601 lines
16 KiB
C++
601 lines
16 KiB
C++
/**
|
|
* @file smallExample.cpp
|
|
* @brief Create small example with two poses and one landmark
|
|
* @brief smallExample
|
|
* @author Carlos Nieto
|
|
* @author Frank dellaert
|
|
*/
|
|
|
|
#include <iostream>
|
|
#include <string>
|
|
#include <boost/optional.hpp>
|
|
|
|
using namespace std;
|
|
|
|
#include "Ordering.h"
|
|
#include "Matrix.h"
|
|
#include "NonlinearFactor.h"
|
|
#include "smallExample.h"
|
|
#include "simulated2D.h"
|
|
|
|
// template definitions
|
|
#include "FactorGraph-inl.h"
|
|
#include "NonlinearFactorGraph-inl.h"
|
|
|
|
namespace gtsam {
|
|
|
|
typedef boost::shared_ptr<NonlinearFactor<VectorConfig> > shared;
|
|
|
|
/* ************************************************************************* */
|
|
boost::shared_ptr<const ExampleNonlinearFactorGraph> sharedNonlinearFactorGraph() {
|
|
// Create
|
|
boost::shared_ptr<ExampleNonlinearFactorGraph> nlfg(
|
|
new ExampleNonlinearFactorGraph);
|
|
|
|
// prior on x1
|
|
double sigma1 = 0.1;
|
|
Vector mu = zero(2);
|
|
shared f1(new simulated2D::Prior(mu, sigma1, "x1"));
|
|
nlfg->push_back(f1);
|
|
|
|
// odometry between x1 and x2
|
|
double sigma2 = 0.1;
|
|
Vector z2(2);
|
|
z2(0) = 1.5;
|
|
z2(1) = 0;
|
|
shared f2(new simulated2D::Odometry(z2, sigma2, "x1", "x2"));
|
|
nlfg->push_back(f2);
|
|
|
|
// measurement between x1 and l1
|
|
double sigma3 = 0.2;
|
|
Vector z3(2);
|
|
z3(0) = 0.;
|
|
z3(1) = -1.;
|
|
shared f3(new simulated2D::Measurement(z3, sigma3, "x1", "l1"));
|
|
nlfg->push_back(f3);
|
|
|
|
// measurement between x2 and l1
|
|
double sigma4 = 0.2;
|
|
Vector z4(2);
|
|
z4(0) = -1.5;
|
|
z4(1) = -1.;
|
|
shared f4(new simulated2D::Measurement(z4, sigma4, "x2", "l1"));
|
|
nlfg->push_back(f4);
|
|
|
|
return nlfg;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
ExampleNonlinearFactorGraph createNonlinearFactorGraph() {
|
|
return *sharedNonlinearFactorGraph();
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
VectorConfig createConfig() {
|
|
VectorConfig c;
|
|
c.insert("x1", Vector_(2, 0.0, 0.0));
|
|
c.insert("x2", Vector_(2, 1.5, 0.0));
|
|
c.insert("l1", Vector_(2, 0.0, -1.0));
|
|
return c;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
boost::shared_ptr<const VectorConfig> sharedNoisyConfig() {
|
|
boost::shared_ptr<VectorConfig> c(new VectorConfig);
|
|
c->insert("x1", Vector_(2, 0.1, 0.1));
|
|
c->insert("x2", Vector_(2, 1.4, 0.2));
|
|
c->insert("l1", Vector_(2, 0.1, -1.1));
|
|
return c;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
VectorConfig createNoisyConfig() {
|
|
return *sharedNoisyConfig();
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
VectorConfig createCorrectDelta() {
|
|
VectorConfig c;
|
|
c.insert("x1", Vector_(2, -0.1, -0.1));
|
|
c.insert("x2", Vector_(2, 0.1, -0.2));
|
|
c.insert("l1", Vector_(2, -0.1, 0.1));
|
|
