500 lines
14 KiB
C++
500 lines
14 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 smallExample.cpp
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* @brief Create small example with two poses and one landmark
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* @brief smallExample
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* @author Carlos Nieto
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* @author Frank dellaert
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*/
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#include <gtsam/nonlinear/Symbol.h>
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#include <gtsam/nonlinear/Ordering.h>
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#include <gtsam/nonlinear/NonlinearFactorGraph.h>
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#include <gtsam/nonlinear/NonlinearFactor.h>
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#include <gtsam/inference/FactorGraph.h>
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#include <gtsam/base/Matrix.h>
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#include <tests/smallExample.h>
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#include <boost/optional.hpp>
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#include <boost/shared_ptr.hpp>
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#include <iostream>
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#include <string>
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using namespace std;
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namespace gtsam {
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namespace example {
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typedef boost::shared_ptr<NonlinearFactor> shared;
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static SharedDiagonal sigma1_0 = noiseModel::Isotropic::Sigma(2,1.0);
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static SharedDiagonal sigma0_1 = noiseModel::Isotropic::Sigma(2,0.1);
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static SharedDiagonal sigma0_2 = noiseModel::Isotropic::Sigma(2,0.2);
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static SharedDiagonal constraintModel = noiseModel::Constrained::All(2);
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static const Index _l1_=0, _x1_=1, _x2_=2;
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static const Index _x_=0, _y_=1, _z_=2;
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// Convenience for named keys
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using symbol_shorthand::X;
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using symbol_shorthand::L;
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/* ************************************************************************* */
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boost::shared_ptr<const Graph> sharedNonlinearFactorGraph() {
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// Create
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boost::shared_ptr<Graph> nlfg(
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new Graph);
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// prior on x1
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Point2 mu;
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shared f1(new simulated2D::Prior(mu, sigma0_1, X(1)));
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nlfg->push_back(f1);
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// odometry between x1 and x2
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Point2 z2(1.5, 0);
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shared f2(new simulated2D::Odometry(z2, sigma0_1, X(1), X(2)));
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nlfg->push_back(f2);
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// measurement between x1 and l1
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Point2 z3(0, -1);
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shared f3(new simulated2D::Measurement(z3, sigma0_2, X(1), L(1)));
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nlfg->push_back(f3);
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// measurement between x2 and l1
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Point2 z4(-1.5, -1.);
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shared f4(new simulated2D::Measurement(z4, sigma0_2, X(2), L(1)));
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nlfg->push_back(f4);
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return nlfg;
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}
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/* ************************************************************************* */
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Graph createNonlinearFactorGraph() {
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return *sharedNonlinearFactorGraph();
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}
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/* ************************************************************************* */
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Values createValues() {
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Values c;
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c.insert(X(1), Point2(0.0, 0.0));
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c.insert(X(2), Point2(1.5, 0.0));
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c.insert(L(1), Point2(0.0, -1.0));
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return c;
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}
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/* ************************************************************************* */
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VectorValues createVectorValues() {
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VectorValues c(vector<size_t>(3, 2));
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c[_l1_] = Vector_(2, 0.0, -1.0);
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c[_x1_] = Vector_(2, 0.0, 0.0);
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c[_x2_] = Vector_(2, 1.5, 0.0);
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return c;
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}
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/* ************************************************************************* */
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boost::shared_ptr<const Values> sharedNoisyValues() {
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boost::shared_ptr<Values> c(new Values);
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c->insert(X(1), Point2(0.1, 0.1));
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c->insert(X(2), Point2(1.4, 0.2));
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c->insert(L(1), Point2(0.1, -1.1));
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return c;
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}
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/* ************************************************************************* */
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Values createNoisyValues() {
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return *sharedNoisyValues();
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}
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/* ************************************************************************* */
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VectorValues createCorrectDelta(const Ordering& ordering) {
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VectorValues c(vector<size_t>(3,2));
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c[ordering[L(1)]] = Vector_(2, -0.1, 0.1);
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c[ordering[X(1)]] = Vector_(2, -0.1, -0.1);
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c[ordering[X(2)]] = Vector_(2, 0.1, -0.2);
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return c;
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}
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/* ************************************************************************* */
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VectorValues createZeroDelta(const Ordering& ordering) {
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VectorValues c(vector<size_t>(3,2));
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c[ordering[L(1)]] = zero(2);
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c[ordering[X(1)]] = zero(2);
