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gtsam/gtsam/slam/tests/testPose2SLAM.cpp

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/* ----------------------------------------------------------------------------
* 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 testPose2SLAM.cpp
* @author Frank Dellaert, Viorela Ila
**/
#include <gtsam/slam/pose2SLAM.h>
#include <gtsam/nonlinear/NonlinearOptimizer.h>
#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
#include <gtsam/inference/FactorGraph.h>
#include <gtsam/base/numericalDerivative.h>
using namespace gtsam;
#include <CppUnitLite/TestHarness.h>
#include <boost/shared_ptr.hpp>
#include <boost/assign/std/list.hpp>
using namespace boost;
using namespace boost::assign;
#include <iostream>
using namespace std;
typedef pose2SLAM::Odometry Pose2Factor;
// common measurement covariance
static double sx=0.5, sy=0.5,st=0.1;
static Matrix cov(Matrix_(3, 3,
sx*sx, 0.0, 0.0,
0.0, sy*sy, 0.0,
0.0, 0.0, st*st
));
static noiseModel::Gaussian::shared_ptr covariance(noiseModel::Gaussian::Covariance(cov));
/* ************************************************************************* */
TEST_UNSAFE( Pose2SLAM, XYT )
{
pose2SLAM::Values values;
values.insertPose(1,Pose2(1,2,3));
values.insertPose(2,Pose2(4,5,6));
EXPECT(assert_equal(Vector_(2,1.0,4.0),values.xs()));
EXPECT(assert_equal(Vector_(2,2.0,5.0),values.ys()));
EXPECT(assert_equal(Vector_(2,3.0,6.0-2*M_PI),values.thetas()));
}
/* ************************************************************************* */
// Test constraint, small displacement
Vector f1(const Pose2& pose1, const Pose2& pose2) {
Pose2 z(2.1130913087, 0.468461064817, 0.436332312999);
Pose2Factor constraint(1, 2, z, covariance);
return constraint.evaluateError(pose1, pose2);
}
TEST_UNSAFE( Pose2SLAM, constraint1 )
{
// create a factor between unknown poses p1 and p2
Pose2 pose1, pose2(2.1130913087, 0.468461064817, 0.436332312999);
Pose2Factor constraint(1, 2, pose2, covariance);
Matrix H1, H2;
Vector actual = constraint.evaluateError(pose1, pose2, H1, H2);
Matrix numericalH1 = numericalDerivative21(&f1 , pose1, pose2);
EXPECT(assert_equal(numericalH1,H1,5e-3));
Matrix numericalH2 = numericalDerivative22(&f1 , pose1, pose2);
EXPECT(assert_equal(numericalH2,H2));
}
/* ************************************************************************* */
// Test constraint, large displacement
Vector f2(const Pose2& pose1, const Pose2& pose2) {
Pose2 z(2,2,M_PI_2);
Pose2Factor constraint(1, 2, z, covariance);
return constraint.evaluateError(pose1, pose2);
}
TEST_UNSAFE( Pose2SLAM, constraint2 )
{
// create a factor between unknown poses p1 and p2
Pose2 pose1, pose2(2,2,M_PI_2);
Pose2Factor constraint(1, 2, pose2, covariance);
Matrix H1, H2;
Vector actual = constraint.evaluateError(pose1, pose2, H1, H2);