return c;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
VectorConfig createZeroDelta() {
|
|
VectorConfig c;
|
|
c.insert("x1", zero(2));
|
|
c.insert("x2", zero(2));
|
|
c.insert("l1", zero(2));
|
|
return c;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
GaussianFactorGraph createGaussianFactorGraph() {
|
|
Matrix I = eye(2);
|
|
VectorConfig c = createNoisyConfig();
|
|
|
|
// Create empty graph
|
|
GaussianFactorGraph fg;
|
|
|
|
// linearized prior on x1: c["x1"]+x1=0 i.e. x1=-c["x1"]
|
|
double sigma1 = 0.1;
|
|
Vector b1 = -c["x1"];
|
|
fg.add("x1", I, b1, sigma1);
|
|
|
|
// odometry between x1 and x2: x2-x1=[0.2;-0.1]
|
|
double sigma2 = 0.1;
|
|
Vector b2 = Vector_(2, 0.2, -0.1);
|
|
fg.add("x1", -I, "x2", I, b2, sigma2);
|
|
|
|
// measurement between x1 and l1: l1-x1=[0.0;0.2]
|
|
double sigma3 = 0.2;
|
|
Vector b3 = Vector_(2, 0.0, 0.2);
|
|
fg.add("x1", -I, "l1", I, b3, sigma3);
|
|
|
|
// measurement between x2 and l1: l1-x2=[-0.2;0.3]
|
|
double sigma4 = 0.2;
|
|
Vector b4 = Vector_(2, -0.2, 0.3);
|
|
fg.add("x2", -I, "l1", I, b4, sigma4);
|
|
|
|
return fg;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
/** create small Chordal Bayes Net x <- y
|
|
* x y d
|
|
* 1 1 9
|
|
* 1 5
|
|
*/
|
|
GaussianBayesNet createSmallGaussianBayesNet() {
|
|
Matrix R11 = Matrix_(1, 1, 1.0), S12 = Matrix_(1, 1, 1.0);
|
|
Matrix R22 = Matrix_(1, 1, 1.0);
|
|
Vector d1(1), d2(1);
|
|
d1(0) = 9;
|
|
d2(0) = 5;
|
|
Vector tau(1);
|
|
tau(0) = 1.0;
|
|
|
|
// define nodes and specify in reverse topological sort (i.e. parents last)
|
|
GaussianConditional::shared_ptr Px_y(new GaussianConditional("x", d1, R11,
|
|
"y", S12, tau)), Py(new GaussianConditional("y", d2, R22, tau));
|
|
GaussianBayesNet cbn;
|
|
cbn.push_back(Px_y);
|
|
cbn.push_back(Py);
|
|
|
|
return cbn;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
// Some nonlinear functions to optimize
|
|
/* ************************************************************************* */
|
|
namespace smallOptimize {
|
|
|
|
Vector h(const Vector& v) {
|
|
double x = v(0);
|
|
return Vector_(2, cos(x), sin(x));
|
|
}
|
|
|
|
Matrix H(const Vector& v) {
|
|
double x = v(0);
|
|
return Matrix_(2, 1, -sin(x), cos(x));
|
|
}
|
|
|
|
struct UnaryFactor: public gtsam::NonlinearFactor1<VectorConfig,
|
|
std::string, Vector> {
|
|
|
|
Vector z_;
|
|
|
|
UnaryFactor(const Vector& z, double sigma, const std::string& key) :
|
|
gtsam::NonlinearFactor1<VectorConfig, std::string, Vector>(sigma, key),
|
|
z_(z) {
|
|
}
|
|
|
|
Vector evaluateError(const Vector& x, boost::optional<Matrix&> A =
|
|
boost::none) const {
|
|
if (A) *A = H(x);
|
|
return h(x) - z_;
|
|
}
|
|
|
|
};
|
|
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
boost::shared_ptr<const ExampleNonlinearFactorGraph> sharedReallyNonlinearFactorGraph() {
|
|
boost::shared_ptr<ExampleNonlinearFactorGraph> fg(
