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jacobians.h File Reference
#include <mrpt/math/num_jacobian.h>
#include <mrpt/math/CQuaternion.h>
#include <mrpt/poses/CPose3D.h>
#include <mrpt/poses/CPosePDF.h>
#include <mrpt/poses/CPose3DQuatPDF.h>
#include <mrpt/poses/CPose3DPDF.h>
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Namespaces

 mrpt
 This is the global namespace for all Mobile Robot Programming Toolkit (MRPT) libraries.
 
 mrpt::math
 This base provides a set of functions for maths stuff.
 
 mrpt::math::jacobians
 A collection of functions to compute jacobians of diverse transformations, etc (some functions are redirections to existing methods elsewhere, so this namespace is actually used with grouping purposes).
 

Functions

void mrpt::math::jacobians::jacob_quat_from_yawpitchroll (mrpt::math::CMatrixFixedNumeric< double, 4, 3 > &out_dq_dr, const double yaw, const double pitch, const double roll)
 Computes the 4x3 Jacobian of the transformation from a 3D pose angles (yaw pitch roll) into a Quaternion, that is, the Jacobian of:

\[ \mathbf{q} = \left( \begin{array}{c} \cos (\phi /2) \cos (\theta /2) \cos (\psi /2) + \sin (\phi /2) \sin (\theta /2) \sin (\psi /2) \\ \sin (\phi /2) \cos (\theta /2) \cos (\psi /2) - \cos (\phi /2) \sin (\theta /2) \sin (\psi /2) \\ \cos (\phi /2) \sin (\theta /2) \cos (\psi /2) + \sin (\phi /2) \cos (\theta /2) \sin (\psi /2) \\ \cos (\phi /2) \cos (\theta /2) \sin (\psi /2) - \sin (\phi /2) \sin (\theta /2) \cos (\psi /2) \\ \end{array}\right) \]

With : $ \phi = roll $, $ \theta = pitch $ and $ \psi = yaw $. More...

 
void mrpt::math::jacobians::jacob_quat_from_yawpitchroll (mrpt::math::CMatrixFixedNumeric< double, 4, 3 > &out_dq_dr, const mrpt::poses::CPose3D &in_pose)
 Computes the 4x3 Jacobian of the transformation from a 3D pose angles (yaw pitch roll) into a Quaternion, that is, the Jacobian of:

\[ \mathbf{q} = \left( \begin{array}{c} \cos (\phi /2) \cos (\theta /2) \cos (\psi /2) + \sin (\phi /2) \sin (\theta /2) \sin (\psi /2) \\ \sin (\phi /2) \cos (\theta /2) \cos (\psi /2) - \cos (\phi /2) \sin (\theta /2) \sin (\psi /2) \\ \cos (\phi /2) \sin (\theta /2) \cos (\psi /2) + \sin (\phi /2) \cos (\theta /2) \sin (\psi /2) \\ \cos (\phi /2) \cos (\theta /2) \sin (\psi /2) - \sin (\phi /2) \sin (\theta /2) \cos (\psi /2) \\ \end{array}\right) \]

With : $ \phi = roll $, $ \theta = pitch $ and $ \psi = yaw $. More...

 
void mrpt::math::jacobians::jacob_yawpitchroll_from_quat (mrpt::math::CMatrixFixedNumeric< double, 3, 4 > &out_dr_dq)
 Computes the 3x4 Jacobian of the transformation from a quaternion (qr qx qy qz) to 3D pose angles (yaw pitch roll). More...
 
template<class QUATERNION , class MATRIXLIKE >
void mrpt::math::jacobians::jacob_quat_rotation (const QUATERNION &quaternion, MATRIXLIKE &out_mat4x4)
 Compute the Jacobian of the rotation composition operation $ p = f(\cdot) = q_{this} \times r $, that is the 4x4 matrix $ \frac{\partial f}{\partial q_{this} } $. More...
 
void mrpt::math::jacobians::jacobs_6D_pose_comp (const mrpt::poses::CPose3D &x, const mrpt::poses::CPose3D &u, CMatrixDouble66 &out_df_dx, CMatrixDouble66 &out_df_du)
 Given the 3D(6D) pose composition $ f(x,u) = x \oplus u $, compute the two 6x6 Jacobians $ \frac{\partial f}{\partial x} $ and $ \frac{\partial f}{\partial u} $. More...
 
void mrpt::math::jacobians::jacobs_6D_pose_comp (const mrpt::poses::CPose3DQuat &x, const mrpt::poses::CPose3DQuat &u, CMatrixDouble77 &out_df_dx, CMatrixDouble77 &out_df_du)
 Given the 3D(6D) pose composition $ f(x,u) = x \oplus u $, compute the two 6x6 Jacobians $ \frac{\partial f}{\partial x} $ and $ \frac{\partial f}{\partial u} $. More...
 
void mrpt::math::jacobians::jacobs_2D_pose_comp (const mrpt::poses::CPosePDFGaussian &x, const mrpt::poses::CPosePDFGaussian &u, CMatrixDouble33 &out_df_dx, CMatrixDouble33 &out_df_du)
 Given the 2D pose composition $ f(x,u) = x \oplus u $, compute the two 3x3 Jacobians $ \frac{\partial f}{\partial x} $ and $ \frac{\partial f}{\partial u} $. More...
 
template<class VECTORLIKE , class VECTORLIKE2 , class VECTORLIKE3 , class MATRIXLIKE , class USERPARAM >
void mrpt::math::jacobians::jacob_numeric_estimate (const VECTORLIKE &x, void(*functor)(const VECTORLIKE &x, const USERPARAM &y, VECTORLIKE3 &out), const VECTORLIKE2 &increments, const USERPARAM &userParam, MATRIXLIKE &out_Jacobian)
 Numerical estimation of the Jacobian of a user-supplied function - this template redirects to mrpt::math::estimateJacobian, see that function for documentation. More...
 



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