Matrix numericalH1 = numericalDerivative21(&f2 , pose1, pose2);
EXPECT(assert_equal(numericalH1,H1,5e-3));
Matrix numericalH2 = numericalDerivative22(&f2 , pose1, pose2);
EXPECT(assert_equal(numericalH2,H2));
}
/* ************************************************************************* */
TEST_UNSAFE( Pose2SLAM, constructor )
{
// create a factor between unknown poses p1 and p2
Pose2 measured(2,2,M_PI_2);
pose2SLAM::Graph graph;
graph.addOdometry(1,2,measured, covariance);
// get the size of the graph
size_t actual = graph.size();
// verify
size_t expected = 1;
CHECK(actual == expected);
}
/* ************************************************************************* */
TEST_UNSAFE( Pose2SLAM, linearization )
{
// create a factor between unknown poses p1 and p2
Pose2 measured(2,2,M_PI_2);
Pose2Factor constraint(1, 2, measured, covariance);
pose2SLAM::Graph graph;
graph.addOdometry(1,2,measured, covariance);
// Choose a linearization point
Pose2 p1(1.1,2,M_PI_2); // robot at (1.1,2) looking towards y (ground truth is at 1,2, see testPose2)
Pose2 p2(-1,4.1,M_PI); // robot at (-1,4) looking at negative (ground truth is at 4.1,2)
pose2SLAM::Values config;
config.insert(1,p1);
config.insert(2,p2);
// Linearize
Ordering ordering(*config.orderingArbitrary());
boost::shared_ptr<FactorGraph<GaussianFactor> > lfg_linearized = graph.linearize(config, ordering);
//lfg_linearized->print("lfg_actual");
// the expected linear factor
FactorGraph<GaussianFactor> lfg_expected;
Matrix A1 = Matrix_(3,3,
0.0,-2.0, -4.2,
2.0, 0.0, -4.2,
0.0, 0.0,-10.0);
Matrix A2 = Matrix_(3,3,
2.0, 0.0, 0.0,
0.0, 2.0, 0.0,
0.0, 0.0, 10.0);
Vector b = Vector_(3,-0.1/sx,0.1/sy,0.0);
SharedDiagonal probModel1 = noiseModel::Unit::Create(3);
lfg_expected.push_back(JacobianFactor::shared_ptr(new JacobianFactor(ordering[1], A1, ordering[2], A2, b, probModel1)));
CHECK(assert_equal(lfg_expected, *lfg_linearized));
}
/* ************************************************************************* */
TEST_UNSAFE(Pose2SLAM, optimize) {
// create a Pose graph with one equality constraint and one measurement
pose2SLAM::Graph fg;
fg.addPoseConstraint(0, Pose2(0,0,0));
fg.addOdometry(0, 1, Pose2(1,2,M_PI_2), covariance);
// Create initial config
Values initial;
initial.insert(0, Pose2(0,0,0));
initial.insert(1, Pose2(0,0,0));
// Choose an ordering and optimize
Ordering ordering;
ordering += 0, 1;
LevenbergMarquardtParams params;
params.relativeErrorTol = 1e-15;
params.ordering = ordering;
Values actual = LevenbergMarquardtOptimizer(fg, initial, params).optimize();
// Check with expected config
Values expected;
expected.insert(0, Pose2(0,0,0));
expected.insert(1, Pose2(1,2,M_PI_2));
CHECK(assert_equal(expected, actual));
// Check marginals
Marginals marginals = fg.marginals(actual);
// Matrix expectedP0 = Infinity, as we have a pose constraint !?
