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Fixed and tested chart derivatives (for Pose2, SLOW EXPMAP)

release/4.3a0
dellaert 2014-12-25 17:43:43 +01:00
parent 7213f0b2eb
commit c8b3bd7598
3 changed files with 96 additions and 36 deletions
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48
gtsam/base/Lie.h
View File

@ -37,6 +37,7 @@ struct LieGroup {
enum { dimension = N }; enum { dimension = N };
typedef OptionalJacobian<N, N> ChartJacobian; typedef OptionalJacobian<N, N> ChartJacobian;
typedef Eigen::Matrix<double, N, N> Jacobian;
typedef Eigen::Matrix<double, N, 1> TangentVector; typedef Eigen::Matrix<double, N, 1> TangentVector;
const Class & derived() const { const Class & derived() const {
@ -71,16 +72,39 @@ struct LieGroup {
return derived().inverse(); return derived().inverse();
} }
Class expmap(const TangentVector& v) const {
return compose(Class::Expmap(v));
}
TangentVector logmap(const Class& g) const {
return Class::Logmap(between(g));
}
Class retract(const TangentVector& v) const {
return compose(Class::ChartAtOrigin::Retract(v));
}
TangentVector localCoordinates(const Class& g) const {
return Class::ChartAtOrigin::Local(between(g));
}
Class retract(const TangentVector& v, // Class retract(const TangentVector& v, //
ChartJacobian H1 = boost::none, // ChartJacobian H1, ChartJacobian H2 = boost::none) const {
ChartJacobian H2 = boost::none) const { Jacobian D_g_v;
return compose(Class::ChartAtOrigin::Retract(v),H1,H2); Class g = Class::ChartAtOrigin::Retract(v,D_g_v);
Class h = compose(g,H1,H2);
if (H2) *H2 = (*H2) * D_g_v;
return h;
} }
TangentVector localCoordinates(const Class& g, // TangentVector localCoordinates(const Class& g, //
ChartJacobian H1 = boost::none, // ChartJacobian H1, ChartJacobian H2 = boost::none) const {
ChartJacobian H2 = boost::none) const { Class h = between(g,H1,H2);
return Class::ChartAtOrigin::Local(between(g,H1,H2)); Jacobian D_v_h;
TangentVector v = Class::ChartAtOrigin::Local(h, D_v_h);
if (H1) *H1 = D_v_h * (*H1);
if (H2) *H2 = D_v_h * (*H2);
return v;
} }
}; };
@ -118,13 +142,21 @@ struct LieGroupTraits : Testable<Class> {
static int GetDimension(const Class&) {return dimension;} static int GetDimension(const Class&) {return dimension;}
static TangentVector Local(const Class& origin, const Class& other) {
return origin.localCoordinates(other);
}
static Class Retract(const Class& origin, const TangentVector& v) {
return origin.retract(v);
}
static TangentVector Local(const Class& origin, const Class& other, static TangentVector Local(const Class& origin, const Class& other,
ChartJacobian Horigin = boost::none, ChartJacobian Hother = boost::none) { ChartJacobian Horigin, ChartJacobian Hother = boost::none) {
return origin.localCoordinates(other, Horigin, Hother); return origin.localCoordinates(other, Horigin, Hother);
} }
static Class Retract(const Class& origin, const TangentVector& v, static Class Retract(const Class& origin, const TangentVector& v,
ChartJacobian Horigin = boost::none, ChartJacobian Hv = boost::none) { ChartJacobian Horigin, ChartJacobian Hv = boost::none) {
return origin.retract(v, Horigin, Hv); return origin.retract(v, Horigin, Hv);
} }

2
gtsam/geometry/Pose2.h
View File

@ -24,6 +24,8 @@
#include <gtsam/geometry/Rot2.h> #include <gtsam/geometry/Rot2.h>
#include <gtsam/base/Lie.h> #include <gtsam/base/Lie.h>
#define SLOW_BUT_CORRECT_EXPMAP
namespace gtsam { namespace gtsam {
/** /**

