Jacobian Class Reference

A Jacobian class. A jacobian with m rows and n columns. More...

#include <Jacobian.hpp>

Public Types
typedef Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >	Base
	The type of the internal Eigen matrix implementation.

Public Member Functions
	Jacobian (size_t m, size_t n)
	Creates an empty \( m\times n \) (uninitialized) Jacobian matrix. More...
	Jacobian ()
	Default constructor.
	Jacobian (size_t n)
	Creates an empty \( 6\times n \) (uninitialized) Jacobian matrix. More...
template<class R >
	Jacobian (const Eigen::MatrixBase< R > &r)
	Creates a Jacobian from a Eigen::MatrixBase. More...
	Jacobian (const rw::math::Transform3D< double > &aTb)
	Creates the velocity transform jacobian \( \robabcdx{a}{b}{a}{b}{\bf{J_v}} \) for transforming both the reference frame and the velocity reference point from one frame b to another frame a. More...
	Jacobian (const rw::math::Rotation3D< double > &aRb)
	Creates the velocity transform jacobian \( \robabcdx{a}{b}{i}{i}{\bf{J_v}} \) for transforming a velocity screw from one frame of reference b to another frame a. More...
	Jacobian (const rw::math::Vector3D< double > &aPb)
	Creates the velocity transform jacobian \( \robabcdx{i}{i}{b}{a}{\bf{J}_v} \) for transforming the reference point of a velocity screw from one frame b to another frame a. More...
size_t	size1 () const
	The number of rows.
size_t	size2 () const
	The number of columns.
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &	e ()
	Accessor for the internal Eigen matrix state.
const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &	e () const
	Accessor for the internal Eigen matrix state.
double &	operator() (size_t row, size_t column)
	Returns reference to matrix element. More...
const double &	operator() (size_t row, size_t column) const
	Returns reference to matrix element. More...
double &	elem (size_t row, size_t col)
	Get an element of the jacobian. More...
void	addRotation (const rw::math::Vector3D<> &part, size_t row, size_t col)
	add rotation jacobian to a specific row and column in this jacobian More...
void	addPosition (const rw::math::Vector3D<> &part, size_t row, size_t col)
	add position jacobian to a specific row and column in this jacobian More...

Static Public Member Functions
static Jacobian	zero (size_t size1, size_t size2)
	Construct zero initialized Jacobian. More...

Friends
std::ostream &	operator<< (std::ostream &out, const Jacobian &v)
	Streaming operator.

Related Functions
(Note that these are not member functions.)
const rw::math::VelocityScrew6D	operator* (const Jacobian &Jq, const rw::math::Q &dq)
	Calculates velocity vector. More...
const rw::math::Q	operator* (const Jacobian &JqInv, const rw::math::VelocityScrew6D<> &v)
	Calculates joint velocities. More...
const Jacobian	operator* (const Jacobian &j1, const Jacobian &j2)
	Multiplies jacobians \( \mathbf{J} = \mathbf{J}_1 * \mathbf{J}_2 \). More...
const Jacobian	operator* (const rw::math::Rotation3D<> &r, const Jacobian &v)
	Rotates each column of v by r. More...
template<>
void	write (const rw::math::Jacobian &sobject, rw::common::OutputArchive &oarchive, const std::string &id)
template<>
void	read (rw::math::Jacobian &sobject, rw::common::InputArchive &iarchive, const std::string &id)

Detailed Description

A Jacobian class. A jacobian with m rows and n columns.

An ordinary robot jacobian defined over the joints 0 to n with configuration q is expressed as a \( 6\times n \) matrix:

\[ \robabx{0}{n}{\bf{J}}(\bf{q}) = [ \robabx{0}{1}{\bf{J}}(\bf{q}), \robabx{1}{2}{\bf{J}}(\bf{q}),..., \robabx{n-1}{n}{\bf{J}}(\bf{q}) ] \]

Constructor & Destructor Documentation

Jacobian() [1/6]

Jacobian ( size_t  m, size_t  n  )

inline

Creates an empty \( m\times n \) (uninitialized) Jacobian matrix.

Parameters

m	[in] number of rows
n	[in] number of columns

Jacobian() [2/6]

Jacobian ( size_t  n )

inlineexplicit

Creates an empty \( 6\times n \) (uninitialized) Jacobian matrix.

Parameters

n	[in] number of columns

Jacobian() [3/6]

Jacobian ( const Eigen::MatrixBase< R > &  r )

inlineexplicit

Creates a Jacobian from a Eigen::MatrixBase.

Parameters

r	[in] an Eigen Matrix

Jacobian() [4/6]

Jacobian ( const rw::math::Transform3D< double > &  aTb )

explicit

Creates the velocity transform jacobian \( \robabcdx{a}{b}{a}{b}{\bf{J_v}} \) for transforming both the reference frame and the velocity reference point from one frame b to another frame a.

Parameters

aTb	[in] \( \robabx{a}{b}{\bf{T}} \)

Returns

\( \robabcdx{a}{b}{a}{b}{\bf{J_v}} \)

\[ \robabcdx{a}{b}{a}{b}{\bf{J_v}} = \left[ \begin{array}{cc} \robabx{a}{b}{\mathbf{R}} & S(\robabx{a}{b}{\mathbf{d}})\robabx{a}{b}{\mathbf{R}} \\ \mathbf{0}^{3x3} & \robabx{a}{b}{\mathbf{R}} \end{array} \right] \]

Change the frame of reference from b to frame a and reference point from frame a to frame b: \( \robabx{a}{b}{\bf{J}} = \robabcdx{a}{b}{a}{b}{\bf{J}_v} \cdot \robabx{b}{a}{\bf{J}} \)

Jacobian() [5/6]

Jacobian ( const rw::math::Rotation3D< double > &  aRb )

explicit

Creates the velocity transform jacobian \( \robabcdx{a}{b}{i}{i}{\bf{J_v}} \) for transforming a velocity screw from one frame of reference b to another frame a.

