577 lines
18 KiB
C++
577 lines
18 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 testNonlinearEquality.cpp
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* @author Alex Cunningham
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*/
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#include <gtsam/slam/PriorFactor.h>
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#include <gtsam/slam/simulated2DConstraints.h>
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#include <gtsam/slam/visualSLAM.h>
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#include <gtsam/nonlinear/Symbol.h>
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#include <gtsam/nonlinear/NonlinearEquality.h>
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#include <gtsam/nonlinear/NonlinearFactorGraph.h>
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#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
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#include <gtsam/geometry/Pose2.h>
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#include <CppUnitLite/TestHarness.h>
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using namespace std;
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using namespace gtsam;
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namespace eq2D = simulated2D::equality_constraints;
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static const double tol = 1e-5;
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typedef PriorFactor<Pose2> PosePrior;
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typedef NonlinearEquality<Pose2> PoseNLE;
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typedef boost::shared_ptr<PoseNLE> shared_poseNLE;
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Symbol key('x',1);
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/* ************************************************************************* */
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TEST ( NonlinearEquality, linearization ) {
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Pose2 value = Pose2(2.1, 1.0, 2.0);
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Values linearize;
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linearize.insert(key, value);
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// create a nonlinear equality constraint
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shared_poseNLE nle(new PoseNLE(key, value));
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// check linearize
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SharedDiagonal constraintModel = noiseModel::Constrained::All(3);
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JacobianFactor expLF(0, eye(3), zero(3), constraintModel);
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GaussianFactor::shared_ptr actualLF = nle->linearize(linearize, *linearize.orderingArbitrary());
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EXPECT(assert_equal(*actualLF, (const GaussianFactor&)expLF));
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}
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/* ********************************************************************** */
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TEST ( NonlinearEquality, linearization_pose ) {
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Symbol key('x',1);
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Pose2 value;
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Values config;
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config.insert(key, value);
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// create a nonlinear equality constraint
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shared_poseNLE nle(new PoseNLE(key, value));
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GaussianFactor::shared_ptr actualLF = nle->linearize(config, *config.orderingArbitrary());
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EXPECT(true);
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}
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/* ********************************************************************** */
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TEST ( NonlinearEquality, linearization_fail ) {
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Pose2 value = Pose2(2.1, 1.0, 2.0);
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Pose2 wrong = Pose2(2.1, 3.0, 4.0);
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Values bad_linearize;
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bad_linearize.insert(key, wrong);
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// create a nonlinear equality constraint
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shared_poseNLE nle(new PoseNLE(key, value));
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// check linearize to ensure that it fails for bad linearization points
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CHECK_EXCEPTION(nle->linearize(bad_linearize, *bad_linearize.orderingArbitrary()), std::invalid_argument);
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}
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/* ********************************************************************** */
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TEST ( NonlinearEquality, linearization_fail_pose ) {
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Symbol key('x',1);
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Pose2 value(2.0, 1.0, 2.0),
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wrong(2.0, 3.0, 4.0);
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Values bad_linearize;
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bad_linearize.insert(key, wrong);
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// create a nonlinear equality constraint
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shared_poseNLE nle(new PoseNLE(key, value));
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// check linearize to ensure that it fails for bad linearization points
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CHECK_EXCEPTION(nle->linearize(bad_linearize, *bad_linearize.orderingArbitrary()), std::invalid_argument);
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}
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/* ********************************************************************** */
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TEST ( NonlinearEquality, linearization_fail_pose_origin ) {
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Symbol key('x',1);
