Public Types
enum	{ NQ = traits<LieGroupDerived>::NQ, NV = traits<LieGroupDerived>::NV }

typedef Derived	LieGroupDerived

typedef int	Index

typedef traits< LieGroupDerived >::Scalar	Scalar

typedef Eigen::Matrix< Scalar, NQ, 1 >	ConfigVector_t

typedef Eigen::Matrix< Scalar, NV, 1 >	TangentVector_t

typedef Eigen::Matrix< Scalar, NV, NV >	JacobianMatrix_t

Public Member Functions
API with return value as argument
template<class ConfigIn_t , class Tangent_t , class ConfigOut_t >
void	integrate (const Eigen::MatrixBase< ConfigIn_t > &q, const Eigen::MatrixBase< Tangent_t > &v, const Eigen::MatrixBase< ConfigOut_t > &qout) const
	Integrate a joint's configuration with a tangent vector during one unit time duration. More...

template<class Config_t , class Tangent_t , class JacobianOut_t >
void	dIntegrate_dq (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Tangent_t > &v, const Eigen::MatrixBase< JacobianOut_t > &J) const
	Computes the Jacobian of the Integrate operation. More...

template<class Config_t , class Tangent_t , class JacobianOut_t >
void	dIntegrate_dv (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Tangent_t > &v, const Eigen::MatrixBase< JacobianOut_t > &J) const
	Computes the Jacobian of the Integrate operation. More...

template<class ConfigL_t , class ConfigR_t , class ConfigOut_t >
void	interpolate (const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1, const Scalar &u, const Eigen::MatrixBase< ConfigOut_t > &qout) const
	Interpolation between two joint's configurations. More...

template<class Config_t >
void	normalize (const Eigen::MatrixBase< Config_t > &qout) const
	Normalize the joint configuration given as input. For instance, the quaternion must be unitary. More...

template<class Config_t >
void	random (const Eigen::MatrixBase< Config_t > &qout) const
	Generate a random joint configuration, normalizing quaternions when necessary. More...

template<class ConfigL_t , class ConfigR_t , class ConfigOut_t >
void	randomConfiguration (const Eigen::MatrixBase< ConfigL_t > &lower_pos_limit, const Eigen::MatrixBase< ConfigR_t > &upper_pos_limit, const Eigen::MatrixBase< ConfigOut_t > &qout) const
	Generate a configuration vector uniformly sampled among provided limits. More...

template<class ConfigL_t , class ConfigR_t , class Tangent_t >
void	difference (const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1, const Eigen::MatrixBase< Tangent_t > &v) const
	Computes the tangent vector that must be integrated during one unit time to go from q0 to q1. More...

template<class ConfigL_t , class ConfigR_t , class JacobianLOut_t , class JacobianROut_t >
void	Jdifference (const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1, const Eigen::MatrixBase< JacobianLOut_t > &J0, const Eigen::MatrixBase< JacobianROut_t > &J1) const
	Computes the Jacobian of the difference operation. More...

template<class ConfigL_t , class ConfigR_t >
Scalar	squaredDistance (const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1) const
	Squared distance between two joint configurations. More...

template<class ConfigL_t , class ConfigR_t >
Scalar	distance (const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1) const
	Distance between two configurations of the joint. More...

template<class ConfigL_t , class ConfigR_t >
bool	isSameConfiguration (const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1, const Scalar &prec=Eigen::NumTraits< Scalar >::dummy_precision()) const
	Check if two configurations are equivalent within the given precision. More...

API that allocates memory
template<class Config_t , class Tangent_t >
ConfigVector_t	integrate (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Tangent_t > &v) const

template<class ConfigL_t , class ConfigR_t >
ConfigVector_t	interpolate (const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1, const Scalar &u) const

ConfigVector_t	random () const

template<class ConfigL_t , class ConfigR_t >
ConfigVector_t	randomConfiguration (const Eigen::MatrixBase< ConfigL_t > &lower_pos_limit, const Eigen::MatrixBase< ConfigR_t > &upper_pos_limit) const

template<class ConfigL_t , class ConfigR_t >
TangentVector_t	difference (const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1) const

Default implementations
template<class ConfigL_t , class ConfigR_t , class ConfigOut_t >
void	interpolate_impl (const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1, const Scalar &u, const Eigen::MatrixBase< ConfigOut_t > &qout) const

template<class Config_t >
void	normalize_impl (const Eigen::MatrixBase< Config_t > &qout) const

template<class ConfigL_t , class ConfigR_t >
Scalar	squaredDistance_impl (const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1) const

template<class ConfigL_t , class ConfigR_t >
bool	isSameConfiguration_impl (const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1, const Scalar &prec) const

Index	nq () const

Index	nv () const
	Get dimension of Lie Group tangent space.

