release/4.3a0
Frank Dellaert 2024-12-15 01:53:02 -05:00
parent c7f651d98d
commit 82e1380603
3 changed files with 12 additions and 21 deletions

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@ -168,14 +168,14 @@ Pose3 Pose3::Expmap(const Vector6& xi, OptionalJacobian<6, 6> Hxi) {
const Vector3 w = xi.head<3>(), v = xi.tail<3>(); const Vector3 w = xi.head<3>(), v = xi.tail<3>();
// Compute rotation using Expmap // Compute rotation using Expmap
Rot3 R = Rot3::Expmap(w); Matrix3 Jw;
Rot3 R = Rot3::Expmap(w, Hxi ? &Jw : nullptr);
// Compute translation and optionally its Jacobian in w // Compute translation and optionally its Jacobian in w
Matrix3 Q; Matrix3 Q;
const Vector3 t = ExpmapTranslation(w, v, Hxi ? &Q : nullptr, R); const Vector3 t = ExpmapTranslation(w, v, Hxi ? &Q : nullptr, R);
if (Hxi) { if (Hxi) {
const Matrix3 Jw = Rot3::ExpmapDerivative(w);
*Hxi << Jw, Z_3x3, *Hxi << Jw, Z_3x3,
Q, Jw; Q, Jw;
} }
@ -246,34 +246,27 @@ class ExpmapFunctor : public so3::DexpFunctor {
static constexpr double one_one_hundred_twentieth = 1.0 / 120.0; static constexpr double one_one_hundred_twentieth = 1.0 / 120.0;
public: public:
ExpmapFunctor(const Vector3& omega, bool nearZeroApprox = false, ExpmapFunctor(const Vector3& omega, bool nearZeroApprox = false)
bool includeHigherOrder = false) : so3::DexpFunctor(omega, nearZeroApprox) {}
: so3::DexpFunctor(omega, nearZeroApprox),
includeHigherOrder(includeHigherOrder) {}
// Compute the bottom-left 3x3 block of the SE(3) Expmap derivative
// TODO(Frank): t = applyLeftJacobian(v), it would be nice to understand
// how to compute mess below from its derivatives in w and v.
Matrix3 computeQ(const Vector3& v) const { Matrix3 computeQ(const Vector3& v) const {
const Matrix3 V = skewSymmetric(v); const Matrix3 V = skewSymmetric(v);
const Matrix3 WVW = W * V * W; const Matrix3 WVW = W * V * W;
if (!nearZero) { if (!nearZero) {
// Simplified from closed-form formula in Barfoot14tro eq. (102) // Simplified from closed-form formula in Barfoot14tro eq. (102)
// Note dexp = I_3x3 - B * W + C * WW and t = dexp * v
return -0.5 * V + C * (W * V + V * W - WVW) + return -0.5 * V + C * (W * V + V * W - WVW) +
(B - 0.5) / theta2 * (WW * V + V * WW - 3 * WVW) - (B - 0.5) / theta2 * (WW * V + V * WW - 3 * WVW) -
0.5 * (B - 3 * C) / theta2 * (WVW * W + W * WVW); 0.5 * (B - 3 * C) / theta2 * (WVW * W + W * WVW);
} else { } else {
Matrix3 Q = -0.5 * V + one_sixth * (W * V + V * W - WVW); return -0.5 * V + one_sixth * (W * V + V * W - WVW) -
Q -= one_twenty_fourth * (WW * V + V * WW - 3 * WVW); one_twenty_fourth * (WW * V + V * WW - 3 * WVW) +
one_one_hundred_twentieth * (WVW * W + W * WVW);
if (includeHigherOrder) {
Q += one_one_hundred_twentieth * (WVW * W + W * WVW);
}
return Q;
} }
} }
private:
bool includeHigherOrder;
}; };
} // namespace pose3 } // namespace pose3
@ -298,7 +291,8 @@ Vector3 Pose3::ExpmapTranslation(const Vector3& w, const Vector3& v,
if (nearZero) { if (nearZero) {
return v + 0.5 * w.cross(v); return v + 0.5 * w.cross(v);
} else { } else {
// Geometric intuition and faster than using functor. // NOTE(Frank): t can also be computed by calling applyLeftJacobian(v), but
// formulas below convey geometric insight and creating functor is not free.
Vector3 t_parallel = w * w.dot(v); // translation parallel to axis Vector3 t_parallel = w * w.dot(v); // translation parallel to axis
Vector3 w_cross_v = w.cross(v); // translation orthogonal to axis Vector3 w_cross_v = w.cross(v); // translation orthogonal to axis
Rot3 rotation = R.value_or(Rot3::Expmap(w)); Rot3 rotation = R.value_or(Rot3::Expmap(w));

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@ -18,8 +18,6 @@
#include <gtsam/base/Testable.h> #include <gtsam/base/Testable.h>
#include <gtsam/base/numericalDerivative.h> #include <gtsam/base/numericalDerivative.h>
#include <gtsam/geometry/Point3.h> #include <gtsam/geometry/Point3.h>
#include "gtsam/base/Matrix.h"
#include "gtsam/base/OptionalJacobian.h"
using namespace std::placeholders; using namespace std::placeholders;
using namespace gtsam; using namespace gtsam;

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@ -19,7 +19,6 @@
#include <gtsam/base/Testable.h> #include <gtsam/base/Testable.h>
#include <gtsam/base/testLie.h> #include <gtsam/base/testLie.h>
#include <gtsam/geometry/SO3.h> #include <gtsam/geometry/SO3.h>
#include <iostream>
using namespace std::placeholders; using namespace std::placeholders;
using namespace std; using namespace std;