MRPT  1.9.9
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mrpt::poses::Lie::SE< 3 > Struct Template Reference

Detailed Description

template<>
struct mrpt::poses::Lie::SE< 3 >

Traits for SE(3), rigid-body transformations in R^3 space.

See indidual members for documentation, or [1] for a general overview.

Definition at line 38 of file SE.h.

#include <mrpt/poses/Lie/SE.h>

Public Types

using tangent_vector = mrpt::math::CVectorFixedDouble< DOFs >
 
using manifold_vector = mrpt::math::CVectorFixedDouble< MANIFOLD_DIM >
 
using type = CPose3D
 
using light_type = mrpt::math::TPose3D
 
using tang2mat_jacob = mrpt::math::CMatrixDouble12_6
 Type for Jacobian: tangent space -> SO(n) matrix. More...
 
using mat2tang_jacob = mrpt::math::CMatrixDouble6_12
 Type for Jacobian: SO(n) matrix -> tangent space. More...
 
using matrix_TxT = mrpt::math::CMatrixDouble66
 Type for Jacobians between so(n) vectors on the tangent space. More...
 
using matrix_MxM = mrpt::math::CMatrixFixed< double, 12, 12 >
 Type for Jacobians between SO(n) 3x4 (sub)matrices in the manifold. More...
 

Static Public Member Functions

static type exp (const tangent_vector &x)
 Retraction to SE(3), a pseudo-exponential map $ x \rightarrow PseudoExp(x^\wedge) $ and its Jacobian. More...
 
static tangent_vector log (const type &P)
 SE(3) pseudo-logarithm map $ \mathbf{R} \rightarrow \log(\mathbf{R}^\vee)$. More...
 
static manifold_vector asManifoldVector (const type &pose)
 Returns a vector with all manifold matrix elements in column-major order. More...
 
static type fromManifoldVector (const manifold_vector &v)
 The inverse operation of asManifoldVector() More...
 
static tang2mat_jacob jacob_dexpe_de (const tangent_vector &x)
 Jacobian for the pseudo-exponential exp(). More...
 
static mat2tang_jacob jacob_dlogv_dv (const type &P)
 Jacobian for the pseudo-logarithm log() See 10.3.11 in [1]. More...
 
static tang2mat_jacob jacob_dexpeD_de (const CPose3D &D)
 Jacobian d (e^eps * D) / d eps , with eps=increment in Lie Algebra. More...
 
static tang2mat_jacob jacob_dDexpe_de (const CPose3D &D)
 Jacobian d (D * e^eps) / d eps , with eps=increment in Lie Algebra. More...
 
static tang2mat_jacob jacob_dAexpeD_de (const CPose3D &A, const CPose3D &D)
 Jacobian d (A * e^eps * D) / d eps , with eps=increment in Lie Algebra. More...
 
static matrix_MxM jacob_dAB_dA (const type &A, const type &B)
 Jacobian of the pose composition A*B for SE(3) 3x4 (sub)matrices, with respect to A. More...
 
static matrix_MxM jacob_dAB_dB (const type &A, const type &B)
 Jacobian of the pose composition A*B for SE(3) 3x4 (sub)matrices, with respect to B. More...
 
static void jacob_dDinvP1invP2_de1e2 (const type &Dinv, const type &P1, const type &P2, mrpt::optional_ref< matrix_TxT > df_de1=std::nullopt, mrpt::optional_ref< matrix_TxT > df_de2=std::nullopt)
 Return one or both of the following 6x6 Jacobians, useful in graph-slam problems:

\[ \frac{\partial pseudoLn(D^{-1} P_1^{-1} P_2}{\partial \epsilon_1} \]

\[ \frac{\partial pseudoLn(D^{-1} P_1^{-1} P_2}{\partial \epsilon_1}\]

With $ \epsilon_1 $ and $ \epsilon_2 $ increments in the linearized manifold for P1 and P2. More...

 

Static Public Attributes

static constexpr size_t DOFs = 6
 Number of actual degrees of freedom for this transformation. More...
 
static constexpr size_t MANIFOLD_DIM = 3 * 4
 Dimensionality of the matrix manifold (3x4=12 upper part of the 4x4) More...
 



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