|
|
new ExampleNonlinearFactorGraph);
|
|
Vector z = Vector_(2, 1.0, 0.0);
|
|
double sigma = 0.1;
|
|
boost::shared_ptr<smallOptimize::UnaryFactor> factor(new smallOptimize::UnaryFactor(
|
|
z, sigma, "x"));
|
|
fg->push_back(factor);
|
|
return fg;
|
|
}
|
|
|
|
ExampleNonlinearFactorGraph createReallyNonlinearFactorGraph() {
|
|
return *sharedReallyNonlinearFactorGraph();
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
pair<ExampleNonlinearFactorGraph, VectorConfig> createNonlinearSmoother(int T) {
|
|
|
|
// noise on measurements and odometry, respectively
|
|
double sigma1 = 1, sigma2 = 1;
|
|
|
|
// Create
|
|
ExampleNonlinearFactorGraph nlfg;
|
|
VectorConfig poses;
|
|
|
|
// prior on x1
|
|
Vector x1 = Vector_(2, 1.0, 0.0);
|
|
string key1 = symbol('x', 1);
|
|
shared prior(new simulated2D::Prior(x1, sigma1, key1));
|
|
nlfg.push_back(prior);
|
|
poses.insert(key1, x1);
|
|
|
|
for (int t = 2; t <= T; t++) {
|
|
// odometry between x_t and x_{t-1}
|
|
Vector odo = Vector_(2, 1.0, 0.0);
|
|
string key = symbol('x', t);
|
|
shared odometry(new simulated2D::Odometry(odo, sigma2, symbol('x', t - 1),
|
|
key));
|
|
nlfg.push_back(odometry);
|
|
|
|
// measurement on x_t is like perfect GPS
|
|
Vector xt = Vector_(2, (double) t, 0.0);
|
|
shared measurement(new simulated2D::Prior(xt, sigma1, key));
|
|
nlfg.push_back(measurement);
|
|
|
|
// initial estimate
|
|
poses.insert(key, xt);
|
|
}
|
|
|
|
return make_pair(nlfg, poses);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
GaussianFactorGraph createSmoother(int T) {
|
|
ExampleNonlinearFactorGraph nlfg;
|
|
VectorConfig poses;
|
|
boost::tie(nlfg, poses) = createNonlinearSmoother(T);
|
|
|
|
GaussianFactorGraph lfg = nlfg.linearize(poses);
|
|
return lfg;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
GaussianFactorGraph createSimpleConstraintGraph() {
|
|
// create unary factor
|
|
// prior on "x", mean = [1,-1], sigma=0.1
|
|
double sigma = 0.1;
|
|
Matrix Ax = eye(2);
|
|
Vector b1(2);
|
|
b1(0) = 1.0;
|
|
b1(1) = -1.0;
|
|
GaussianFactor::shared_ptr f1(new GaussianFactor("x", Ax, b1, sigma));
|
|
|
|
// create binary constraint factor
|
|
// between "x" and "y", that is going to be the only factor on "y"
|
|
// |1 0||x_1| + |-1 0||y_1| = |0|
|
|
// |0 1||x_2| | 0 -1||y_2| |0|
|
|
Matrix Ax1 = eye(2);
|
|
Matrix Ay1 = eye(2) * -1;
|
|
Vector b2 = Vector_(2, 0.0, 0.0);
|
|
GaussianFactor::shared_ptr f2(new GaussianFactor("x", Ax1, "y", Ay1, b2,
|
|
0.0));
|
|
|
|
// construct the graph
|
|
GaussianFactorGraph fg;
|
|
fg.push_back(f1);
|
|
fg.push_back(f2);
|
|
|
|
return fg;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
VectorConfig createSimpleConstraintConfig() {
|
|
VectorConfig config;
|
|
Vector v = Vector_(2, 1.0, -1.0);
|
|
config.insert("x", v);
|
|
config.insert("y", v);
|
|
return config;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
