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