// Matrix actualP0 = marginals.marginalCovariance(0);
// EQUALITY(expectedP0, actualP0);
Matrix expectedP1 = cov; // the second pose really should have just the noise covariance
Matrix actualP1 = marginals.marginalCovariance(1);
EQUALITY(expectedP1, actualP1);
}
/* ************************************************************************* */
// test optimization with 3 poses, note we use plain Keys here, not symbols
TEST_UNSAFE(Pose2SLAM, optimizeThreePoses) {
// Create a hexagon of poses
pose2SLAM::Values hexagon = pose2SLAM::circle(3,1.0);
Pose2 p0 = hexagon.pose(0), p1 = hexagon.pose(1);
// create a Pose graph with one equality constraint and one measurement
pose2SLAM::Graph fg;
fg.addPoseConstraint(0, p0);
Pose2 delta = p0.between(p1);
fg.addOdometry(0, 1, delta, covariance);
fg.addOdometry(1, 2, delta, covariance);
fg.addOdometry(2, 0, delta, covariance);
// Create initial config
pose2SLAM::Values initial;
initial.insertPose(0, p0);
initial.insertPose(1, hexagon.pose(1).retract(Vector_(3,-0.1, 0.1,-0.1)));
initial.insertPose(2, hexagon.pose(2).retract(Vector_(3, 0.1,-0.1, 0.1)));
// Choose an ordering
Ordering ordering;
ordering += 0,1,2;
// optimize
LevenbergMarquardtParams params;
params.relativeErrorTol = 1e-15;
params.ordering = ordering;
Values actual = LevenbergMarquardtOptimizer(fg, initial, params).optimize();
// Check with ground truth
CHECK(assert_equal((const Values&)hexagon, actual));
}
/* ************************************************************************* */
// test optimization with 6 poses arranged in a hexagon and a loop closure
TEST_UNSAFE(Pose2SLAM, optimizeCircle) {
// Create a hexagon of poses
pose2SLAM::Values hexagon = pose2SLAM::circle(6,1.0);
Pose2 p0 = hexagon.pose(0), p1 = hexagon.pose(1);
// create a Pose graph with one equality constraint and one measurement
pose2SLAM::Graph fg;
fg.addPoseConstraint(0, p0);
Pose2 delta = p0.between(p1);
fg.addOdometry(0,1, delta, covariance);
fg.addOdometry(1,2, delta, covariance);
fg.addOdometry(2,3, delta, covariance);
fg.addOdometry(3,4, delta, covariance);
fg.addOdometry(4,5, delta, covariance);
fg.addOdometry(5,0, delta, covariance);
// Create initial config
pose2SLAM::Values initial;
initial.insertPose(0, p0);
initial.insertPose(1, hexagon.pose(1).retract(Vector_(3,-0.1, 0.1,-0.1)));
initial.insertPose(2, hexagon.pose(2).retract(Vector_(3, 0.1,-0.1, 0.1)));
initial.insertPose(3, hexagon.pose(3).retract(Vector_(3,-0.1, 0.1,-0.1)));
initial.insertPose(4, hexagon.pose(4).retract(Vector_(3, 0.1,-0.1, 0.1)));
initial.insertPose(5, hexagon.pose(5).retract(Vector_(3,-0.1, 0.1,-0.1)));
// Choose an ordering
Ordering ordering;
ordering += 0,1,2,3,4,5;
// optimize
LevenbergMarquardtParams params;
params.relativeErrorTol = 1e-15;
params.ordering = ordering;
Values actual = LevenbergMarquardtOptimizer(fg, initial, params).optimize();
// Check with ground truth
CHECK(assert_equal((const Values&)hexagon, actual));
// Check loop closure
CHECK(assert_equal(delta, actual.at<Pose2>(5).between(actual.at<Pose2>(0))));
// Pose2SLAMOptimizer myOptimizer("3");
// Matrix A1 = myOptimizer.a1();
// LONGS_EQUAL(3, A1.rows());
// LONGS_EQUAL(17, A1.cols()); // 7 + 7 + 3
//
// Matrix A2 = myOptimizer.a2();
// LONGS_EQUAL(3, A1.rows());
// LONGS_EQUAL(7, A2.cols()); // 7