GaussianFactorGraph createSingleConstraintGraph() {
|
|
// create unary factor
|
|
// prior on "x", mean = [1,-1], sigma=0.1
|
|
double sigma = 0.1;
|
|
Matrix Ax = eye(2);
|
|
Vector b1(2);
|
|
b1(0) = 1.0;
|
|
b1(1) = -1.0;
|
|
GaussianFactor::shared_ptr f1(new GaussianFactor("x", Ax, b1, sigma));
|
|
|
|
// create binary constraint factor
|
|
// between "x" and "y", that is going to be the only factor on "y"
|
|
// |1 2||x_1| + |10 0||y_1| = |1|
|
|
// |2 1||x_2| |0 10||y_2| |2|
|
|
Matrix Ax1(2, 2);
|
|
Ax1(0, 0) = 1.0;
|
|
Ax1(0, 1) = 2.0;
|
|
Ax1(1, 0) = 2.0;
|
|
Ax1(1, 1) = 1.0;
|
|
Matrix Ay1 = eye(2) * 10;
|
|
Vector b2 = Vector_(2, 1.0, 2.0);
|
|
GaussianFactor::shared_ptr f2(new GaussianFactor("x", Ax1, "y", Ay1, b2,
|
|
0.0));
|
|
|
|
// construct the graph
|
|
GaussianFactorGraph fg;
|
|
fg.push_back(f1);
|
|
fg.push_back(f2);
|
|
|
|
return fg;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
VectorConfig createSingleConstraintConfig() {
|
|
VectorConfig config;
|
|
config.insert("x", Vector_(2, 1.0, -1.0));
|
|
config.insert("y", Vector_(2, 0.2, 0.1));
|
|
return config;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
GaussianFactorGraph createMultiConstraintGraph() {
|
|
// unary factor 1
|
|
double sigma = 0.1;
|
|
Matrix A = eye(2);
|
|
Vector b = Vector_(2, -2.0, 2.0);
|
|
GaussianFactor::shared_ptr lf1(new GaussianFactor("x", A, b, sigma));
|
|
|
|
// constraint 1
|
|
Matrix A11(2, 2);
|
|
A11(0, 0) = 1.0;
|
|
A11(0, 1) = 2.0;
|
|
A11(1, 0) = 2.0;
|
|
A11(1, 1) = 1.0;
|
|
|
|
Matrix A12(2, 2);
|
|
A12(0, 0) = 10.0;
|
|
A12(0, 1) = 0.0;
|
|
A12(1, 0) = 0.0;
|
|
A12(1, 1) = 10.0;
|
|
|
|
Vector b1(2);
|
|
b1(0) = 1.0;
|
|
b1(1) = 2.0;
|
|
GaussianFactor::shared_ptr lc1(new GaussianFactor("x", A11, "y", A12, b1,
|
|
0.0));
|
|
|
|
// constraint 2
|
|
Matrix A21(2, 2);
|
|
A21(0, 0) = 3.0;
|
|
A21(0, 1) = 4.0;
|
|
A21(1, 0) = -1.0;
|
|
A21(1, 1) = -2.0;
|
|
|
|
Matrix A22(2, 2);
|
|
A22(0, 0) = 1.0;
|
|
A22(0, 1) = 1.0;
|
|
A22(1, 0) = 1.0;
|
|
A22(1, 1) = 2.0;
|
|
|
|
Vector b2(2);
|
|
b2(0) = 3.0;
|
|
b2(1) = 4.0;
|
|
GaussianFactor::shared_ptr lc2(new GaussianFactor("x", A21, "z", A22, b2,
|
|
0.0));
|
|
|
|
// construct the graph
|
|
GaussianFactorGraph fg;
|
|
fg.push_back(lf1);
|
|
fg.push_back(lc1);
|
|
fg.push_back(lc2);
|
|
|
|
return fg;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
VectorConfig createMultiConstraintConfig() {
|
|
VectorConfig config;
|
|
config.insert("x", Vector_(2, -2.0, 2.0));
|
|
config.insert("y", Vector_(2, -0.1, 0.4));
|
|
config.insert("z", Vector_(2, -4.0, 5.0));
|
|
return config;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
//GaussianFactorGraph createConstrainedGaussianFactorGraph()
|
|
//{
|
|
// GaussianFactorGraph graph;
|
|
//
|
|
// // add an equality factor
|
|
// Vector v1(2); v1(0)=1.;v1(1)=2.;
|
|