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Pose2 value,
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wrong(2.0, 3.0, 4.0);
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Values bad_linearize;
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bad_linearize.insert(key, wrong);
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// create a nonlinear equality constraint
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shared_poseNLE nle(new PoseNLE(key, value));
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// check linearize to ensure that it fails for bad linearization points
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CHECK_EXCEPTION(nle->linearize(bad_linearize, *bad_linearize.orderingArbitrary()), std::invalid_argument);
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}
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/* ************************************************************************* */
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TEST ( NonlinearEquality, error ) {
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Pose2 value = Pose2(2.1, 1.0, 2.0);
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Pose2 wrong = Pose2(2.1, 3.0, 4.0);
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Values feasible, bad_linearize;
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feasible.insert(key, value);
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bad_linearize.insert(key, wrong);
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// create a nonlinear equality constraint
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shared_poseNLE nle(new PoseNLE(key, value));
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// check error function outputs
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Vector actual = nle->unwhitenedError(feasible);
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EXPECT(assert_equal(actual, zero(3)));
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actual = nle->unwhitenedError(bad_linearize);
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EXPECT(assert_equal(actual, repeat(3, std::numeric_limits<double>::infinity())));
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}
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/* ************************************************************************* */
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TEST ( NonlinearEquality, equals ) {
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Pose2 value1 = Pose2(2.1, 1.0, 2.0);
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Pose2 value2 = Pose2(2.1, 3.0, 4.0);
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// create some constraints to compare
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shared_poseNLE nle1(new PoseNLE(key, value1));
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shared_poseNLE nle2(new PoseNLE(key, value1));
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shared_poseNLE nle3(new PoseNLE(key, value2));
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// verify
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EXPECT(nle1->equals(*nle2)); // basic equality = true
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EXPECT(nle2->equals(*nle1)); // test symmetry of equals()
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EXPECT(!nle1->equals(*nle3)); // test config
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}
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/* ************************************************************************* */
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TEST ( NonlinearEquality, allow_error_pose ) {
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Symbol key1('x',1);
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Pose2 feasible1(1.0, 2.0, 3.0);
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double error_gain = 500.0;
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PoseNLE nle(key1, feasible1, error_gain);
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// the unwhitened error should provide logmap to the feasible state
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Pose2 badPoint1(0.0, 2.0, 3.0);
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Vector actVec = nle.evaluateError(badPoint1);
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Vector expVec = Vector_(3, -0.989992, -0.14112, 0.0);
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EXPECT(assert_equal(expVec, actVec, 1e-5));
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// the actual error should have a gain on it
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Values config;
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config.insert(key1, badPoint1);
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double actError = nle.error(config);
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DOUBLES_EQUAL(500.0, actError, 1e-9);
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// check linearization
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GaussianFactor::shared_ptr actLinFactor = nle.linearize(config, *config.orderingArbitrary());
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Matrix A1 = eye(3,3);
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Vector b = expVec;
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SharedDiagonal model = noiseModel::Constrained::All(3);
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GaussianFactor::shared_ptr expLinFactor(new JacobianFactor(0, A1, b, model));
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EXPECT(assert_equal(*expLinFactor, *actLinFactor, 1e-5));
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}
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/* ************************************************************************* */
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TEST ( NonlinearEquality, allow_error_optimize ) {
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Symbol key1('x',1);
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Pose2 feasible1(1.0, 2.0, 3.0);
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double error_gain = 500.0;
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PoseNLE nle(key1, feasible1, error_gain);
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// add to a graph
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NonlinearFactorGraph graph;
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graph.add(nle);
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// initialize away from the ideal
