hx0));
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Vector expected_b = Vector_(3, -0.1/sx, 0.1/sy, 0.0);
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CHECK(assert_equal(expected_b,-factor.whitenedError(x0)));
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CHECK(assert_equal(expected_b,linear->getb()));
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}
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/* ************************************************************************* */
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// The error |A*dx-b| approximates (h(x0+dx)-z) = -error_vector
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// Hence i.e., b = approximates z-h(x0) = error_vector(x0)
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LieVector h(const Pose2& p1,const Pose2& p2) {
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return LieVector(covariance->whiten(factor.evaluateError(p1,p2)));
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}
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|
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/* ************************************************************************* */
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TEST( Pose2Factor, linearize )
|
|
{
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// Choose a linearization point at ground truth
|
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Pose2 p1(1,2,M_PI_2);
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Pose2 p2(-1,4,M_PI);
|
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pose2SLAM::Values x0;
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x0.insert(pose2SLAM::PoseKey(1),p1);
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x0.insert(pose2SLAM::PoseKey(2),p2);
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|
|
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// expected linearization
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Matrix expectedH1 = covariance->Whiten(Matrix_(3,3,
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0.0,-1.0,-2.0,
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1.0, 0.0,-2.0,
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0.0, 0.0,-1.0
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));
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Matrix expectedH2 = covariance->Whiten(Matrix_(3,3,
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1.0, 0.0, 0.0,
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0.0, 1.0, 0.0,
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0.0, 0.0, 1.0
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));
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Vector expected_b = Vector_(3, 0.0, 0.0, 0.0);
|
|
|
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// expected linear factor
|
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Ordering ordering(*x0.orderingArbitrary());
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SharedDiagonal probModel1 = noiseModel::Unit::Create(3);
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JacobianFactor expected(ordering["x1"], expectedH1, ordering["x2"], expectedH2, expected_b, probModel1);
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|
|
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// Actual linearization
|
|
boost::shared_ptr<JacobianFactor> actual =
|
|
boost::dynamic_pointer_cast<JacobianFactor>(factor.linearize(x0, ordering));
|
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CHECK(assert_equal(expected,*actual));
|
|
|
|
// Numerical do not work out because BetweenFactor is approximate ?
|
|
Matrix numericalH1 = numericalDerivative21(h, p1, p2);
|
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CHECK(assert_equal(expectedH1,numericalH1));
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Matrix numericalH2 = numericalDerivative22(h, p1, p2);
|
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CHECK(assert_equal(expectedH2,numericalH2));
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
int main() {
|
|
TestResult tr;
|
|
return TestRegistry::runAllTests(tr);
|
|
}
|
|
/* ************************************************************************* */
|