// GaussianFactor::shared_ptr f1(new GaussianFactor(v1, "x0"));
|
|
// graph.push_back_eq(f1);
|
|
//
|
|
// // add a normal linear factor
|
|
// Matrix A21 = -1 * eye(2);
|
|
//
|
|
// Matrix A22 = eye(2);
|
|
//
|
|
// Vector b(2);
|
|
// b(0) = 2 ; b(1) = 3;
|
|
//
|
|
// double sigma = 0.1;
|
|
// GaussianFactor::shared_ptr f2(new GaussianFactor("x0", A21/sigma, "x1", A22/sigma, b/sigma));
|
|
// graph.push_back(f2);
|
|
// return graph;
|
|
//}
|
|
|
|
/* ************************************************************************* */
|
|
// ConstrainedNonlinearFactorGraph<NonlinearFactor<VectorConfig> , VectorConfig> createConstrainedNonlinearFactorGraph() {
|
|
// ConstrainedNonlinearFactorGraph<NonlinearFactor<VectorConfig> , VectorConfig> graph;
|
|
// VectorConfig c = createConstrainedConfig();
|
|
//
|
|
// // equality constraint for initial pose
|
|
// GaussianFactor::shared_ptr f1(new GaussianFactor(c["x0"], "x0"));
|
|
// graph.push_back_eq(f1);
|
|
//
|
|
// // odometry between x0 and x1
|
|
// double sigma = 0.1;
|
|
// shared f2(new Simulated2DOdometry(c["x1"] - c["x0"], sigma, "x0", "x1"));
|
|
// graph.push_back(f2); // TODO
|
|
// return graph;
|
|
// }
|
|
|
|
/* ************************************************************************* */
|
|
//VectorConfig createConstrainedConfig()
|
|
//{
|
|
// VectorConfig config;
|
|
//
|
|
// Vector x0(2); x0(0)=1.0; x0(1)=2.0;
|
|
// config.insert("x0", x0);
|
|
//
|
|
// Vector x1(2); x1(0)=3.0; x1(1)=5.0;
|
|
// config.insert("x1", x1);
|
|
//
|
|
// return config;
|
|
//}
|
|
|
|
/* ************************************************************************* */
|
|
//VectorConfig createConstrainedLinConfig()
|
|
//{
|
|
// VectorConfig config;
|
|
//
|
|
// Vector x0(2); x0(0)=1.0; x0(1)=2.0; // value doesn't actually matter
|
|
// config.insert("x0", x0);
|
|
//
|
|
// Vector x1(2); x1(0)=2.3; x1(1)=5.3;
|
|
// config.insert("x1", x1);
|
|
//
|
|
// return config;
|
|
//}
|
|
|
|
/* ************************************************************************* */
|
|
//VectorConfig createConstrainedCorrectDelta()
|
|
//{
|
|
// VectorConfig config;
|
|
//
|
|
// Vector x0(2); x0(0)=0.; x0(1)=0.;
|
|
// config.insert("x0", x0);
|
|
//
|
|
// Vector x1(2); x1(0)= 0.7; x1(1)= -0.3;
|
|
// config.insert("x1", x1);
|
|
//
|
|
// return config;
|
|
//}
|
|
|
|
/* ************************************************************************* */
|
|
//ConstrainedGaussianBayesNet createConstrainedGaussianBayesNet()
|
|
//{
|
|
// ConstrainedGaussianBayesNet cbn;
|
|
// VectorConfig c = createConstrainedConfig();
|
|
//
|
|
// // add regular conditional gaussian - no parent
|
|
// Matrix R = eye(2);
|
|
// Vector d = c["x1"];
|
|
// double sigma = 0.1;
|
|
// GaussianConditional::shared_ptr f1(new GaussianConditional(d/sigma, R/sigma));
|
|
// cbn.insert("x1", f1);
|
|
//
|
|
// // add a delta function to the cbn