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Pose2 initPose(0.0, 2.0, 3.0);
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Values init;
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init.insert(key1, initPose);
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// optimize
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Ordering ordering;
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ordering.push_back(key1);
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Values result = LevenbergMarquardtOptimizer(graph, init, ordering).optimize();
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// verify
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Values expected;
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expected.insert(key1, feasible1);
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EXPECT(assert_equal(expected, result));
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}
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/* ************************************************************************* */
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TEST ( NonlinearEquality, allow_error_optimize_with_factors ) {
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// create a hard constraint
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Symbol key1('x',1);
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Pose2 feasible1(1.0, 2.0, 3.0);
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// initialize away from the ideal
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Values init;
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Pose2 initPose(0.0, 2.0, 3.0);
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init.insert(key1, initPose);
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double error_gain = 500.0;
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PoseNLE nle(key1, feasible1, error_gain);
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// create a soft prior that conflicts
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PosePrior prior(key1, initPose, noiseModel::Isotropic::Sigma(3, 0.1));
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// add to a graph
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NonlinearFactorGraph graph;
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graph.add(nle);
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graph.add(prior);
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// optimize
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Ordering ordering;
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ordering.push_back(key1);
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Values actual = LevenbergMarquardtOptimizer(graph, init, ordering).optimize();
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// verify
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Values expected;
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expected.insert(key1, feasible1);
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EXPECT(assert_equal(expected, actual));
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}
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/* ************************************************************************* */
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SharedDiagonal hard_model = noiseModel::Constrained::All(2);
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SharedDiagonal soft_model = noiseModel::Isotropic::Sigma(2, 1.0);
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/* ************************************************************************* */
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TEST( testNonlinearEqualityConstraint, unary_basics ) {
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Point2 pt(1.0, 2.0);
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Symbol key1('x',1);
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double mu = 1000.0;
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eq2D::UnaryEqualityConstraint constraint(pt, key, mu);
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Values config1;
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config1.insert(key, pt);
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EXPECT(constraint.active(config1));
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EXPECT(assert_equal(zero(2), constraint.evaluateError(pt), tol));
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EXPECT(assert_equal(zero(2), constraint.unwhitenedError(config1), tol));
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EXPECT_DOUBLES_EQUAL(0.0, constraint.error(config1), tol);
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Values config2;
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Point2 ptBad1(2.0, 2.0);
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config2.insert(key, ptBad1);
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EXPECT(constraint.active(config2));
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EXPECT(assert_equal(Vector_(2, 1.0, 0.0), constraint.evaluateError(ptBad1), tol));
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EXPECT(assert_equal(Vector_(2, 1.0, 0.0), constraint.unwhitenedError(config2), tol));
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EXPECT_DOUBLES_EQUAL(500.0, constraint.error(config2), tol);
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}
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/* ************************************************************************* */
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TEST( testNonlinearEqualityConstraint, unary_linearization ) {
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Point2 pt(1.0, 2.0);
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Symbol key1('x',1);
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double mu = 1000.0;
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Ordering ordering;
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ordering += key;
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eq2D::UnaryEqualityConstraint constraint(pt, key, mu);
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Values config1;
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config1.insert(key, pt);
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GaussianFactor::shared_ptr actual1 = constraint.linearize(config1, ordering);
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GaussianFactor::shared_ptr expected1(new JacobianFactor(ordering[key], eye(2,2), zero(2), hard_model));
