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Merge remote-tracking branch 'origin/feature/SO3_refactor' into feature/ImuFactorPush2

release/4.3a0
Frank Dellaert 2016-02-01 09:48:18 -08:00
parent 7c2560e977 8c6383c711
commit 255c3a8ec3
2 changed files with 123 additions and 97 deletions
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172
gtsam/geometry/SO3.cpp
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@ -25,128 +25,106 @@
namespace gtsam { namespace gtsam {
/* ************************************************************************* */ namespace so3 {
// Functor implementing Exponential map
struct ExpmapImpl {
const double theta2;
Matrix3 W, K, KK;
bool nearZero;
double theta, sin_theta, one_minus_cos; // only defined if !nearZero
void init() { void ExpmapFunctor::init() {
nearZero = (theta2 <= std::numeric_limits<double>::epsilon()); nearZero = (theta2 <= std::numeric_limits<double>::epsilon());
if (nearZero) return; if (nearZero) return;
theta = std::sqrt(theta2); // rotation angle theta = std::sqrt(theta2); // rotation angle
sin_theta = std::sin(theta); sin_theta = std::sin(theta);
const double s2 = std::sin(theta / 2.0); const double s2 = std::sin(theta / 2.0);
one_minus_cos = 2.0 * s2 * s2; // numerically better than [1 - cos(theta)] one_minus_cos = 2.0 * s2 * s2; // numerically better than [1 - cos(theta)]
} }
// Constructor with element of Lie algebra so(3) ExpmapFunctor::ExpmapFunctor(const Vector3& omega) : theta2(omega.dot(omega)) {
ExpmapImpl(const Vector3& omega) : theta2(omega.dot(omega)) { const double wx = omega.x(), wy = omega.y(), wz = omega.z();
const double wx = omega.x(), wy = omega.y(), wz = omega.z(); W << 0.0, -wz, +wy, +wz, 0.0, -wx, -wy, +wx, 0.0;
W << 0.0, -wz, +wy, +wz, 0.0, -wx, -wy, +wx, 0.0; init();
init(); if (!nearZero) {
if (!nearZero) { theta = std::sqrt(theta2);
theta = std::sqrt(theta2); K = W / theta;
K = W / theta; KK = K * K;
KK = K * K;
}
} }
}
// Constructor with axis-angle ExpmapFunctor::ExpmapFunctor(const Vector3& axis, double angle)
ExpmapImpl(const Vector3& axis, double angle) : theta2(angle * angle) { : theta2(angle * angle) {
const double ax = axis.x(), ay = axis.y(), az = axis.z(); const double ax = axis.x(), ay = axis.y(), az = axis.z();
K << 0.0, -az, +ay, +az, 0.0, -ax, -ay, +ax, 0.0; K << 0.0, -az, +ay, +az, 0.0, -ax, -ay, +ax, 0.0;
W = K * angle; W = K * angle;
init(); init();
if (!nearZero) { if (!nearZero) {
theta = angle; theta = angle;
KK = K * K; KK = K * K;
}
} }
}
// Rodrgues formula SO3 ExpmapFunctor::expmap() const {
SO3 expmap() const { if (nearZero)
if (nearZero) return I_3x3 + W;
return I_3x3 + W; else
else return I_3x3 + sin_theta * K + one_minus_cos * K * K;
return I_3x3 + sin_theta * K + one_minus_cos * K * K; }
DexpFunctor::DexpFunctor(const Vector3& omega)
: ExpmapFunctor(omega), omega(omega) {
if (nearZero) return;
a = one_minus_cos / theta;
b = 1.0 - sin_theta / theta;
}
SO3 DexpFunctor::dexp() const {
if (nearZero)
return I_3x3 - 0.5 * W;
else
return I_3x3 - a * K + b * KK;
}
Vector3 DexpFunctor::applyDexp(const Vector3& v, OptionalJacobian<3, 3> H1,
OptionalJacobian<3, 3> H2) const {
if (nearZero) {
if (H1) *H1 = 0.5 * skewSymmetric(v);
if (H2) *H2 = I_3x3;
return v - 0.5 * omega.cross(v);
} }
}; const Vector3 Kv = omega.cross(v / theta);
const Vector3 KKv = omega.cross(Kv / theta);
if (H1) {
// TODO(frank): Iserles hints that there should be a form I + c*K + d*KK
const Matrix3 T = skewSymmetric(v / theta);
const double Da = (sin_theta - 2.0 * a) / theta2;
const double Db = (one_minus_cos - 3.0 * b) / theta2;
*H1 = (-Da * Kv + Db * KKv) * omega.transpose() + a * T -
skewSymmetric(Kv * b / theta) - b * K * T;
}
if (H2) *H2 = dexp();
return v - a * Kv + b * KKv;
}
} // namespace so3
/* ************************************************************************* */ /* ************************************************************************* */
SO3 SO3::AxisAngle(const Vector3& axis, double theta) { SO3 SO3::AxisAngle(const Vector3& axis, double theta) {
return ExpmapImpl(axis, theta).expmap(); return so3::ExpmapFunctor(axis, theta).expmap();
} }
/* ************************************************************************* */
// Functor that implements Exponential map *and* its derivatives
struct DexpImpl : ExpmapImpl {
const Vector3 omega;
double a, b; // constants used in dexp and applyDexp
// Constructor with element of Lie algebra so(3)
DexpImpl(const Vector3& omega) : ExpmapImpl(omega), omega(omega) {
if (nearZero) return;
a = one_minus_cos / theta;
b = 1.0 - sin_theta / theta;
}
// NOTE(luca): Right Jacobian for Exponential map in SO(3) - equation
// (10.86) and following equations in G.S. Chirikjian, "Stochastic Models,
// Information Theory, and Lie Groups", Volume 2, 2008.