//
// Vector b1 = myOptimizer.b1();
// LONGS_EQUAL(9, b1.size()); // 3 + 3 + 3
//
// Vector b2 = myOptimizer.b2();
// LONGS_EQUAL(3, b2.size()); // 3
//
// // Here, call matlab to
// // A=[A1;A2], b=[b1;b2]
// // R=qr(A1)
// // call pcg on A,b, with preconditioner R -> get x
//
// Vector x = myOptimizer.optimize();
// LONGS_EQUAL(9, x.size()); // 3 + 3 + 3
//
// myOptimizer.update(x);
//
// Values expected;
// expected.insert(0, Pose2(0.,0.,0.));
// expected.insert(1, Pose2(1.,0.,0.));
// expected.insert(2, Pose2(2.,0.,0.));
//
// // Check with ground truth
// CHECK(assert_equal(expected, *myOptimizer.theta()));
}
/* ************************************************************************* */
TEST_UNSAFE(Pose2SLAM, optimize2) {
// Pose2SLAMOptimizer myOptimizer("100");
// Matrix A1 = myOptimizer.a1();
// Matrix A2 = myOptimizer.a2();
// cout << "A1: " << A1.rows() << " " << A1.cols() << endl;
// cout << "A2: " << A2.rows() << " " << A2.cols() << endl;
//
// //cout << "error: " << myOptimizer.error() << endl;
// for(int i = 0; i<10; i++) {
// myOptimizer.linearize();
// Vector x = myOptimizer.optimize();
// myOptimizer.update(x);
// }
// //cout << "error: " << myOptimizer.error() << endl;
// CHECK(myOptimizer.error() < 1.);
}
///* ************************************************************************* */
// SL-NEEDED? TEST_UNSAFE(Pose2SLAM, findMinimumSpanningTree) {
// pose2SLAM::Graph G, T, C;
// G.addConstraint(1, 2, Pose2(0.,0.,0.), I3);
// G.addConstraint(1, 3, Pose2(0.,0.,0.), I3);
// G.addConstraint(2, 3, Pose2(0.,0.,0.), I3);
//
// PredecessorMap<pose2SLAM::pose2SLAM::PoseKey> tree =
// G.findMinimumSpanningTree<pose2SLAM::pose2SLAM::PoseKey, Pose2Factor>();
// CHECK(tree[1] == 1);
// CHECK(tree[2] == 1);
// CHECK(tree[3] == 1);
//}
//
///* ************************************************************************* */
// SL-NEEDED? TEST_UNSAFE(Pose2SLAM, split) {
// pose2SLAM::Graph G, T, C;
// G.addConstraint(1, 2, Pose2(0.,0.,0.), I3);
// G.addConstraint(1, 3, Pose2(0.,0.,0.), I3);
// G.addConstraint(2, 3, Pose2(0.,0.,0.), I3);
//
// PredecessorMap<pose2SLAM::pose2SLAM::PoseKey> tree;
// tree.insert(1,2);
// tree.insert(2,2);
// tree.insert(3,2);
//
// G.split<pose2SLAM::pose2SLAM::PoseKey, Pose2Factor>(tree, T, C);
// LONGS_EQUAL(2, T.size());
// LONGS_EQUAL(1, C.size());
//}
using namespace pose2SLAM;
/* ************************************************************************* */
TEST_UNSAFE(Pose2Values, pose2Circle )
{
// expected is 4 poses tangent to circle with radius 1m
pose2SLAM::Values expected;
expected.insert(0, Pose2( 1, 0, M_PI_2));
expected.insert(1, Pose2( 0, 1, - M_PI ));
expected.insert(2, Pose2(-1, 0, - M_PI_2));
expected.insert(3, Pose2( 0, -1, 0 ));
pose2SLAM::Values actual = pose2SLAM::circle(4,1.0);
CHECK(assert_equal(expected,actual));
}
/* ************************************************************************* */
TEST_UNSAFE(Pose2SLAM, expmap )
{
// expected is circle shifted to right
pose2SLAM::Values expected;
expected.insert(0, Pose2( 1.1, 0, M_PI_2));
expected.insert(1, Pose2( 0.1, 1, - M_PI ));
expected.insert(2, Pose2(-0.9, 0, - M_PI_2));
expected.insert(3, Pose2( 0.1, -1, 0 ));
// Note expmap coordinates are in local coordinates, so shifting to right requires thought !!!
