383 lines
12 KiB
C++
383 lines
12 KiB
C++
/*
|
|
* @file testSQPOptimizer.cpp
|
|
* @brief tests the optimization algorithm for nonlinear graphs with nonlinear constraints
|
|
* @author Alex Cunningham
|
|
*/
|
|
|
|
#include <CppUnitLite/TestHarness.h>
|
|
#include <boost/assign/std/list.hpp> // for operator +=
|
|
#include <boost/assign/std/map.hpp> // for insert
|
|
#include <boost/bind.hpp>
|
|
|
|
#define GTSAM_MAGIC_KEY
|
|
|
|
#include <simulated2D.h>
|
|
#include "NonlinearFactorGraph.h"
|
|
#include "NonlinearConstraint.h"
|
|
#include "NonlinearEquality.h"
|
|
#include "VectorConfig.h"
|
|
#include "Ordering.h"
|
|
#include "NonlinearOptimizer.h"
|
|
#include "SQPOptimizer.h"
|
|
|
|
// implementations
|
|
#include "NonlinearConstraint-inl.h"
|
|
#include "NonlinearOptimizer-inl.h"
|
|
#include "SQPOptimizer-inl.h"
|
|
|
|
using namespace std;
|
|
using namespace gtsam;
|
|
using namespace boost;
|
|
using namespace boost::assign;
|
|
using namespace simulated2D;
|
|
|
|
static sharedGaussian sigma(noiseModel::Isotropic::Sigma(1,0.1));
|
|
|
|
// typedefs
|
|
typedef simulated2D::Config Config2D;
|
|
typedef boost::shared_ptr<Config2D> shared_config;
|
|
typedef NonlinearFactorGraph<Config2D> NLGraph;
|
|
typedef boost::shared_ptr<NonlinearFactor<Config2D> > shared;
|
|
|
|
namespace map_warp_example {
|
|
typedef NonlinearConstraint1<
|
|
Config2D, simulated2D::PoseKey, Point2> NLC1;
|
|
typedef NonlinearConstraint2<
|
|
Config2D, simulated2D::PointKey, Point2, simulated2D::PointKey, Point2> NLC2;
|
|
} // \namespace map_warp_example
|
|
|
|
|
|
/* ********************************************************************* */
|
|
TEST ( SQPOptimizer, basic ) {
|
|
// create a basic optimizer
|
|
NLGraph graph;
|
|
Ordering ordering;
|
|
shared_config config(new Config2D);
|
|
|
|
SQPOptimizer<NLGraph, Config2D> optimizer(graph, ordering, config);
|
|
|
|
// verify components
|
|
CHECK(assert_equal(graph, *(optimizer.graph())));
|
|
CHECK(assert_equal(ordering, *(optimizer.ordering())));
|
|
CHECK(assert_equal(*config, *(optimizer.config())));
|
|
}
|
|
|
|
/* ********************************************************************* */
|
|
// Example that moves two separate maps into the same frame of reference
|
|
// Note that this is a linear example, so it should converge in one step
|
|
/* ********************************************************************* */
|
|
|
|
namespace sqp_LinearMapWarp2 {
|
|
// binary constraint between landmarks
|
|
/** g(x) = x-y = 0 */
|
|
Vector g_func(const Config2D& config, const PointKey& key1, const PointKey& key2) {
|
|
Point2 p = config[key1]-config[key2];
|
|
return Vector_(2, p.x(), p.y());
|
|
}
|
|
|
|
/** jacobian at l1 */
|
|
Matrix jac_g1(const Config2D& config) {
|
|
return eye(2);
|
|
}
|
|
|
|
/** jacobian at l2 */
|
|
Matrix jac_g2(const Config2D& config) {
|
|
return -1*eye(2);
|
|
}
|
|
} // \namespace sqp_LinearMapWarp2
|
|
|
|
namespace sqp_LinearMapWarp1 {
|
|
// Unary Constraint on x1
|
|
/** g(x) = x -[1;1] = 0 */
|
|
Vector g_func(const Config2D& config, const PoseKey& key) {
|
|
Point2 p = config[key]-Point2(1.0, 1.0);
|
|
return Vector_(2, p.x(), p.y());
|
|
}
|
|
|
|
/** jacobian at x1 */
|
|
Matrix jac_g(const Config2D& config) {
|
|
return eye(2);
|
|
}
|
|