|
|
// ConstrainedGaussianConditional::shared_ptr f2(new ConstrainedGaussianConditional); //(c["x0"], "x0"));
|
|
// cbn.insert_df("x0", f2);
|
|
//
|
|
// return cbn;
|
|
//}
|
|
|
|
/* ************************************************************************* */
|
|
// Create key for simulated planar graph
|
|
string key(int x, int y) {
|
|
stringstream ss;
|
|
ss << "x" << x << y;
|
|
return ss.str();
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
pair<GaussianFactorGraph, VectorConfig> planarGraph(size_t N) {
|
|
|
|
// create empty graph
|
|
NonlinearFactorGraph<VectorConfig> nlfg;
|
|
|
|
// Create almost hard constraint on x11, sigma=0 will work for PCG not for normal
|
|
double sigma0 = 1e-3;
|
|
shared constraint(new simulated2D::Prior(Vector_(2, 1.0, 1.0), sigma0, "x11"));
|
|
nlfg.push_back(constraint);
|
|
|
|
double sigma = 0.01;
|
|
|
|
// Create horizontal constraints, 1...N*(N-1)
|
|
Vector z1 = Vector_(2, 1.0, 0.0); // move right
|
|
for (size_t x = 1; x < N; x++)
|
|
for (size_t y = 1; y <= N; y++) {
|
|
shared f(new simulated2D::Odometry(z1, sigma, key(x, y), key(x + 1, y)));
|
|
nlfg.push_back(f);
|
|
}
|
|
|
|
// Create vertical constraints, N*(N-1)+1..2*N*(N-1)
|
|
Vector z2 = Vector_(2, 0.0, 1.0); // move up
|
|
for (size_t x = 1; x <= N; x++)
|
|
for (size_t y = 1; y < N; y++) {
|
|
shared f(new simulated2D::Odometry(z2, sigma, key(x, y), key(x, y + 1)));
|
|
nlfg.push_back(f);
|
|
}
|
|
|
|
// Create linearization and ground xtrue config
|
|
VectorConfig zeros, xtrue;
|
|
for (size_t x = 1; x <= N; x++)
|
|
for (size_t y = 1; y <= N; y++) {
|
|
zeros.add(key(x, y), zero(2));
|
|
xtrue.add(key(x, y), Vector_(2, (double) x, double(y)));
|
|
}
|
|
|
|
// linearize around zero
|
|
GaussianFactorGraph A = nlfg.linearize(zeros);
|
|
|
|
return make_pair(A, xtrue);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
Ordering planarOrdering(size_t N) {
|
|
Ordering ordering;
|
|
for (size_t y = N; y >= 1; y--)
|
|
for (size_t x = N; x >= 1; x--)
|
|
ordering.push_back(key(x, y));
|
|
return ordering;
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
pair<GaussianFactorGraph, GaussianFactorGraph> splitOffPlanarTree(size_t N,
|
|
const GaussianFactorGraph& original) {
|
|
GaussianFactorGraph T, C;
|
|
|
|
// Add the x11 constraint to the tree
|
|
T.push_back(original[0]);
|
|
|
|
// Add all horizontal constraints to the tree
|
|
size_t i = 1;
|
|
for (size_t x = 1; x < N; x++)
|
|
for (size_t y = 1; y <= N; y++, i++)
|
|
T.push_back(original[i]);
|
|
|
|
// Add first vertical column of constraints to T, others to C
|
|
for (size_t x = 1; x <= N; x++)
|
|
for (size_t y = 1; y < N; y++, i++)
|
|
if (x == 1)
|
|
T.push_back(original[i]);
|
|
else
|
|
C.push_back(original[i]);
|
|
|
|
return make_pair(T, C);
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
|
|
} // namespace gtsam
|