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EXPECT(assert_equal(*expected1, *actual1, tol));
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Values config2;
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Point2 ptBad(2.0, 2.0);
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config2.insert(key, ptBad);
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GaussianFactor::shared_ptr actual2 = constraint.linearize(config2, ordering);
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GaussianFactor::shared_ptr expected2(new JacobianFactor(ordering[key], eye(2,2), Vector_(2,-1.0,0.0), hard_model));
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EXPECT(assert_equal(*expected2, *actual2, tol));
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}
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/* ************************************************************************* */
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TEST( testNonlinearEqualityConstraint, unary_simple_optimization ) {
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// create a single-node graph with a soft and hard constraint to
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// ensure that the hard constraint overrides the soft constraint
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Point2 truth_pt(1.0, 2.0);
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Symbol key('x',1);
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double mu = 10.0;
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eq2D::UnaryEqualityConstraint::shared_ptr constraint(
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new eq2D::UnaryEqualityConstraint(truth_pt, key, mu));
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Point2 badPt(100.0, -200.0);
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simulated2D::Prior::shared_ptr factor(
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new simulated2D::Prior(badPt, soft_model, key));
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NonlinearFactorGraph graph;
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graph.push_back(constraint);
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graph.push_back(factor);
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Values initValues;
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initValues.insert(key, badPt);
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// verify error values
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EXPECT(constraint->active(initValues));
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Values expected;
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expected.insert(key, truth_pt);
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EXPECT(constraint->active(expected));
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EXPECT_DOUBLES_EQUAL(0.0, constraint->error(expected), tol);
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Values actual = LevenbergMarquardtOptimizer(graph, initValues).optimize();
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EXPECT(assert_equal(expected, actual, tol));
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}
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/* ************************************************************************* */
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TEST( testNonlinearEqualityConstraint, odo_basics ) {
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Point2 x1(1.0, 2.0), x2(2.0, 3.0), odom(1.0, 1.0);
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Symbol key1('x',1), key2('x',2);
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double mu = 1000.0;
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eq2D::OdoEqualityConstraint constraint(odom, key1, key2, mu);
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Values config1;
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config1.insert(key1, x1);
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config1.insert(key2, x2);
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EXPECT(constraint.active(config1));
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EXPECT(assert_equal(zero(2), constraint.evaluateError(x1, x2), tol));
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EXPECT(assert_equal(zero(2), constraint.unwhitenedError(config1), tol));
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EXPECT_DOUBLES_EQUAL(0.0, constraint.error(config1), tol);
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Values config2;
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Point2 x1bad(2.0, 2.0);
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Point2 x2bad(2.0, 2.0);
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config2.insert(key1, x1bad);
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config2.insert(key2, x2bad);
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EXPECT(constraint.active(config2));
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EXPECT(assert_equal(Vector_(2, -1.0, -1.0), constraint.evaluateError(x1bad, x2bad), tol));
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EXPECT(assert_equal(Vector_(2, -1.0, -1.0), constraint.unwhitenedError(config2), tol));
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EXPECT_DOUBLES_EQUAL(1000.0, constraint.error(config2), tol);
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}
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/* ************************************************************************* */
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TEST( testNonlinearEqualityConstraint, odo_linearization ) {
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Point2 x1(1.0, 2.0), x2(2.0, 3.0), odom(1.0, 1.0);
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Symbol key1('x',1), key2('x',2);
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double mu = 1000.0;
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Ordering ordering;
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ordering += key1, key2;
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eq2D::OdoEqualityConstraint constraint(odom, key1, key2, mu);
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Values config1;
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config1.insert(key1, x1);
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config1.insert(key2, x2);
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GaussianFactor::shared_ptr actual1 = constraint.linearize(config1, ordering);
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GaussianFactor::shared_ptr expected1(