// expmap(omega + v) \approx expmap(omega) * expmap(dexp * v)
// This maps a perturbation v in the tangent space to
// a perturbation on the manifold Expmap(dexp * v) */
SO3 dexp() const {
if (nearZero)
return I_3x3 - 0.5 * W;
else
return I_3x3 - a * K + b * KK;
}
// Just multiplies with dexp()
Vector3 applyDexp(const Vector3& v, OptionalJacobian<3, 3> H1,
OptionalJacobian<3, 3> H2) const {
if (nearZero) {
if (H1) *H1 = 0.5 * skewSymmetric(v);
if (H2) *H2 = I_3x3;
return v - 0.5 * omega.cross(v);
}
const Vector3 Kv = omega.cross(v / theta);
const Vector3 KKv = omega.cross(Kv / theta);
if (H1) {
// TODO(frank): Iserles hints that there should be a form I + c*K + d*KK
const Matrix3 T = skewSymmetric(v / theta);
const double Da = (sin_theta - 2.0 * a) / theta2;
const double Db = (one_minus_cos - 3.0 * b) / theta2;
*H1 = (-Da * Kv + Db * KKv) * omega.transpose() + a * T -
skewSymmetric(Kv * b / theta) - b * K * T;
}
if (H2) *H2 = dexp();
return v - a * Kv + b * KKv;
}
};
/* ************************************************************************* */
SO3 SO3::Expmap(const Vector3& omega, ChartJacobian H) { SO3 SO3::Expmap(const Vector3& omega, ChartJacobian H) {
if (H) { if (H) {
DexpImpl impl(omega); so3::DexpFunctor impl(omega);
*H = impl.dexp(); *H = impl.dexp();
return impl.expmap(); return impl.expmap();
} else } else
return ExpmapImpl(omega).expmap(); return so3::ExpmapFunctor(omega).expmap();
} }
Matrix3 SO3::ExpmapDerivative(const Vector3& omega) { Matrix3 SO3::ExpmapDerivative(const Vector3& omega) {
return DexpImpl(omega).dexp(); return so3::DexpFunctor(omega).dexp();
} }
Vector3 SO3::ApplyExpmapDerivative(const Vector3& omega, const Vector3& v, Vector3 SO3::ApplyExpmapDerivative(const Vector3& omega, const Vector3& v,
OptionalJacobian<3, 3> H1, OptionalJacobian<3, 3> H1,
OptionalJacobian<3, 3> H2) { OptionalJacobian<3, 3> H2) {
return DexpImpl(omega).applyDexp(v, H1, H2); return so3::DexpFunctor(omega).applyDexp(v, H1, H2);
} }
/* ************************************************************************* */ /* ************************************************************************* */

48
gtsam/geometry/SO3.h
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@ -135,6 +135,54 @@ public:
/// @} /// @}
}; };
// This namespace exposes two functors that allow for saving computation when
// exponential map and its derivatives are needed at the same location in so<3>
namespace so3 {
/// Functor implementing Exponential map
class ExpmapFunctor {
protected:
const double theta2;
Matrix3 W, K, KK;
bool nearZero;
double theta, sin_theta, one_minus_cos; // only defined if !nearZero
void init();
public:
/// Constructor with element of Lie algebra so(3)
ExpmapFunctor(const Vector3& omega);
/// Constructor with axis-angle
ExpmapFunctor(const Vector3& axis, double angle);
/// Rodrgues formula
SO3 expmap() const;
};
/// Functor that implements Exponential map *and* its derivatives
class DexpFunctor : public ExpmapFunctor {
const Vector3 omega;
double a, b;
public:
/// Constructor with element of Lie algebra so(3)
DexpFunctor(const Vector3& omega);
// NOTE(luca): Right Jacobian for Exponential map in SO(3) - equation
// (10.86) and following equations in G.S. Chirikjian, "Stochastic Models,
// Information Theory, and Lie Groups", Volume 2, 2008.
// expmap(omega + v) \approx expmap(omega) * expmap(dexp * v)
// This maps a perturbation v in the tangent space to
// a perturbation on the manifold Expmap(dexp * v) */
SO3 dexp() const;
/// Multiplies with dexp(), with optional derivatives
Vector3 applyDexp(const Vector3& v, OptionalJacobian<3, 3> H1,
OptionalJacobian<3, 3> H2) const;
};
} // namespace so3
template<> template<>
struct traits<SO3> : public internal::LieGroup<SO3> { struct traits<SO3> : public internal::LieGroup<SO3> {
}; };