371 lines
12 KiB
C++
371 lines
12 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 testQPSimple.cpp
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* @brief Unit tests for testQPSimple
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* @author Krunal Chande
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* @author Duy-Nguyen Ta
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* @author Luca Carlone
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* @date Dec 15, 2014
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*/
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#include <gtsam/base/numericalDerivative.h>
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#include <gtsam/geometry/Pose3.h>
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#include <gtsam/inference/Symbol.h>
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#include <gtsam/nonlinear/LinearContainerFactor.h>
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#include <gtsam/slam/PriorFactor.h>
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#include <gtsam_unstable/linear/QPSolver.h>
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#include <gtsam_unstable/nonlinear/SQPSimple.h>
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#include <gtsam_unstable/nonlinear/NonlinearInequality.h>
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#include <CppUnitLite/TestHarness.h>
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#include <iostream>
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using namespace std;
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using namespace gtsam::symbol_shorthand;
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using namespace gtsam;
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const double tol = 1e-10;
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//******************************************************************************
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// x + y - 1 = 0
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class ConstraintProblem1 : public NonlinearConstraint2<double, double> {
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typedef NonlinearConstraint2<double, double> Base;
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public:
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ConstraintProblem1(Key xK, Key yK, Key dualKey) : Base(xK, yK, dualKey, 1) {}
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// x + y - 1
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Vector evaluateError(const double& x, const double& y,
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boost::optional<Matrix&> H1 = boost::none, boost::optional<Matrix&> H2 =
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boost::none) const {
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if (H1) *H1 = eye(1);
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if (H2) *H2 = eye(1);
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return (Vector(1) << x + y - 1.0).finished();
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}
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};
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TEST(testSQPSimple, QPProblem) {
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const Key dualKey = 0;
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// Simple quadratic cost: x1^2 + x2^2
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// Note the Hessian encodes:
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// 0.5*x1'*G11*x1 + x1'*G12*x2 + 0.5*x2'*G22*x2 - x1'*g1 - x2'*g2 + 0.5*f
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// Hence here we have G11 = 2, G12 = 0, G22 = 2, g1 = 0, g2 = 0, f = 0
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HessianFactor hf(X(1), Y(1), 2.0 * ones(1,1), zero(1), zero(1),
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2*ones(1,1), zero(1) , 0);
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LinearEqualityFactorGraph equalities;
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LinearEquality linearConstraint(X(1), ones(1), Y(1), ones(1), 1*ones(1), dualKey); // x + y - 1 = 0
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equalities.push_back(linearConstraint);
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// Compare against QP
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QP qp;
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qp.cost.add(hf);
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qp.equalities = equalities;
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// instantiate QPsolver
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QPSolver qpSolver(qp);
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// create initial values for optimization
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VectorValues initialVectorValues;
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initialVectorValues.insert(X(1), zero(1));
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initialVectorValues.insert(Y(1), ones(1));
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VectorValues expectedSolution = qpSolver.optimize(initialVectorValues).first;
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//Instantiate NLP
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NLP nlp;
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Values linPoint;
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linPoint.insert<Vector1>(X(1), zero(1));
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linPoint.insert<Vector1>(Y(1), zero(1));
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nlp.cost.add(LinearContainerFactor(hf, linPoint)); // wrap it using linearcontainerfactor
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nlp.linearEqualities.add(ConstraintProblem1(X(1), Y(1), dualKey));
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Values initialValues;
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initialValues.insert(X(1), 0.0);
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initialValues.insert(Y(1), 0.0);
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// Instantiate SQP
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SQPSimple sqpSimple(nlp);
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Values actualValues = sqpSimple.optimize(initialValues).first;
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DOUBLES_EQUAL(expectedSolution.at(X(1))[0], actualValues.at<double>(X(1)), 1e-100);
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DOUBLES_EQUAL(expectedSolution.at(Y(1))[0], actualValues.at<double>(Y(1)), 1e-100);
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}