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new JacobianFactor(ordering[key1], -eye(2,2), ordering[key2],
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eye(2,2), zero(2), hard_model));
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EXPECT(assert_equal(*expected1, *actual1, tol));
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Values config2;
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Point2 x1bad(2.0, 2.0);
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Point2 x2bad(2.0, 2.0);
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config2.insert(key1, x1bad);
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config2.insert(key2, x2bad);
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GaussianFactor::shared_ptr actual2 = constraint.linearize(config2, ordering);
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GaussianFactor::shared_ptr expected2(
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new JacobianFactor(ordering[key1], -eye(2,2), ordering[key2],
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eye(2,2), Vector_(2, 1.0, 1.0), hard_model));
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EXPECT(assert_equal(*expected2, *actual2, tol));
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}
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/* ************************************************************************* */
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TEST( testNonlinearEqualityConstraint, odo_simple_optimize ) {
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// create a two-node graph, connected by an odometry constraint, with
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// a hard prior on one variable, and a conflicting soft prior
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// on the other variable - the constraints should override the soft constraint
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Point2 truth_pt1(1.0, 2.0), truth_pt2(3.0, 2.0);
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Symbol key1('x',1), key2('x',2);
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// hard prior on x1
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eq2D::UnaryEqualityConstraint::shared_ptr constraint1(
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new eq2D::UnaryEqualityConstraint(truth_pt1, key1));
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// soft prior on x2
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Point2 badPt(100.0, -200.0);
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simulated2D::Prior::shared_ptr factor(
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new simulated2D::Prior(badPt, soft_model, key2));
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// odometry constraint
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eq2D::OdoEqualityConstraint::shared_ptr constraint2(
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new eq2D::OdoEqualityConstraint(
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truth_pt1.between(truth_pt2), key1, key2));
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NonlinearFactorGraph graph;
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graph.push_back(constraint1);
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graph.push_back(constraint2);
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graph.push_back(factor);
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Values initValues;
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initValues.insert(key1, Point2());
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initValues.insert(key2, badPt);
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Values actual = LevenbergMarquardtOptimizer(graph, initValues).optimize();
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Values expected;
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expected.insert(key1, truth_pt1);
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expected.insert(key2, truth_pt2);
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CHECK(assert_equal(expected, actual, tol));
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}
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/* ********************************************************************* */
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TEST (testNonlinearEqualityConstraint, two_pose ) {
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/*
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* Determining a ground truth linear system
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* with two poses seeing one landmark, with each pose
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* constrained to a particular value
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*/
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NonlinearFactorGraph graph;
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Symbol x1('x',1), x2('x',2);
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Symbol l1('l',1), l2('l',2);
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Point2 pt_x1(1.0, 1.0),
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pt_x2(5.0, 6.0);
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graph.add(eq2D::UnaryEqualityConstraint(pt_x1, x1));
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graph.add(eq2D::UnaryEqualityConstraint(pt_x2, x2));
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Point2 z1(0.0, 5.0);
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SharedNoiseModel sigma(noiseModel::Isotropic::Sigma(2, 0.1));
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graph.add(simulated2D::Measurement(z1, sigma, x1,l1));
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Point2 z2(-4.0, 0.0);
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graph.add(simulated2D::Measurement(z2, sigma, x2,l2));
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graph.add(eq2D::PointEqualityConstraint(l1, l2));
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Values initialEstimate;
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initialEstimate.insert(x1, pt_x1);
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initialEstimate.insert(x2, Point2());
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initialEstimate.insert(l1, Point2(1.0, 6.0)); // ground truth
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initialEstimate.insert(l2, Point2(-4.0, 0.0)); // starting with a separate reference frame
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Values actual = LevenbergMarquardtOptimizer(graph, initialEstimate).optimize();