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c[ordering[X(2)]] = zero(2);
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return c;
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}
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/* ************************************************************************* */
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JacobianFactorGraph createGaussianFactorGraph(const Ordering& ordering) {
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// Create empty graph
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JacobianFactorGraph fg;
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SharedDiagonal unit2 = noiseModel::Unit::Create(2);
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// linearized prior on x1: c[_x1_]+x1=0 i.e. x1=-c[_x1_]
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fg.push_back(boost::make_shared<JacobianFactor>(ordering[X(1)], 10*eye(2), -1.0*ones(2), unit2));
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// odometry between x1 and x2: x2-x1=[0.2;-0.1]
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fg.push_back(boost::make_shared<JacobianFactor>(ordering[X(1)], -10*eye(2),ordering[X(2)], 10*eye(2), Vector_(2, 2.0, -1.0), unit2));
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// measurement between x1 and l1: l1-x1=[0.0;0.2]
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fg.push_back(boost::make_shared<JacobianFactor>(ordering[X(1)], -5*eye(2), ordering[L(1)], 5*eye(2), Vector_(2, 0.0, 1.0), unit2));
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// measurement between x2 and l1: l1-x2=[-0.2;0.3]
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fg.push_back(boost::make_shared<JacobianFactor>(ordering[X(2)], -5*eye(2), ordering[L(1)], 5*eye(2), Vector_(2, -1.0, 1.5), unit2));
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return fg;
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}
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/* ************************************************************************* */
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/** create small Chordal Bayes Net x <- y
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* x y d
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* 1 1 9
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* 1 5
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*/
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GaussianBayesNet createSmallGaussianBayesNet() {
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Matrix R11 = Matrix_(1, 1, 1.0), S12 = Matrix_(1, 1, 1.0);
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Matrix R22 = Matrix_(1, 1, 1.0);
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Vector d1(1), d2(1);
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d1(0) = 9;
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d2(0) = 5;
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Vector tau(1);
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tau(0) = 1.0;
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// define nodes and specify in reverse topological sort (i.e. parents last)
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GaussianConditional::shared_ptr Px_y(new GaussianConditional(_x_, d1, R11, _y_, S12, tau));
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GaussianConditional::shared_ptr Py(new GaussianConditional(_y_, d2, R22, tau));
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GaussianBayesNet cbn;
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cbn.push_back(Px_y);
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cbn.push_back(Py);
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return cbn;
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}
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/* ************************************************************************* */
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// Some nonlinear functions to optimize
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/* ************************************************************************* */
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namespace smallOptimize {
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Point2 h(const Point2& v) {
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return Point2(cos(v.x()), sin(v.y()));
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}
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Matrix H(const Point2& v) {
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return Matrix_(2, 2,
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-sin(v.x()), 0.0,
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0.0, cos(v.y()));
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}
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struct UnaryFactor: public gtsam::NoiseModelFactor1<Point2> {
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Point2 z_;
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UnaryFactor(const Point2& z, const SharedNoiseModel& model, Key key) :
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gtsam::NoiseModelFactor1<Point2>(model, key), z_(z) {
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}
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Vector evaluateError(const Point2& x, boost::optional<Matrix&> A = boost::none) const {
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if (A) *A = H(x);
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return (h(x) - z_).vector();
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}
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};
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}
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/* ************************************************************************* */
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boost::shared_ptr<const Graph> sharedReallyNonlinearFactorGraph() {
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boost::shared_ptr<Graph> fg(new Graph);
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Vector z = Vector_(2, 1.0, 0.0);
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double sigma = 0.1;
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boost::shared_ptr<smallOptimize::UnaryFactor> factor(
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new smallOptimize::UnaryFactor(z, noiseModel::Isotropic::Sigma(2,sigma), X(1)));
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fg->push_back(factor);
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return fg;
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}
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Graph createReallyNonlinearFactorGraph() {
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return *sharedReallyNonlinearFactorGraph();
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}
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/* ************************************************************************* */
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pair<Graph, Values> createNonlinearSmoother(int T) {
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// Create
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Graph nlfg;
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Values poses;
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// prior on x1
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Point2 x1(1.0, 0.0);
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shared prior(new simulated2D::Prior(x1, sigma1_0, X(1)));
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nlfg.push_back(prior);
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poses.insert(X(1), x1);
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for (int t = 2; t <= T; t++) {
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// odometry between x_t and x_{t-1}
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Point2 odo(1.0, 0.0);
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shared odometry(new simulated2D::Odometry(odo, sigma1_0, X(t - 1), X(t)));
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nlfg.push_back(odometry);
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// measurement on x_t is like perfect GPS
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Point2 xt(t, 0);
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shared measurement(new simulated2D::Prior(xt, sigma1_0, X(t)));
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nlfg.push_back(measurement);
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// initial estimate