} // \namespace sqp_LinearMapWarp12
|
|
|
|
typedef SQPOptimizer<NLGraph, Config2D> Optimizer;
|
|
|
|
/**
|
|
* Creates the graph with each robot seeing the landmark, and it is
|
|
* known that it is the same landmark
|
|
*/
|
|
NLGraph linearMapWarpGraph() {
|
|
using namespace map_warp_example;
|
|
// keys
|
|
PoseKey x1(1), x2(2);
|
|
PointKey l1(1), l2(2);
|
|
|
|
// constant constraint on x1
|
|
list<Symbol> keyx; keyx += "x1";
|
|
shared_ptr<NLC1> c1(new NLC1(boost::bind(sqp_LinearMapWarp1::g_func, _1, x1),
|
|
x1, boost::bind(sqp_LinearMapWarp1::jac_g, _1),
|
|
2, "L1"));
|
|
|
|
// measurement from x1 to l1
|
|
Point2 z1(0.0, 5.0);
|
|
shared f1(new simulated2D::Measurement(z1, sigma, 1,1));
|
|
|
|
// measurement from x2 to l2
|
|
Point2 z2(-4.0, 0.0);
|
|
shared f2(new simulated2D::Measurement(z2, sigma, 2,2));
|
|
|
|
// equality constraint between l1 and l2
|
|
list<Symbol> keys; keys += "l1", "l2";
|
|
shared_ptr<NLC2> c2 (new NLC2(
|
|
boost::bind(sqp_LinearMapWarp2::g_func, _1, l1, l2),
|
|
l1, boost::bind(sqp_LinearMapWarp2::jac_g1, _1),
|
|
l2, boost::bind(sqp_LinearMapWarp2::jac_g2, _1),
|
|
2, "L12"));
|
|
|
|
// construct the graph
|
|
NLGraph graph;
|
|
graph.push_back(c1);
|
|
graph.push_back(c2);
|
|
graph.push_back(f1);
|
|
graph.push_back(f2);
|
|
|
|
return graph;
|
|
}
|
|
|
|
/* ********************************************************************* */
|
|
TEST ( SQPOptimizer, map_warp_initLam ) {
|
|
bool verbose = false;
|
|
// get a graph
|
|
NLGraph graph = linearMapWarpGraph();
|
|
|
|
// keys
|
|
PoseKey x1(1), x2(2);
|
|
PointKey l1(1), l2(2);
|
|
|
|
// create an initial estimate
|
|
shared_config initialEstimate(new Config2D);
|
|
initialEstimate->insert(x1, Point2(1.0, 1.0));
|
|
initialEstimate->insert(l1, Point2(1.0, 6.0));
|
|
initialEstimate->insert(l2, Point2(-4.0, 0.0)); // starting with a separate reference frame
|
|
initialEstimate->insert(x2, Point2(0.0, 0.0)); // other pose starts at origin
|
|
|
|
// create an initial estimate for the lagrange multiplier
|
|
shared_ptr<VectorConfig> initLagrange(new VectorConfig);
|
|
initLagrange->insert("L12", Vector_(2, 1.0, 1.0));
|
|
initLagrange->insert("L1", Vector_(2, 1.0, 1.0));
|
|
|
|
// create an ordering
|
|
Ordering ordering;
|
|
ordering += "x1", "x2", "l1", "l2", "L12", "L1";
|
|
|
|
// create an optimizer
|
|
Optimizer optimizer(graph, ordering, initialEstimate, initLagrange);
|
|
if (verbose) optimizer.print("Initialized Optimizer");
|
|
|
|
// perform an iteration of optimization
|
|
Optimizer oneIteration = optimizer.iterate(Optimizer::SILENT);
|
|
|
|
// get the config back out and verify
|
|
Config2D actual = *(oneIteration.config());
|
|
Config2D expected;
|
|
expected.insert(x1, Point2(1.0, 1.0));
|
|
expected.insert(l1, Point2(1.0, 6.0));
|
|
expected.insert(l2, Point2(1.0, 6.0));
|
|
expected.insert(x2, Point2(5.0, 6.0));
|
|
CHECK(assert_equal(expected, actual));
|
|
}
|
|
|
|
/* ********************************************************************* */
|
|
TEST ( SQPOptimizer, map_warp ) {
|
|
bool verbose = false;
|
|
// get a graph
|
|
NLGraph graph = linearMapWarpGraph();
|
|
if (verbose) graph.print("Initial map warp graph");
|
|
|
|
// keys
|
|
PoseKey x1(1), x2(2);
|
|
PointKey l1(1), l2(2);
|
|
|
|