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//******************************************************************************
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class CircleConstraint : public NonlinearConstraint2<double, double> {
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typedef NonlinearConstraint2<double, double> Base;
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public:
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CircleConstraint(Key xK, Key yK, Key dualKey) : Base(xK, yK, dualKey, 1) {}
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Vector evaluateError(const double& x, const double& y,
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boost::optional<Matrix&> H1 = boost::none, boost::optional<Matrix&> H2 =
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boost::none) const {
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if (H1) *H1 = (Matrix(1,1) << 2*(x-1)).finished();
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if (H2) *H2 = (Matrix(1,1) << 2*y).finished();
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return (Vector(1) << (x-1)*(x-1) + y*y - 0.25).finished();
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}
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void evaluateHessians(const double& x, const double& y,
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std::vector<Matrix>& G11, std::vector<Matrix>& G12,
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std::vector<Matrix>& G22) const {
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G11.push_back((Matrix(1,1) << 2).finished());
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G12.push_back((Matrix(1,1) << 0).finished());
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G22.push_back((Matrix(1,1) << 2).finished());
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}
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};
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TEST_UNSAFE(testSQPSimple, quadraticCostNonlinearConstraint) {
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const Key dualKey = 0;
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//Instantiate NLP
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NLP nlp;
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// Simple quadratic cost: x1^2 + x2^2 +1000
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// Note the Hessian encodes:
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// 0.5*x1'*G11*x1 + x1'*G12*x2 + 0.5*x2'*G22*x2 - x1'*g1 - x2'*g2 + 0.5*f
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// Hence here we have G11 = 2, G12 = 0, G22 = 2, g1 = 0, g2 = 0, f = 0
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Values linPoint;
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linPoint.insert<Vector1>(X(1), zero(1));
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linPoint.insert<Vector1>(Y(1), zero(1));
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HessianFactor hf(X(1), Y(1), 2.0 * ones(1,1), zero(1), zero(1),
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2*ones(1,1), zero(1) , 1000);
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nlp.cost.add(LinearContainerFactor(hf, linPoint)); // wrap it using linearcontainerfactor
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nlp.nonlinearEqualities.add(CircleConstraint(X(1), Y(1), dualKey));
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Values initialValues;
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initialValues.insert<double>(X(1), 4.0);
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initialValues.insert<double>(Y(1), 10.0);
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Values expectedSolution;
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expectedSolution.insert<double>(X(1), 0.5);
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expectedSolution.insert<double>(Y(1), 0.0);
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// Instantiate SQP
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SQPSimple sqpSimple(nlp);
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Values actualSolution = sqpSimple.optimize(initialValues).first;
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CHECK(assert_equal(expectedSolution, actualSolution, 1e-10));
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}
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//******************************************************************************
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class LineConstraintX : public NonlinearConstraint1<Pose3> {
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typedef NonlinearConstraint1<Pose3> Base;
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public:
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LineConstraintX(Key key, Key dualKey) : Base(key, dualKey, 1) {
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}
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double computeError(const Pose3& pose) const {
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return pose.x();
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}
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void evaluateHessians(const Pose3& pose, std::vector<Matrix>& G11) const {
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Matrix G11all = Z_6x6;
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Vector rT1 = pose.rotation().matrix().row(0);
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G11all.block<3,3>(3,0) = skewSymmetric(rT1);
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G11.push_back(G11all);
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}
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Vector evaluateError(const Pose3& pose, boost::optional<Matrix&> H = boost::none) const {
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if (H)
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*H = (Matrix(1,6) << zeros(1,3), pose.rotation().matrix().row(0)).finished();
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return (Vector(1) << pose.x()).finished();
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}
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};
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TEST(testSQPSimple, poseOnALine) {
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const Key dualKey = 0;
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//Instantiate NLP
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NLP nlp;
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nlp.cost.add(PriorFactor<Pose3>(X(1), Pose3(Rot3::ypr(0.1, 0.2, 0.3), Point3(1, 0, 0)), noiseModel::Unit::Create(6)));