82
gtsam/geometry/tests/testPose2.cpp
View File

@ -32,8 +32,6 @@ using namespace boost::assign;
using namespace gtsam; using namespace gtsam;
using namespace std; using namespace std;
//#define SLOW_BUT_CORRECT_EXPMAP
GTSAM_CONCEPT_TESTABLE_INST(Pose2) GTSAM_CONCEPT_TESTABLE_INST(Pose2)
GTSAM_CONCEPT_LIE_INST(Pose2) GTSAM_CONCEPT_LIE_INST(Pose2)
@ -180,9 +178,9 @@ TEST(Pose2, logmap) {
Pose2 pose0(M_PI/2.0, Point2(1, 2)); Pose2 pose0(M_PI/2.0, Point2(1, 2));
Pose2 pose(M_PI/2.0+0.018, Point2(1.015, 2.01)); Pose2 pose(M_PI/2.0+0.018, Point2(1.015, 2.01));
#ifdef SLOW_BUT_CORRECT_EXPMAP #ifdef SLOW_BUT_CORRECT_EXPMAP
Vector expected = Vector3(0.00986473, -0.0150896, 0.018); Vector3 expected(0.00986473, -0.0150896, 0.018);
#else #else
Vector expected = Vector3(0.01, -0.015, 0.018); Vector3 expected(0.01, -0.015, 0.018);
#endif #endif
Vector actual = pose0.localCoordinates(pose); Vector actual = pose0.localCoordinates(pose);
EXPECT(assert_equal(expected, actual, 1e-5)); EXPECT(assert_equal(expected, actual, 1e-5));
@ -771,41 +769,69 @@ TEST(Pose2, align_4) {
//****************************************************************************** //******************************************************************************
TEST(Pose2 , Traits) { TEST(Pose2 , Traits) {
Pose2 t1(M_PI/4.0, Point2(sqrt(0.5), sqrt(0.5))); Pose2 id;
Pose2 t2(M_PI/2.0, Point2(0.0, 2.0)); Pose2 t1(M_PI / 4.0, Point2(sqrt(0.5), sqrt(0.5)));
Pose2 t2(M_PI / 2.0, Point2(0.0, 2.0));
check_group_invariants(t1, t2); check_group_invariants(t1, t2);
check_manifold_invariants(t1, t2); check_manifold_invariants(t1, t2);
Pose2 expected, actual; Matrix H1, H2;
Matrix actualH1, actualH2; typedef traits_x<Pose2> T;
Matrix numericalH1, numericalH2;
expected = t1 * t2; EXPECT(assert_equal(t1, T::Compose(id, t1, H1, H2)));
actual = traits_x<Pose2>::Compose(t1, t2, actualH1, actualH2); EXPECT(assert_equal(numericalDerivative21(T::Compose, id, t1), H1));
EXPECT(assert_equal(expected,actual)); EXPECT(assert_equal(numericalDerivative22(T::Compose, id, t1), H2));
numericalH1 = numericalDerivative21(traits_x<Pose2>::Compose, t1, t2); EXPECT(assert_equal(t2, T::Compose(id, t2, H1, H2)));
EXPECT(assert_equal(numericalH1,actualH1)); EXPECT(assert_equal(numericalDerivative21(T::Compose, id, t2), H1));
EXPECT(assert_equal(numericalDerivative22(T::Compose, id, t2), H2));
numericalH2 = numericalDerivative22(traits_x<Pose2>::Compose, t1, t2); EXPECT(assert_equal(t1 * t2,T::Compose(t1, t2, H1, H2)));
EXPECT(assert_equal(numericalH2,actualH2)); EXPECT(assert_equal(numericalDerivative21(T::Compose, t1, t2), H1));
EXPECT(assert_equal(numericalDerivative22(T::Compose, t1, t2), H2));
expected = t1.inverse() * t2; EXPECT(assert_equal(t1.inverse() * t2,T::Between(t1, t2, H1, H2)));
actual = traits_x<Pose2>::Between(t1, t2, actualH1, actualH2); EXPECT(assert_equal(numericalDerivative21(T::Between, t1, t2), H1));
EXPECT(assert_equal(expected,actual)); EXPECT(assert_equal(numericalDerivative22(T::Between, t1, t2), H2));
numericalH1 = numericalDerivative21(traits_x<Pose2>::Between, t1, t2); EXPECT(assert_equal(t1.inverse(),T::Inverse(t1, H1)));
EXPECT(assert_equal(numericalH1,actualH1)); EXPECT(assert_equal(numericalDerivative11(T::Inverse, t1),H1));
numericalH2 = numericalDerivative22(traits_x<Pose2>::Between, t1, t2); Vector3 z = T::Local(id, id);
EXPECT(assert_equal(numericalH2,actualH2)); EXPECT(assert_equal(id, T::Retract(id,z, H1, H2)));
EXPECT(assert_equal(numericalDerivative21(T::Retract, id, z), H1));
EXPECT(assert_equal(numericalDerivative22(T::Retract, id, z), H2));
expected = t1.inverse(); EXPECT(assert_equal(z, id.localCoordinates(id, H1, H2)));
actual = traits_x<Pose2>::Inverse(t1, actualH1); EXPECT(assert_equal(numericalDerivative21(T::Local, id, id), H1));
EXPECT(assert_equal(expected,actual)); EXPECT(assert_equal(numericalDerivative22(T::Local, id, id), H2));
numericalH1 = numericalDerivative11(traits_x<Pose2>::Inverse, t1); Vector3 w1 = T::Local(id, t1);
EXPECT(assert_equal(numericalH1,actualH1)); EXPECT(assert_equal(t1, T::Retract(id,w1, H1, H2)));
EXPECT(assert_equal(numericalDerivative21(T::Retract, id, w1), H1));
EXPECT(assert_equal(numericalDerivative22(T::Retract, id, w1), H2));
EXPECT(assert_equal(w1, id.localCoordinates(t1, H1, H2)));
EXPECT(assert_equal(numericalDerivative21(T::Local, id, t1), H1));
EXPECT(assert_equal(numericalDerivative22(T::Local, id, t1), H2));
Vector3 w2 = T::Local(id, t2);
EXPECT(assert_equal(t2, T::Retract(id,w2, H1, H2)));
EXPECT(assert_equal(numericalDerivative21(T::Retract, id, w2), H1));
EXPECT(assert_equal(numericalDerivative22(T::Retract, id, w2), H2));
EXPECT(assert_equal(w2, id.localCoordinates(t2, H1, H2)));
EXPECT(assert_equal(numericalDerivative21(T::Local, id, t2), H1));
EXPECT(assert_equal(numericalDerivative22(T::Local, id, t2), H2));
Vector3 w12 = T::Local(t1, t2);
EXPECT(assert_equal(t2, T::Retract(t1,w12, H1, H2)));
EXPECT(assert_equal(numericalDerivative21(T::Retract, t1, w12), H1));
EXPECT(assert_equal(numericalDerivative22(T::Retract, t1, w12), H2));
EXPECT(assert_equal(w12, t1.localCoordinates(t2, H1, H2)));
EXPECT(assert_equal(numericalDerivative21(T::Local, t1, t2), H1));
EXPECT(assert_equal(numericalDerivative22(T::Local, t1, t2), H2));
} }
/* ************************************************************************* */ /* ************************************************************************* */