// create an initial estimate
|
|
shared_config initialEstimate(new Config2D);
|
|
initialEstimate->insert(x1, Point2(1.0, 1.0));
|
|
initialEstimate->insert(l1, Point2(.0, 6.0));
|
|
initialEstimate->insert(l2, Point2(-4.0, 0.0)); // starting with a separate reference frame
|
|
initialEstimate->insert(x2, Point2(0.0, 0.0)); // other pose starts at origin
|
|
|
|
// create an ordering
|
|
Ordering ordering;
|
|
ordering += "x1", "x2", "l1", "l2";
|
|
|
|
// create an optimizer
|
|
Optimizer optimizer(graph, ordering, initialEstimate);
|
|
|
|
// perform an iteration of optimization
|
|
Optimizer oneIteration = optimizer.iterate(Optimizer::SILENT);
|
|
|
|
// get the config back out and verify
|
|
Config2D actual = *(oneIteration.config());
|
|
Config2D expected;
|
|
expected.insert(x1, Point2(1.0, 1.0));
|
|
expected.insert(l1, Point2(1.0, 6.0));
|
|
expected.insert(l2, Point2(1.0, 6.0));
|
|
expected.insert(x2, Point2(5.0, 6.0));
|
|
CHECK(assert_equal(expected, actual));
|
|
}
|
|
|
|
/* ********************************************************************* */
|
|
// This is an obstacle avoidance demo, where there is a trajectory of
|
|
// three points, where there is a circular obstacle in the middle. There
|
|
// is a binary inequality constraint connecting the obstacle to the
|
|
// states, which enforces a minimum distance.
|
|
/* ********************************************************************* */
|
|
|
|
typedef NonlinearConstraint2<Config2D, PoseKey, Point2, PointKey, Point2> AvoidConstraint;
|
|
typedef shared_ptr<AvoidConstraint> shared_a;
|
|
typedef NonlinearEquality<Config2D, simulated2D::PoseKey, Point2> PoseConstraint;
|
|
typedef shared_ptr<PoseConstraint> shared_pc;
|
|
typedef NonlinearEquality<Config2D, simulated2D::PointKey, Point2> ObstacleConstraint;
|
|
typedef shared_ptr<ObstacleConstraint> shared_oc;
|
|
|
|
|
|
namespace sqp_avoid1 {
|
|
// avoidance radius
|
|
double radius = 1.0;
|
|
|
|
// binary avoidance constraint
|
|
/** g(x) = ||x2-obs||^2 - radius^2 > 0 */
|
|
Vector g_func(const Config2D& config, const PoseKey& x, const PointKey& obs) {
|
|
double dist2 = config[x].dist(config[obs]);
|
|
double thresh = radius*radius;
|
|
return Vector_(1, dist2-thresh);
|
|
}
|
|
|
|
/** jacobian at pose */
|
|
Matrix jac_g1(const Config2D& config, const PoseKey& x, const PointKey& obs) {
|
|
Point2 p = config[x]-config[obs];
|
|
return Matrix_(1,2, 2.0*p.x(), 2.0*p.y());
|
|
}
|
|
|
|
/** jacobian at obstacle */
|
|
Matrix jac_g2(const Config2D& config, const PoseKey& x, const PointKey& obs) {
|
|
Point2 p = config[x]-config[obs];
|
|
return Matrix_(1,2, -2.0*p.x(), -2.0*p.y());
|
|
}
|
|
}
|
|
|
|
pair<NLGraph, Config2D> obstacleAvoidGraph() {
|
|
// Keys
|
|
PoseKey x1(1), x2(2), x3(3);
|
|
PointKey l1(1);
|
|
|
|
// Constrained Points
|
|
Point2 pt_x1,
|
|
pt_x3(10.0, 0.0),
|
|
pt_l1(5.0, -0.5);
|
|
|
|
shared_pc e1(new PoseConstraint(x1, pt_x1));
|
|
shared_pc e2(new PoseConstraint(x3, pt_x3));
|
|
shared_oc e3(new ObstacleConstraint(l1, pt_l1));
|
|
|
|
// measurement from x1 to x2
|
|
Point2 x1x2(5.0, 0.0);
|
|
shared f1(new simulated2D::Odometry(x1x2, sigma, 1,2));
|
|
|
|
// measurement from x2 to x3
|
|
Point2 x2x3(5.0, 0.0);
|
|
shared f2(new simulated2D::Odometry(x2x3, sigma, 2,3));
|
|
|
|