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Values expected;
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expected.insert(x1, pt_x1);
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expected.insert(l1, Point2(1.0, 6.0));
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expected.insert(l2, Point2(1.0, 6.0));
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expected.insert(x2, Point2(5.0, 6.0));
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CHECK(assert_equal(expected, actual, 1e-5));
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}
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/* ********************************************************************* */
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TEST (testNonlinearEqualityConstraint, map_warp ) {
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// get a graph
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NonlinearFactorGraph graph;
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// keys
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Symbol x1('x',1), x2('x',2);
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Symbol l1('l',1), l2('l',2);
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// constant constraint on x1
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Point2 pose1(1.0, 1.0);
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graph.add(eq2D::UnaryEqualityConstraint(pose1, x1));
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SharedDiagonal sigma = noiseModel::Isotropic::Sigma(1,0.1);
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// measurement from x1 to l1
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Point2 z1(0.0, 5.0);
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graph.add(simulated2D::Measurement(z1, sigma, x1, l1));
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// measurement from x2 to l2
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Point2 z2(-4.0, 0.0);
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graph.add(simulated2D::Measurement(z2, sigma, x2, l2));
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// equality constraint between l1 and l2
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graph.add(eq2D::PointEqualityConstraint(l1, l2));
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|
|
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// create an initial estimate
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Values initialEstimate;
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initialEstimate.insert(x1, Point2( 1.0, 1.0));
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initialEstimate.insert(l1, Point2( 1.0, 6.0));
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initialEstimate.insert(l2, Point2(-4.0, 0.0)); // starting with a separate reference frame
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initialEstimate.insert(x2, Point2( 0.0, 0.0)); // other pose starts at origin
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|
|
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// optimize
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Values actual = LevenbergMarquardtOptimizer(graph, initialEstimate).optimize();
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|
|
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Values expected;
|
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expected.insert(x1, Point2(1.0, 1.0));
|
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expected.insert(l1, Point2(1.0, 6.0));
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expected.insert(l2, Point2(1.0, 6.0));
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expected.insert(x2, Point2(5.0, 6.0));
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CHECK(assert_equal(expected, actual, tol));
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}
|
|
|
|
// make a realistic calibration matrix
|
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double fov = 60; // degrees
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size_t w=640,h=480;
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Cal3_S2 K(fov,w,h);
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boost::shared_ptr<Cal3_S2> shK(new Cal3_S2(K));
|
|
|
|
// typedefs for visual SLAM example
|
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typedef visualSLAM::Graph VGraph;
|
|
|
|
// factors for visual slam
|
|
typedef NonlinearEquality2<Point3> Point3Equality;
|
|
|
|
/* ********************************************************************* */
|
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TEST (testNonlinearEqualityConstraint, stereo_constrained ) {
|
|
|
|
// create initial estimates
|
|
Rot3 faceDownY(Matrix_(3,3,
|
|
1.0, 0.0, 0.0,
|
|
0.0, 0.0, 1.0,
|
|
0.0, -1.0, 0.0));
|
|
Pose3 pose1(faceDownY, Point3()); // origin, left camera
|
|
SimpleCamera camera1(K, pose1);
|
|
Pose3 pose2(faceDownY, Point3(2.0, 0.0, 0.0)); // 2 units to the left
|
|
SimpleCamera camera2(K, pose2);
|
|
Point3 landmark(1.0, 5.0, 0.0); //centered between the cameras, 5 units away
|
|
|
|
// keys
|
|
Symbol x1('x',1), x2('x',2);
|
|
Symbol l1('l',1), l2('l',2);
|
|
|
|
// create graph
|
|
VGraph graph;
|
|
|
|
// create equality constraints for poses
|
|
graph.addPoseConstraint(x1, camera1.pose());
|
|
graph.addPoseConstraint(x2, camera2.pose());
|
|
|
|
// create factors
|
|
SharedDiagonal vmodel = noiseModel::Unit::Create(3);
|
|
graph.addMeasurement(camera1.project(landmark), vmodel, x1, l1, shK);
|
|
graph.addMeasurement(camera2.project(landmark), vmodel, x2, l2, shK);
|
|
|
|
// add equality constraint
|
|
graph.add(Point3Equality(l1, l2));
|
|
|
|
// create initial data
|
|
Point3 landmark1(0.5, 5.0, 0.0);
|
|
Point3 landmark2(1.5, 5.0, 0.0);
|
|
|
|
Values initValues;
|
|
initValues.insert(x1, pose1);
|
|
initValues.insert(x2, pose2);
|
|
initValues.insert(l1, landmark1);
|
|
initValues.insert(l2, landmark2);
|
|
|
|
// optimize
|
|
Values actual = LevenbergMarquardtOptimizer(graph, initValues).optimize();
|
|
|
|
// create config
|
|
Values truthValues;
|
|
truthValues.insert(x1, camera1.pose());
|
|
truthValues.insert(x2, camera2.pose());
|
|
truthValues.insert(l1, landmark);
|
|
truthValues.insert(l2, landmark);
|
|
|
|
// check if correct
|
|
CHECK(assert_equal(truthValues, actual, 1e-5));
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
int main() { TestResult tr; return TestRegistry::runAllTests(tr); }
|
|
/* ************************************************************************* */
|