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LineConstraintX constraint(X(1), dualKey);
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nlp.nonlinearEqualities.add(constraint);
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Values initialValues;
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initialValues.insert(X(1), Pose3(Rot3::ypr(0.3, 0.2, 0.3), Point3(1,0,0)));
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Values expectedSolution;
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expectedSolution.insert(X(1), Pose3(Rot3::ypr(0.1, 0.2, 0.3), Point3()));
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// Instantiate SQP
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SQPSimple sqpSimple(nlp);
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Values actualSolution = sqpSimple.optimize(initialValues).first;
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CHECK(assert_equal(expectedSolution, actualSolution, 1e-10));
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Pose3 pose(Rot3::ypr(0.1, 0.2, 0.3), Point3());
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Matrix hessian = numericalHessian<Pose3>(boost::bind(&LineConstraintX::computeError, constraint, _1), pose, 1e-2);
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}
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//******************************************************************************
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/// x + y - 1 <= 0
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class InequalityProblem1 : public NonlinearInequality2<double, double> {
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typedef NonlinearInequality2<double, double> Base;
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public:
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InequalityProblem1(Key xK, Key yK, Key dualKey) : Base(xK, yK, dualKey) {}
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double computeError(const double& x, const double& y,
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boost::optional<Matrix&> H1 = boost::none, boost::optional<Matrix&> H2 =
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boost::none) const {
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if (H1) *H1 = eye(1);
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if (H2) *H2 = eye(1);
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return x + y - 1.0;
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}
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};
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TEST(testSQPSimple, inequalityConstraint) {
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const Key dualKey = 0;
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// Simple quadratic cost: x^2 + y^2
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// Note the Hessian encodes:
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// 0.5*x1'*G11*x1 + x1'*G12*x2 + 0.5*x2'*G22*x2 - x1'*g1 - x2'*g2 + 0.5*f
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// Hence here we have G11 = 2, G12 = 0, G22 = 2, g1 = 0, g2 = 0, f = 0
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HessianFactor hf(X(1), Y(1), 2.0 * ones(1,1), zero(1), zero(1),
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2*ones(1,1), zero(1) , 0);
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LinearInequalityFactorGraph inequalities;
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LinearInequality linearConstraint(X(1), ones(1), Y(1), ones(1), 1.0, dualKey); // x + y - 1 <= 0
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inequalities.push_back(linearConstraint);
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// Compare against QP
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QP qp;
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qp.cost.add(hf);
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qp.inequalities = inequalities;
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// instantiate QPsolver
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QPSolver qpSolver(qp);
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// create initial values for optimization
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VectorValues initialVectorValues;
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initialVectorValues.insert(X(1), zero(1));
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initialVectorValues.insert(Y(1), zero(1));
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VectorValues expectedSolution = qpSolver.optimize(initialVectorValues).first;
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//Instantiate NLP
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NLP nlp;
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Values linPoint;
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linPoint.insert<Vector1>(X(1), zero(1));
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linPoint.insert<Vector1>(Y(1), zero(1));
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nlp.cost.add(LinearContainerFactor(hf, linPoint)); // wrap it using linearcontainerfactor
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nlp.linearInequalities.add(InequalityProblem1(X(1), Y(1), dualKey));
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Values initialValues;
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initialValues.insert(X(1), 1.0);
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initialValues.insert(Y(1), -10.0);
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// Instantiate SQP
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SQPSimple sqpSimple(nlp);
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Values actualValues = sqpSimple.optimize(initialValues).first;
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DOUBLES_EQUAL(expectedSolution.at(X(1))[0], actualValues.at<double>(X(1)), 1e-10);
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DOUBLES_EQUAL(expectedSolution.at(Y(1))[0], actualValues.at<double>(Y(1)), 1e-10);
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}
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//******************************************************************************
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const size_t X_AXIS = 0;
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const size_t Y_AXIS = 1;
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const size_t Z_AXIS = 2;
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/**
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* Inequality boundary constraint on one axis (x, y or z)