// create a binary inequality constraint that forces the middle point away from
|
|
// the obstacle
|
|
shared_a c1(new AvoidConstraint(boost::bind(sqp_avoid1::g_func, _1, x2, l1),
|
|
x2, boost::bind(sqp_avoid1::jac_g1, _1, x2, l1),
|
|
l1,boost::bind(sqp_avoid1::jac_g2, _1, x2, l1),
|
|
1, "L20", false));
|
|
|
|
// construct the graph
|
|
NLGraph graph;
|
|
graph.push_back(e1);
|
|
graph.push_back(e2);
|
|
graph.push_back(e3);
|
|
graph.push_back(c1);
|
|
graph.push_back(f1);
|
|
graph.push_back(f2);
|
|
|
|
// make a config of the fixed values, for convenience
|
|
Config2D config;
|
|
config.insert(x1, pt_x1);
|
|
config.insert(x3, pt_x3);
|
|
config.insert(l1, pt_l1);
|
|
|
|
return make_pair(graph, config);
|
|
}
|
|
|
|
/* ********************************************************************* */
|
|
TEST ( SQPOptimizer, inequality_avoid ) {
|
|
// create the graph
|
|
NLGraph graph; Config2D feasible;
|
|
boost::tie(graph, feasible) = obstacleAvoidGraph();
|
|
|
|
// create the rest of the config
|
|
shared_ptr<Config2D> init(new Config2D(feasible));
|
|
PoseKey x2(2);
|
|
init->insert(x2, Point2(5.0, 100.0));
|
|
|
|
// create an ordering
|
|
Ordering ord;
|
|
ord += "x1", "x2", "x3", "l1";
|
|
|
|
// create an optimizer
|
|
Optimizer optimizer(graph, ord, init);
|
|
|
|
// perform an iteration of optimization
|
|
// NOTE: the constraint will be inactive in the first iteration,
|
|
// so it will violate the constraint after one iteration
|
|
Optimizer afterOneIteration = optimizer.iterate(Optimizer::SILENT);
|
|
|
|
Config2D exp1(feasible);
|
|
exp1.insert(x2, Point2(5.0, 0.0));
|
|
CHECK(assert_equal(exp1, *(afterOneIteration.config())));
|
|
|
|
// the second iteration will activate the constraint and force the
|
|
// config to a viable configuration.
|
|
Optimizer after2ndIteration = afterOneIteration.iterate(Optimizer::SILENT);
|
|
|
|
Config2D exp2(feasible);
|
|
exp2.insert(x2, Point2(5.0, 0.5));
|
|
CHECK(assert_equal(exp2, *(after2ndIteration.config())));
|
|
}
|
|
|
|
/* ********************************************************************* */
|
|
TEST ( SQPOptimizer, inequality_avoid_iterative ) {
|
|
// create the graph
|
|
NLGraph graph; Config2D feasible;
|
|
boost::tie(graph, feasible) = obstacleAvoidGraph();
|
|
|
|
// create the rest of the config
|
|
shared_ptr<Config2D> init(new Config2D(feasible));
|
|
PoseKey x2(2);
|
|
init->insert(x2, Point2(5.0, 100.0));
|
|
|
|
// create an ordering
|
|
Ordering ord;
|
|
ord += "x1", "x2", "x3", "l1";
|
|
|
|
// create an optimizer
|
|
Optimizer optimizer(graph, ord, init);
|
|
|
|
double relThresh = 1e-5; // minimum change in error between iterations
|
|
double absThresh = 1e-5; // minimum error necessary to converge
|
|
double constraintThresh = 1e-9; // minimum constraint error to be feasible
|
|
Optimizer final = optimizer.iterateSolve(relThresh, absThresh, constraintThresh);
|
|
|
|
// verify
|
|
Config2D exp2(feasible);
|
|
exp2.insert(x2, Point2(5.0, 0.5));
|
|
CHECK(assert_equal(exp2, *(final.config()))); // FAILS
|
|
}
|
|
|
|
/* ************************************************************************* */
|
|
int main() { TestResult tr; return TestRegistry::runAllTests(tr); }
|
|
/* ************************************************************************* */
|