450 lines
15 KiB
C++
450 lines
15 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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#include <Simulated2DMeasurement.h>
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#include <Simulated2DOdometry.h>
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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 "NonlinearOptimizer.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 "NonlinearOptimizer-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::assign;
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// typedefs
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typedef boost::shared_ptr<VectorConfig> shared_config;
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typedef NonlinearFactorGraph<VectorConfig> NLGraph;
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typedef boost::shared_ptr<NonlinearFactor<VectorConfig> > shared;
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typedef boost::shared_ptr<NonlinearConstraint<VectorConfig> > shared_c;
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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 VectorConfig);
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SQPOptimizer<NLGraph, VectorConfig> 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 VectorConfig& config, const list<string>& keys) {
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return config[keys.front()]-config[keys.back()];
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}
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/** gradient at l1 */
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Matrix grad_g1(const VectorConfig& config, const list<string>& keys) {
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return eye(2);
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}
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/** gradient at l2 */
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Matrix grad_g2(const VectorConfig& config, const list<string>& keys) {
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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 VectorConfig& config, const list<string>& keys) {
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return config[keys.front()]-Vector_(2, 1.0, 1.0);
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}
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/** gradient at x1 */
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Matrix grad_g(const VectorConfig& config, const list<string>& keys) {
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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, VectorConfig> 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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// constant constraint on x1
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boost::shared_ptr<NonlinearConstraint1<VectorConfig> > c1(
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new NonlinearConstraint1<VectorConfig>(
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"x1", *sqp_LinearMapWarp1::grad_g,
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*sqp_LinearMapWarp1::g_func, 2, "L_x1"));
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// measurement from x1 to l1
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Vector z1 = Vector_(2, 0.0, 5.0);
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double sigma1 = 0.1;
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shared f1(new Simulated2DMeasurement(z1, sigma1, "x1", "l1"));
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// measurement from x2 to l2
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Vector z2 = Vector_(2, -4.0, 0.0);
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double sigma2 = 0.1;
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shared f2(new Simulated2DMeasurement(z2, sigma2, "x2", "l2"));
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// equality constraint between l1 and l2
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boost::shared_ptr<NonlinearConstraint2<VectorConfig> > c2(
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new NonlinearConstraint2<VectorConfig>(
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"l1", *sqp_LinearMapWarp2::grad_g1,
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"l2", *sqp_LinearMapWarp2::grad_g2,
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*sqp_LinearMapWarp2::g_func, 2, "L_l1l2"));
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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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// create an initial estimate
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shared_config initialEstimate(new VectorConfig);
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initialEstimate->insert("x1", Vector_(2, 1.0, 1.0));
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initialEstimate->insert("l1", Vector_(2, 1.0, 6.0));
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initialEstimate->insert("l2", Vector_(2, -4.0, 0.0)); // starting with a separate reference frame
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initialEstimate->insert("x2", Vector_(2, 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_config initLagrange(new VectorConfig);
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initLagrange->insert("L_l1l2", Vector_(2, 1.0, 1.0));
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initLagrange->insert("L_x1", 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", "L_l1l2", "L_x1";
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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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VectorConfig actual = *(oneIteration.config());
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VectorConfig expected;
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expected.insert("x1", Vector_(2, 1.0, 1.0));
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expected.insert("l1", Vector_(2, 1.0, 6.0));
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expected.insert("l2", Vector_(2, 1.0, 6.0));
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expected.insert("x2", Vector_(2, 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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// create an initial estimate
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shared_config initialEstimate(new VectorConfig);
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initialEstimate->insert("x1", Vector_(2, 1.0, 1.0));
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initialEstimate->insert("l1", Vector_(2, 1.0, 6.0));
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initialEstimate->insert("l2", Vector_(2, -4.0, 0.0)); // starting with a separate reference frame
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initialEstimate->insert("x2", Vector_(2, 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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VectorConfig actual = *(oneIteration.config());
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VectorConfig expected;
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expected.insert("x1", Vector_(2, 1.0, 1.0));
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expected.insert("l1", Vector_(2, 1.0, 6.0));
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expected.insert("l2", Vector_(2, 1.0, 6.0));
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expected.insert("x2", Vector_(2, 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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bool vector_compare(const std::string& key,
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const VectorConfig& feasible,
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const VectorConfig& input) {
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Vector feas, lin;
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feas = feasible[key];
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lin = input[key];
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return equal_with_abs_tol(lin, feas, 1e-5);
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}
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typedef NonlinearConstraint1<VectorConfig> NLC1;
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typedef boost::shared_ptr<NLC1> shared_NLC1;
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typedef NonlinearConstraint2<VectorConfig> NLC2;
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typedef boost::shared_ptr<NLC2> shared_NLC2;
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typedef NonlinearEquality<VectorConfig> NLE;
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typedef boost::shared_ptr<NLE> shared_NLE;
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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 VectorConfig& config, const list<string>& keys) {
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Vector delta = config[keys.front()]-config[keys.back()];
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double dist2 = sum(emul(delta, delta));
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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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/** gradient at pose */
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Matrix grad_g1(const VectorConfig& config, const list<string>& keys) {
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Vector x2 = config[keys.front()], obs = config[keys.back()];
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Vector grad = 2.0*(x2-obs);
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return Matrix_(1,2, grad(0), grad(1));
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}