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* axis <= bound
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*/
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class AxisUpperBound : public NonlinearInequality1<Pose3> {
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typedef NonlinearInequality1<Pose3> Base;
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size_t axis_;
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double bound_;
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public:
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AxisUpperBound(Key key, size_t axis, double bound, Key dualKey) : Base(key, dualKey), axis_(axis), bound_(bound) {
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}
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double computeError(const Pose3& pose, boost::optional<Matrix&> H = boost::none) const {
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if (H)
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*H = (Matrix(1,6) << zeros(1,3), pose.rotation().matrix().row(axis_)).finished();
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return pose.translation().vector()[axis_] - bound_;
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}
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};
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/**
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* Inequality boundary constraint on one axis (x, y or z)
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* bound <= axis
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*/
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class AxisLowerBound : public NonlinearInequality1<Pose3> {
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typedef NonlinearInequality1<Pose3> Base;
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size_t axis_;
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double bound_;
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public:
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AxisLowerBound(Key key, size_t axis, double bound, Key dualKey) : Base(key, dualKey), axis_(axis), bound_(bound) {
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}
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double computeError(const Pose3& pose, boost::optional<Matrix&> H = boost::none) const {
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if (H)
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*H = (Matrix(1,6) << zeros(1,3), -pose.rotation().matrix().row(axis_)).finished();
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return -pose.translation().vector()[axis_] + bound_;
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}
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};
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TEST(testSQPSimple, poseWithABoundary) {
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const Key dualKey = 0;
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//Instantiate NLP
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NLP nlp;
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nlp.cost.add(PriorFactor<Pose3>(X(1), Pose3(Rot3::ypr(0.1, 0.2, 0.3), Point3(1, 0, 0)), noiseModel::Unit::Create(6)));
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AxisUpperBound constraint(X(1), X_AXIS, 0, dualKey);
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nlp.linearInequalities.add(constraint);
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Values initialValues;
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initialValues.insert(X(1), Pose3(Rot3::ypr(0.3, 0.2, 0.3), Point3(1, 0, 0)));
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Values expectedSolution;
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expectedSolution.insert(X(1), Pose3(Rot3::ypr(0.1, 0.2, 0.3), Point3(0, 0, 0)));
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// Instantiate SQP
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SQPSimple sqpSimple(nlp);
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Values actualSolution = sqpSimple.optimize(initialValues).first;
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CHECK(assert_equal(expectedSolution, actualSolution, 1e-10));
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}
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TEST(testSQPSimple, poseWithinA2DBox) {
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const Key dualKey = 0;
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//Instantiate NLP
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NLP nlp;
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nlp.cost.add(PriorFactor<Pose3>(X(1), Pose3(Rot3::ypr(0.1, 0.2, 0.3), Point3(10, 0.5, 0)), noiseModel::Unit::Create(6)));
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nlp.linearInequalities.add(AxisLowerBound(X(1), X_AXIS, -1, dualKey));
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nlp.linearInequalities.add(AxisUpperBound(X(1), X_AXIS, 1, dualKey));
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nlp.linearInequalities.add(AxisLowerBound(X(1), Y_AXIS, -1, dualKey));
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nlp.linearInequalities.add(AxisUpperBound(X(1), Y_AXIS, 1, dualKey));
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Values initialValues;
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initialValues.insert(X(1), Pose3(Rot3::ypr(0.3, 0.2, 0.3), Point3(1, 0, 0)));
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Values expectedSolution;
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expectedSolution.insert(X(1), Pose3(Rot3::ypr(0.1, 0.2, 0.3), Point3(1, 0.5, 0)));
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// Instantiate SQP
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SQPSimple sqpSimple(nlp);
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Values actualSolution = sqpSimple.optimize(initialValues).first;
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CHECK(assert_equal(expectedSolution, actualSolution, 1e-10));
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}
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//******************************************************************************
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int main() {
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TestResult tr;
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return TestRegistry::runAllTests(tr);
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}
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//******************************************************************************
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