pose2SLAM::Values circle(pose2SLAM::circle(4,1.0));
Ordering ordering(*circle.orderingArbitrary());
VectorValues delta(circle.dims(ordering));
delta[ordering[0]] = Vector_(3, 0.0,-0.1,0.0);
delta[ordering[1]] = Vector_(3, -0.1,0.0,0.0);
delta[ordering[2]] = Vector_(3, 0.0,0.1,0.0);
delta[ordering[3]] = Vector_(3, 0.1,0.0,0.0);
pose2SLAM::Values actual = circle.retract(delta, ordering);
CHECK(assert_equal(expected,actual));
}
// Common measurement covariance
static SharedNoiseModel sigmas = sharedSigmas(Vector_(3,sx,sy,st));
/* ************************************************************************* */
// Very simple test establishing Ax-b \approx z-h(x)
TEST_UNSAFE( Pose2Prior, error )
{
// Choose a linearization point
Pose2 p1(1, 0, 0); // robot at (1,0)
pose2SLAM::Values x0;
x0.insert(1, p1);
// Create factor
pose2SLAM::Prior factor(1, p1, sigmas);
// Actual linearization
Ordering ordering(*x0.orderingArbitrary());
boost::shared_ptr<JacobianFactor> linear =
boost::dynamic_pointer_cast<JacobianFactor>(factor.linearize(x0, ordering));
// Check error at x0, i.e. delta = zero !
VectorValues delta(VectorValues::Zero(x0.dims(ordering)));
delta[ordering[1]] = zero(3);
Vector error_at_zero = Vector_(3,0.0,0.0,0.0);
CHECK(assert_equal(error_at_zero,factor.whitenedError(x0)));
CHECK(assert_equal(-error_at_zero,linear->error_vector(delta)));
// Check error after increasing p2
VectorValues addition(VectorValues::Zero(x0.dims(ordering)));
addition[ordering[1]] = Vector_(3, 0.1, 0.0, 0.0);
VectorValues plus = delta + addition;
pose2SLAM::Values x1 = x0.retract(plus, ordering);
Vector error_at_plus = Vector_(3,0.1/sx,0.0,0.0); // h(x)-z = 0.1 !
CHECK(assert_equal(error_at_plus,factor.whitenedError(x1)));
CHECK(assert_equal(error_at_plus,linear->error_vector(plus)));
}
/* ************************************************************************* */
// common Pose2Prior for tests below
static gtsam::Pose2 priorVal(2,2,M_PI_2);
static pose2SLAM::Prior priorFactor(1, priorVal, sigmas);
/* ************************************************************************* */
// The error |A*dx-b| approximates (h(x0+dx)-z) = -error_vector
// Hence i.e., b = approximates z-h(x0) = error_vector(x0)
LieVector hprior(const Pose2& p1) {
return LieVector(sigmas->whiten(priorFactor.evaluateError(p1)));
}
/* ************************************************************************* */
TEST_UNSAFE( Pose2Prior, linearize )
{
// Choose a linearization point at ground truth
pose2SLAM::Values x0;
x0.insertPose(1, priorVal);
// Actual linearization
Ordering ordering(*x0.orderingArbitrary());
boost::shared_ptr<JacobianFactor> actual =
boost::dynamic_pointer_cast<JacobianFactor>(priorFactor.linearize(x0, ordering));
// Test with numerical derivative
Matrix numericalH = numericalDerivative11(hprior, priorVal);
CHECK(assert_equal(numericalH,actual->getA(actual->find(ordering[1]))));
}
/* ************************************************************************* */
// Very simple test establishing Ax-b \approx z-h(x)
TEST_UNSAFE( Pose2Factor, error )
{
// Choose a linearization point
Pose2 p1; // robot at origin
Pose2 p2(1, 0, 0); // robot at (1,0)
pose2SLAM::Values x0;
x0.insertPose(1, p1);
x0.insertPose(2, p2);
// Create factor
Pose2 z = p1.between(p2);
Pose2Factor factor(1, 2, z, covariance);
// Actual linearization
Ordering ordering(*x0.orderingArbitrary());
boost::shared_ptr<JacobianFactor> linear =
boost::dynamic_pointer_cast<JacobianFactor>(factor.linearize(x0, ordering));
// Check error at x0, i.e. delta = zero !