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poses.insert(X(t), xt);
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}
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return make_pair(nlfg, poses);
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}
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/* ************************************************************************* */
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pair<FactorGraph<GaussianFactor>, Ordering> createSmoother(int T, boost::optional<Ordering> ordering) {
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Graph nlfg;
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Values poses;
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boost::tie(nlfg, poses) = createNonlinearSmoother(T);
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if(!ordering) ordering = *poses.orderingArbitrary();
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return make_pair(*nlfg.linearize(poses, *ordering), *ordering);
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}
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/* ************************************************************************* */
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JacobianFactorGraph createSimpleConstraintGraph() {
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// create unary factor
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// prior on _x_, mean = [1,-1], sigma=0.1
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Matrix Ax = eye(2);
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Vector b1(2);
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b1(0) = 1.0;
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b1(1) = -1.0;
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JacobianFactor::shared_ptr f1(new JacobianFactor(_x_, Ax, b1, sigma0_1));
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// create binary constraint factor
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// between _x_ and _y_, that is going to be the only factor on _y_
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// |1 0||x_1| + |-1 0||y_1| = |0|
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// |0 1||x_2| | 0 -1||y_2| |0|
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Matrix Ax1 = eye(2);
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Matrix Ay1 = eye(2) * -1;
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Vector b2 = Vector_(2, 0.0, 0.0);
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JacobianFactor::shared_ptr f2(new JacobianFactor(_x_, Ax1, _y_, Ay1, b2,
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constraintModel));
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// construct the graph
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JacobianFactorGraph fg;
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fg.push_back(f1);
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fg.push_back(f2);
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return fg;
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}
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/* ************************************************************************* */
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VectorValues createSimpleConstraintValues() {
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VectorValues config(vector<size_t>(2,2));
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Vector v = Vector_(2, 1.0, -1.0);
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config[_x_] = v;
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config[_y_] = v;
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return config;
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}
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/* ************************************************************************* */
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JacobianFactorGraph createSingleConstraintGraph() {
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// create unary factor
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// prior on _x_, mean = [1,-1], sigma=0.1
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Matrix Ax = eye(2);
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Vector b1(2);
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b1(0) = 1.0;
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b1(1) = -1.0;
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//GaussianFactor::shared_ptr f1(new JacobianFactor(_x_, sigma0_1->Whiten(Ax), sigma0_1->whiten(b1), sigma0_1));
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JacobianFactor::shared_ptr f1(new JacobianFactor(_x_, Ax, b1, sigma0_1));
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// create binary constraint factor
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// between _x_ and _y_, that is going to be the only factor on _y_
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// |1 2||x_1| + |10 0||y_1| = |1|
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// |2 1||x_2| |0 10||y_2| |2|
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Matrix Ax1(2, 2);
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Ax1(0, 0) = 1.0;
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Ax1(0, 1) = 2.0;
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Ax1(1, 0) = 2.0;
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Ax1(1, 1) = 1.0;
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Matrix Ay1 = eye(2) * 10;
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Vector b2 = Vector_(2, 1.0, 2.0);
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JacobianFactor::shared_ptr f2(new JacobianFactor(_x_, Ax1, _y_, Ay1, b2,
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constraintModel));
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// construct the graph
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JacobianFactorGraph fg;
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fg.push_back(f1);
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fg.push_back(f2);
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return fg;
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}
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/* ************************************************************************* */
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VectorValues createSingleConstraintValues() {
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VectorValues config(vector<size_t>(2,2));
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config[_x_] = Vector_(2, 1.0, -1.0);
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config[_y_] = Vector_(2, 0.2, 0.1);
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return config;
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}
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/* ************************************************************************* */
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JacobianFactorGraph createMultiConstraintGraph() {
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// unary factor 1
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Matrix A = eye(2);
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Vector b = Vector_(2, -2.0, 2.0);
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JacobianFactor::shared_ptr lf1(new JacobianFactor(_x_, A, b, sigma0_1));
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// constraint 1
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Matrix A11(2, 2);
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A11(0, 0) = 1.0;
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A11(0, 1) = 2.0;
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A11(1, 0) = 2.0;
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A11(1, 1) = 1.0;
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Matrix A12(2, 2);
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A12(0, 0) = 10.0;
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A12(0, 1) = 0.0;
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A12(1, 0) = 0.0;
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A12(1, 1) = 10.0;
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Vector b1(2);
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b1(0) = 1.0;
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b1(1) = 2.0;
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JacobianFactor::shared_ptr lc1(new JacobianFactor(_x_, A11, _y_, A12, b1,
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constraintModel));