ConfigVector_t	neutral () const
	Get neutral element as a vector.

std::string	name () const
	Get name of instance.

Derived &	derived ()

const Derived &	derived () const

Protected Member Functions
	LieGroupBase ()

	LieGroupBase (const LieGroupBase &)

Detailed Description

template<typename Derived>
struct se3::LieGroupBase< Derived >

Definition at line 49 of file operation-base.hpp.

Constructor & Destructor Documentation

LieGroupBase ( )

inlineprotected

Default constructor.

Prevent the construction of derived class.

Definition at line 292 of file operation-base.hpp.

LieGroupBase ( const LieGroupBase< Derived > & )

inlineprotected

Copy constructor

Prevent the copy of derived class.

Definition at line 297 of file operation-base.hpp.

Member Function Documentation

void difference	(	const Eigen::MatrixBase< ConfigL_t > &	q0,
		const Eigen::MatrixBase< ConfigR_t > &	q1,
		const Eigen::MatrixBase< Tangent_t > &	v
	)		const

Computes the tangent vector that must be integrated during one unit time to go from q0 to q1.

Parameters

[in]	q0	the initial configuration vector.
[in]	q1	the terminal configuration vector.
[out]	v	the corresponding velocity.

Definition at line 130 of file operation-base.hxx.

Referenced by LieGroupBase< Derived >::isSameConfiguration().

void dIntegrate_dq	(	const Eigen::MatrixBase< Config_t > &	q,
		const Eigen::MatrixBase< Tangent_t > &	v,
		const Eigen::MatrixBase< JacobianOut_t > &	J
	)		const

Computes the Jacobian of the Integrate operation.

Parameters

[in]	q	configuration
[in]	v	tangent velocity.
[out]	J	the Jacobian of the Integrate operation wrt q.

Definition at line 42 of file operation-base.hxx.

void dIntegrate_dv	(	const Eigen::MatrixBase< Config_t > &	q,
		const Eigen::MatrixBase< Tangent_t > &	v,
		const Eigen::MatrixBase< JacobianOut_t > &	J
	)		const

Computes the Jacobian of the Integrate operation.

Parameters

[in]	q	configuration
[in]	v	tangent velocity.
[out]	J	the Jacobian of the Integrate operation wrt v.

Definition at line 55 of file operation-base.hxx.

LieGroupBase< Derived >::Scalar distance	(	const Eigen::MatrixBase< ConfigL_t > &	q0,
		const Eigen::MatrixBase< ConfigR_t > &	q1
	)		const

Distance between two configurations of the joint.

Parameters

[in]	q0	the initial configuration vector.
[in]	q1	the terminal configuration vector.

Returns: The corresponding distance.

Definition at line 171 of file operation-base.hxx.

References se3::squaredDistance().

void integrate	(	const Eigen::MatrixBase< ConfigIn_t > &	q,
		const Eigen::MatrixBase< Tangent_t > &	v,
		const Eigen::MatrixBase< ConfigOut_t > &	qout
	)		const

Integrate a joint's configuration with a tangent vector during one unit time duration.

Parameters

[in]	q	the initial configuration.
[in]	v	the tangent velocity.
[out]	qout	the configuration integrated.

Definition at line 29 of file operation-base.hxx.

Referenced by LieGroupBase< Derived >::isSameConfiguration().

void interpolate	(	const Eigen::MatrixBase< ConfigL_t > &	q0,
		const Eigen::MatrixBase< ConfigR_t > &	q1,
		const Scalar &	u,
		const Eigen::MatrixBase< ConfigOut_t > &	qout
	)		const

Interpolation between two joint's configurations.

Parameters

[in]	q0	the initial configuration to interpolate.
[in]	q1	the final configuration to interpolate.
[in]	u	in [0;1] the absicca along the interpolation.
[out]	qout	the interpolated configuration (q0 if u = 0, q1 if u = 1)
[in]	q0	Initial configuration to interpolate
[in]	q1	Final configuration to interpolate
[in]	u	u in [0;1] position along the interpolation.