VectorValues delta(x0.dims(ordering));
delta[ordering[1]] = zero(3);
delta[ordering[2]] = zero(3);
Vector error_at_zero = Vector_(3,0.0,0.0,0.0);
CHECK(assert_equal(error_at_zero,factor.unwhitenedError(x0)));
CHECK(assert_equal(-error_at_zero, linear->error_vector(delta)));
// Check error after increasing p2
VectorValues plus = delta;
plus[ordering[2]] = Vector_(3, 0.1, 0.0, 0.0);
pose2SLAM::Values x1 = x0.retract(plus, ordering);
Vector error_at_plus = Vector_(3,0.1/sx,0.0,0.0); // h(x)-z = 0.1 !
CHECK(assert_equal(error_at_plus,factor.whitenedError(x1)));
CHECK(assert_equal(error_at_plus,linear->error_vector(plus)));
}
/* ************************************************************************* */
// common Pose2Factor for tests below
static Pose2 measured(2,2,M_PI_2);
static Pose2Factor factor(1,2,measured, covariance);
/* ************************************************************************* */
TEST_UNSAFE( Pose2Factor, rhs )
{
// Choose a linearization point
Pose2 p1(1.1,2,M_PI_2); // robot at (1.1,2) looking towards y (ground truth is at 1,2, see testPose2)
Pose2 p2(-1,4.1,M_PI); // robot at (-1,4.1) looking at negative (ground truth is at -1,4)
pose2SLAM::Values x0;
x0.insert(1,p1);
x0.insert(2,p2);
// Actual linearization
Ordering ordering(*x0.orderingArbitrary());
boost::shared_ptr<JacobianFactor> linear =
boost::dynamic_pointer_cast<JacobianFactor>(factor.linearize(x0, ordering));
// Check RHS
Pose2 hx0 = p1.between(p2);
CHECK(assert_equal(Pose2(2.1, 2.1, M_PI_2),hx0));
Vector expected_b = Vector_(3, -0.1/sx, 0.1/sy, 0.0);
CHECK(assert_equal(expected_b,-factor.whitenedError(x0)));
CHECK(assert_equal(expected_b,linear->getb()));
}
/* ************************************************************************* */
// The error |A*dx-b| approximates (h(x0+dx)-z) = -error_vector
// Hence i.e., b = approximates z-h(x0) = error_vector(x0)
LieVector h(const Pose2& p1,const Pose2& p2) {
return LieVector(covariance->whiten(factor.evaluateError(p1,p2)));
}
/* ************************************************************************* */
TEST_UNSAFE( Pose2Factor, linearize )
{
// Choose a linearization point at ground truth
Pose2 p1(1,2,M_PI_2);
Pose2 p2(-1,4,M_PI);
pose2SLAM::Values x0;
x0.insert(1,p1);
x0.insert(2,p2);
// expected linearization
Matrix expectedH1 = covariance->Whiten(Matrix_(3,3,
0.0,-1.0,-2.0,
1.0, 0.0,-2.0,
0.0, 0.0,-1.0
));
Matrix expectedH2 = covariance->Whiten(Matrix_(3,3,
1.0, 0.0, 0.0,
0.0, 1.0, 0.0,
0.0, 0.0, 1.0
));
Vector expected_b = Vector_(3, 0.0, 0.0, 0.0);
// expected linear factor
Ordering ordering(*x0.orderingArbitrary());
SharedDiagonal probModel1 = noiseModel::Unit::Create(3);
JacobianFactor expected(ordering[1], expectedH1, ordering[2], expectedH2, expected_b, probModel1);
// Actual linearization
boost::shared_ptr<JacobianFactor> actual =
boost::dynamic_pointer_cast<JacobianFactor>(factor.linearize(x0, ordering));
CHECK(assert_equal(expected,*actual));
// Numerical do not work out because BetweenFactor is approximate ?
Matrix numericalH1 = numericalDerivative21(h, p1, p2);
CHECK(assert_equal(expectedH1,numericalH1));
Matrix numericalH2 = numericalDerivative22(h, p1, p2);
CHECK(assert_equal(expectedH2,numericalH2));
}
/* ************************************************************************* */
int main() {
TestResult tr;
return TestRegistry::runAllTests(tr);
}
/* ************************************************************************* */
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