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// constraint 2
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Matrix A21(2, 2);
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A21(0, 0) = 3.0;
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A21(0, 1) = 4.0;
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A21(1, 0) = -1.0;
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A21(1, 1) = -2.0;
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Matrix A22(2, 2);
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A22(0, 0) = 1.0;
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A22(0, 1) = 1.0;
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A22(1, 0) = 1.0;
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A22(1, 1) = 2.0;
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Vector b2(2);
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b2(0) = 3.0;
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b2(1) = 4.0;
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JacobianFactor::shared_ptr lc2(new JacobianFactor(_x_, A21, _z_, A22, b2,
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constraintModel));
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// construct the graph
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JacobianFactorGraph fg;
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fg.push_back(lf1);
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fg.push_back(lc1);
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fg.push_back(lc2);
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return fg;
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}
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/* ************************************************************************* */
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VectorValues createMultiConstraintValues() {
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VectorValues config(vector<size_t>(3,2));
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config[_x_] = Vector_(2, -2.0, 2.0);
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config[_y_] = Vector_(2, -0.1, 0.4);
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config[_z_] = Vector_(2, -4.0, 5.0);
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return config;
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}
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/* ************************************************************************* */
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// Create key for simulated planar graph
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Symbol key(int x, int y) {
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return X(1000*x+y);
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}
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/* ************************************************************************* */
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boost::tuple<GaussianFactorGraph, VectorValues> planarGraph(size_t N) {
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// create empty graph
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NonlinearFactorGraph nlfg;
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// Create almost hard constraint on x11, sigma=0 will work for PCG not for normal
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shared constraint(new simulated2D::Prior(Point2(1.0, 1.0), sharedSigma(2,1e-3), key(1,1)));
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nlfg.push_back(constraint);
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// Create horizontal constraints, 1...N*(N-1)
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Point2 z1(1.0, 0.0); // move right
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for (size_t x = 1; x < N; x++)
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for (size_t y = 1; y <= N; y++) {
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shared f(new simulated2D::Odometry(z1, sharedSigma(2,0.01), key(x, y), key(x + 1, y)));
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nlfg.push_back(f);
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}
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// Create vertical constraints, N*(N-1)+1..2*N*(N-1)
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Point2 z2(0.0, 1.0); // move up
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for (size_t x = 1; x <= N; x++)
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for (size_t y = 1; y < N; y++) {
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shared f(new simulated2D::Odometry(z2, sharedSigma(2,0.01), key(x, y), key(x, y + 1)));
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nlfg.push_back(f);
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}
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// Create linearization and ground xtrue config
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Values zeros;
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for (size_t x = 1; x <= N; x++)
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for (size_t y = 1; y <= N; y++)
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zeros.insert(key(x, y), Point2());
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Ordering ordering(planarOrdering(N));
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VectorValues xtrue(zeros.dims(ordering));
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for (size_t x = 1; x <= N; x++)
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for (size_t y = 1; y <= N; y++)
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xtrue[ordering[key(x, y)]] = Point2(x,y).vector();
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// linearize around zero
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return boost::make_tuple(*nlfg.linearize(zeros, ordering), xtrue);
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}
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/* ************************************************************************* */
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Ordering planarOrdering(size_t N) {
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Ordering ordering;
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for (size_t y = N; y >= 1; y--)
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for (size_t x = N; x >= 1; x--)
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ordering.push_back(key(x, y));
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return ordering;
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}
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/* ************************************************************************* */
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pair<JacobianFactorGraph, JacobianFactorGraph > splitOffPlanarTree(size_t N,
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const JacobianFactorGraph& original) {
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JacobianFactorGraph T, C;
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// Add the x11 constraint to the tree
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T.push_back(original[0]);
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// Add all horizontal constraints to the tree
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size_t i = 1;
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for (size_t x = 1; x < N; x++)
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for (size_t y = 1; y <= N; y++, i++)
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T.push_back(original[i]);
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// Add first vertical column of constraints to T, others to C
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for (size_t x = 1; x <= N; x++)
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for (size_t y = 1; y < N; y++, i++)
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if (x == 1)
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T.push_back(original[i]);
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else
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C.push_back(original[i]);
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return make_pair(T, C);
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}
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/* ************************************************************************* */
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} // example
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} // namespace gtsam
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