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/** gradient at obstacle */
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Matrix grad_g2(const VectorConfig& config, const list<string>& keys) {
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Vector x2 = config[keys.front()], obs = config[keys.back()];
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Vector grad = -2.0*(x2-obs);
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return Matrix_(1,2, grad(0), grad(1));
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}
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}
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pair<NLGraph, VectorConfig> obstacleAvoidGraph() {
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// fix start, end, obstacle positions
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VectorConfig feasible;
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feasible.insert("x1", Vector_(2, 0.0, 0.0));
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feasible.insert("x3", Vector_(2, 10.0, 0.0));
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feasible.insert("obs", Vector_(2, 5.0, -0.5));
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shared_NLE e1(new NLE("x1", feasible, 2, *vector_compare));
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shared_NLE e2(new NLE("x3", feasible, 2, *vector_compare));
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shared_NLE e3(new NLE("obs", feasible, 2, *vector_compare));
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// measurement from x1 to x2
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Vector x1x2 = Vector_(2, 5.0, 0.0);
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double sigma1 = 0.1;
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shared f1(new Simulated2DOdometry(x1x2, sigma1, "x1", "x2"));
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// measurement from x2 to x3
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Vector x2x3 = Vector_(2, 5.0, 0.0);
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double sigma2 = 0.1;
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shared f2(new Simulated2DOdometry(x2x3, sigma2, "x2", "x3"));
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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_NLC2 c1(new NLC2("x2", *sqp_avoid1::grad_g1,
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"obs", *sqp_avoid1::grad_g2,
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*sqp_avoid1::g_func, 1, "L_x2obs", 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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return make_pair(graph, feasible);
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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; VectorConfig 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_config init(new VectorConfig(feasible));
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init->insert("x2", Vector_(2, 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", "obs";
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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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VectorConfig exp1(feasible);
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exp1.insert("x2", Vector_(2, 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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VectorConfig exp2(feasible);
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exp2.insert("x2", Vector_(2, 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; VectorConfig 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_config init(new VectorConfig(feasible));
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init->insert("x2", Vector_(2, 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", "obs";
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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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VectorConfig exp2(feasible);
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exp2.insert("x2", Vector_(2, 5.0, 0.5));
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CHECK(assert_equal(exp2, *(final.config())));
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}
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/* ********************************************************************* */
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// Use boost bind to parameterize the function
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namespace sqp_avoid2 {
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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(double radius, const VectorConfig& config, const list<string>& keys) {
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Vector delta = config[keys.front()]-config[keys.back()];
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double dist2 = sum(emul(delta, delta));
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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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/** gradient at pose */
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Matrix grad_g1(const VectorConfig& config, const list<string>& keys) {
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Vector x2 = config[keys.front()], obs = config[keys.back()];
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Vector grad = 2.0*(x2-obs);
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return Matrix_(1,2, grad(0), grad(1));
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}
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/** gradient at obstacle */
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Matrix grad_g2(const VectorConfig& config, const list<string>& keys) {
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Vector x2 = config[keys.front()], obs = config[keys.back()];
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Vector grad = -2.0*(x2-obs);
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return Matrix_(1,2, grad(0), grad(1));
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}
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}
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pair<NLGraph, VectorConfig> obstacleAvoidGraphGeneral() {
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// fix start, end, obstacle positions
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VectorConfig feasible;
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feasible.insert("x1", Vector_(2, 0.0, 0.0));
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feasible.insert("x3", Vector_(2, 10.0, 0.0));
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feasible.insert("obs", Vector_(2, 5.0, -0.5));
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shared_NLE e1(new NLE("x1", feasible, 2, *vector_compare));
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shared_NLE e2(new NLE("x3", feasible, 2, *vector_compare));
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shared_NLE e3(new NLE("obs", feasible, 2, *vector_compare));
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// measurement from x1 to x2
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Vector x1x2 = Vector_(2, 5.0, 0.0);
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double sigma1 = 0.1;
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shared f1(new Simulated2DOdometry(x1x2, sigma1, "x1", "x2"));
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// measurement from x2 to x3
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Vector x2x3 = Vector_(2, 5.0, 0.0);
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double sigma2 = 0.1;
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shared f2(new Simulated2DOdometry(x2x3, sigma2, "x2", "x3"));
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double radius = 1.0;
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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_NLC2 c1(new NLC2("x2", boost::bind(sqp_avoid2::grad_g1, _1, _2),
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"obs", boost::bind(sqp_avoid2::grad_g2, _1, _2),
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boost::bind(sqp_avoid2::g_func, radius, _1, _2), 1, "L_x2obs", 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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return make_pair(graph, feasible);
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}
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/* ********************************************************************* */
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TEST ( SQPOptimizer, inequality_avoid_iterative_bind ) {
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// create the graph
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NLGraph graph; VectorConfig feasible;
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boost::tie(graph, feasible) = obstacleAvoidGraphGeneral();
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// create the rest of the config
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shared_config init(new VectorConfig(feasible));
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init->insert("x2", Vector_(2, 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", "obs";
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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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VectorConfig exp2(feasible);
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exp2.insert("x2", Vector_(2, 5.0, 0.5));
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CHECK(assert_equal(exp2, *(final.config())));
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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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