Returns: The interpolated configuration (q0 if u = 0, q1 if u = 1)

Definition at line 77 of file operation-base.hxx.

References LieGroupBase< Derived >::normalize().

Referenced by LieGroupBase< Derived >::isSameConfiguration().

bool isSameConfiguration	(	const Eigen::MatrixBase< ConfigL_t > &	q0,
		const Eigen::MatrixBase< ConfigR_t > &	q1,
		const Scalar &	prec = `Eigen::NumTraits<Scalar>::dummy_precision()`
	)		const

Check if two configurations are equivalent within the given precision.

Parameters

[in]	q0	Configuration 0
[in]	q1	Configuration 1

Definition at line 180 of file operation-base.hxx.

References se3::difference(), LieGroupBase< Derived >::difference(), se3::integrate(), LieGroupBase< Derived >::integrate(), se3::interpolate(), LieGroupBase< Derived >::interpolate(), se3::randomConfiguration(), and LieGroupBase< Derived >::randomConfiguration().

void Jdifference	(	const Eigen::MatrixBase< ConfigL_t > &	q0,
		const Eigen::MatrixBase< ConfigR_t > &	q1,
		const Eigen::MatrixBase< JacobianLOut_t > &	J0,
		const Eigen::MatrixBase< JacobianROut_t > &	J1
	)		const

Computes the Jacobian of the difference operation.

Parameters

[in]	q0	the initial configuration vector.
[in]	q1	the terminal configuration vector.
[out]	J0	the Jacobian of the difference operation with respect to q0.
[out]	J1	the Jacobian of the difference operation with respect to q1.

Definition at line 143 of file operation-base.hxx.

void normalize ( const Eigen::MatrixBase< Config_t > & qout ) const

Normalize the joint configuration given as input. For instance, the quaternion must be unitary.

Parameters

[out] qout the normalized joint configuration.

Definition at line 92 of file operation-base.hxx.

Referenced by LieGroupBase< Derived >::interpolate().

LieGroupBase< Derived >::Index nq ( ) const

Get dimension of Lie Group vector representation

For instance, for SO(3), the dimension of the vector representation is 4 (quaternion) while the dimension of the tangent space is 3.

Definition at line 290 of file operation-base.hxx.

References LieGroupBase< Derived >::nq().

Referenced by LieGroupBase< Derived >::nq().

void random ( const Eigen::MatrixBase< Config_t > & qout ) const

Generate a random joint configuration, normalizing quaternions when necessary.

Warning: Do not take into account the joint limits. To shoot a configuration uniformingly depending on joint limits, see randomConfiguration.

Parameters

[out] qout the random joint configuration.

Warning: Do not take into account the joint limits. To shoot a configuration uniformingly depending on joint limits, see randomConfiguration

Returns: The joint configuration

Definition at line 109 of file operation-base.hxx.

void randomConfiguration	(	const Eigen::MatrixBase< ConfigL_t > &	lower_pos_limit,
		const Eigen::MatrixBase< ConfigR_t > &	upper_pos_limit,
		const Eigen::MatrixBase< ConfigOut_t > &	qout
	)		const

Generate a configuration vector uniformly sampled among provided limits.

Parameters

[in]	lower_pos_limit	the lower joint limit vector.
[in]	upper_pos_limit	the upper joint limit vector.
[out]	qout	the random joint configuration in the two bounds.

Definition at line 117 of file operation-base.hxx.

Referenced by LieGroupBase< Derived >::isSameConfiguration().

LieGroupBase< Derived >::Scalar squaredDistance	(	const Eigen::MatrixBase< ConfigL_t > &	q0,
		const Eigen::MatrixBase< ConfigR_t > &	q1
	)		const

Squared distance between two joint configurations.

Parameters

[in]	q0	the initial configuration vector.
[in]	q1	the terminal configuration vector.
[out]	d	the corresponding distance betwenn q0 and q1.

Definition at line 159 of file operation-base.hxx.

The documentation for this struct was generated from the following files:

Public Types

Public Member Functions

Protected Member Functions

Detailed Description

template<typename Derived> struct se3::LieGroupBase< Derived >

Constructor & Destructor Documentation

Member Function Documentation

template<typename Derived>
struct se3::LieGroupBase< Derived >