Parameters

aRb	[in] \( \robabx{a}{b}{\bf{R}} \)

Returns

\( \robabcdx{a}{b}{i}{i}{\bf{J}_v} \)

\[ \robabcdx{a}{b}{i}{i}{\bf{J_v}} = \left[ \begin{array}{cc} \robabx{a}{b}{\mathbf{R}} & \mathbf{0}^{3x3} \\ \mathbf{0}^{3x3} & \robabx{a}{b}{\mathbf{R}} \end{array} \right] \]

Change the frame of reference from b to frame a : \( \robabx{a}{c}{\bf{J}} = \robabcdx{a}{b}{c}{c}{\bf{J}_v} \cdot \robabx{b}{c}{\bf{J}} \)

Jacobian() [6/6]

Jacobian ( const rw::math::Vector3D< double > &  aPb )

explicit

Creates the velocity transform jacobian \( \robabcdx{i}{i}{b}{a}{\bf{J}_v} \) for transforming the reference point of a velocity screw from one frame b to another frame a.

Parameters

aPb	[in] \( \robabx{a}{b}{\bf{P}} \)

Returns

\( \robabcdx{i}{i}{b}{a}{\bf{J}_v} \)

\[ \robabcdx{i}{i}{b}{a}{\bf{J}_v} = \left[ \begin{array}{cc} \bf{I}^{3x3} & S(\robabx{a}{b}{\bf{P}}) \\ \bf{0}^{3x3} & \bf{I}^{3x3} \end{array} \right] \]

transforming the reference point of a Jacobian from frame c to frame d : \( \robabx{a}{d}{\mathbf{J}} = \robabcdx{a}{a}{c}{d}{\mathbf{J_v}} \cdot \robabx{a}{c}{\mathbf{J}} \)

Member Function Documentation

addPosition()

void addPosition	(	const rw::math::Vector3D<> &	part,
		size_t	row,
		size_t	col
	)

add position jacobian to a specific row and column in this jacobian

Parameters

part
row
col

addRotation()

void addRotation	(	const rw::math::Vector3D<> &	part,
		size_t	row,
		size_t	col
	)

add rotation jacobian to a specific row and column in this jacobian

Parameters

part
row
col

elem()

double& elem ( size_t  row, size_t  col  )

inline

Get an element of the jacobian.

Parameters

row	[in] the row.
col	[in] the column.

Returns

reference to the element.

operator()() [1/2]

double& operator() ( size_t  row, size_t  column  )

inline

Returns reference to matrix element.

Parameters

row	[in] row
column	[in] column

Returns

reference to the element

operator()() [2/2]

const double& operator() ( size_t  row, size_t  column  ) const

inline

Returns reference to matrix element.

Parameters

row	[in] row
column	[in] column

Returns

reference to the element

zero()

static Jacobian zero ( size_t  size1, size_t  size2  )

inlinestatic

Construct zero initialized Jacobian.

Parameters

size1	[in] number of rows.
size2	[in] number of columns.

Returns

zero-initialized jacobian.

Friends And Related Function Documentation

operator*() [1/4]

const Jacobian operator* ( const Jacobian &  j1, const Jacobian &  j2  )

related

Multiplies jacobians \( \mathbf{J} = \mathbf{J}_1 * \mathbf{J}_2 \).

Parameters

j1	[in] \( \mathbf{J}_1 \)
j2	[in] \( \mathbf{J}_2 \)

Returns

\( \mathbf{J} \)

operator*() [2/4]

const rw::math::VelocityScrew6D operator* ( const Jacobian &  Jq, const rw::math::Q &  dq  )

related

Calculates velocity vector.

Parameters

Jq	[in] the jacobian \( \mathbf{J}_{\mathbf{q}} \)
dq	[in] the joint velocity vector \( \dot{\mathbf{q}} \)

Returns

the velocity vector \( \mathbf{\nu} \)

operator*() [3/4]

const rw::math::Q operator* ( const Jacobian &  JqInv, const rw::math::VelocityScrew6D<> &  v  )

related

Calculates joint velocities.

Parameters

JqInv	[in] the inverse jacobian \( \mathbf{J}_{\mathbf{q}}^{-1} \)
v	[in] the velocity vector \( \mathbf{\nu} \)

Returns

the joint velocity vector \( \dot{\mathbf{q}} \)

operator*() [4/4]

const Jacobian operator* ( const rw::math::Rotation3D<> &  r, const Jacobian &  v  )

related

Rotates each column of v by r.

The Jacobian must be of height 6.

read()

void read ( rw::math::Jacobian &  sobject, rw::common::InputArchive &  iarchive, const std::string &  id  )

related

Enable read-serialization of class T by overloading this method. Data is read from iarchive and filled into sobject.

Parameters

sobject	[out] the object in which the data should be streamed into
iarchive	[in] the InputArchive from which to read data.
id	[in] The id of the serialized sobject.

Note

the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

write()

void write ( const rw::math::Jacobian &  sobject, rw::common::OutputArchive &  oarchive, const std::string &  id  )

related

Enable write-serialization of class T by overloading this method. Data is written to oarchive from the sobject.

Parameters

sobject	[in] the object from which the data should be streamed.
oarchive	[out] the OutputArchive in which data should be written.
id	[in] The id of the serialized sobject.

Note

the id can be empty in which case the overloaded method should provide a default identifier. E.g. the Vector3D class defined "Vector3D" as its default id.

---

The documentation for this class was generated from the following file:

• Jacobian.hpp