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

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

typedef int	Index

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

typedef Derived	LieGroupDerived

typedef traits< LieGroupDerived >::Scalar	Scalar

typedef Eigen::Matrix< Scalar, NV, 1, Options >	TangentVector_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 Jacobian_t >
void	integrateCoeffWiseJacobian (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Jacobian_t > &J) const
	Computes the Jacobian of the integrate operator around zero. More...

template<ArgumentPosition arg, class Config_t , class Tangent_t , class JacobianOut_t >
void	dIntegrate (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Tangent_t > &v, const Eigen::MatrixBase< JacobianOut_t > &J) const
	Computes the Jacobian of a small variation of the configuration vector or the tangent vector into tangent space at identity. More...

template<class Config_t , class Tangent_t , class JacobianOut_t >
void	dIntegrate (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Tangent_t > &v, const Eigen::MatrixBase< JacobianOut_t > &J, const ArgumentPosition arg) const
	Computes the Jacobian of a small variation of the configuration vector or the tangent vector into tangent space at identity. 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 a small variation of the configuration vector into tangent space at identity. 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 a small variation of the tangent vector into tangent space at identity. 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 PINOCCHIO_DEPRECATED

template<ArgumentPosition arg, class ConfigL_t , class ConfigR_t , class JacobianOut_t >
void	dDifference (const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1, const Eigen::MatrixBase< JacobianOut_t > &J) const
	Computes the Jacobian of the difference operation with respect to q0 or q1. 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 pinocchio::LieGroupBase< Derived >

Definition at line 35 of file liegroup-base.hpp.

Constructor & Destructor Documentation

LieGroupBase ( )

inlineprotected

Default constructor.

Prevent the construction of derived class.

Definition at line 347 of file liegroup-base.hpp.

LieGroupBase ( const LieGroupBase< Derived > & )

inlineprotected

Copy constructor

Prevent the copy of derived class.

Definition at line 352 of file liegroup-base.hpp.

Member Function Documentation

void dDifference	(	const Eigen::MatrixBase< ConfigL_t > &	q0,
		const Eigen::MatrixBase< ConfigR_t > &	q1,
		const Eigen::MatrixBase< JacobianOut_t > &	J
	)		const

Computes the Jacobian of the difference operation with respect to q0 or q1.

Parameters

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

Template Parameters

arg	ARG0 (resp. ARG1) to get the Jacobian with respect to q0 (resp. q1).

Parameters

[out] J the Jacobian of the difference operation.

Referenced by LieGroupBase< CartesianProductOperation< LieGroup1, LieGroup2 > >::dIntegrate().

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.

Referenced by LieGroupBase< CartesianProductOperation< LieGroup1, LieGroup2 > >::dIntegrate().

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

inline

Computes the Jacobian of a small variation of the configuration vector or the tangent vector into tangent space at identity.

This Jacobian corresponds to the Jacobian of \( (\mathbf{q} \oplus \delta \mathbf{q}) \oplus \mathbf{v} \) with \( \delta \mathbf{q} \rightarrow 0 \) if arg == ARG0 or \( \delta \mathbf{v} \rightarrow 0 \) if arg == ARG1.

Parameters

[in]	q	configuration vector.
[in]	v	tangent vector.

Template Parameters

arg	ARG0 (resp. ARG1) to get the Jacobian with respect to q (resp. v).

Parameters

[out] J the Jacobian of the Integrate operation w.r.t. the argument arg.

Definition at line 96 of file liegroup-base.hpp.

Referenced by LieGroupBase< CartesianProductOperation< LieGroup1, LieGroup2 > >::dIntegrate().

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

Computes the Jacobian of a small variation of the configuration vector or the tangent vector into tangent space at identity.

This Jacobian corresponds to the Jacobian of \( (\mathbf{q} \oplus \delta \mathbf{q}) \oplus \mathbf{v} \) with \( \delta \mathbf{q} \rightarrow 0 \) if arg == ARG0 or \( \delta \mathbf{v} \rightarrow 0 \) if arg == ARG1.

Parameters

[in]	q	configuration vector.
[in]	v	tangent vector.
[in]	arg	ARG0 (resp. ARG1) to get the Jacobian with respect to q (resp. v).
[out]	J	the Jacobian of the Integrate operation w.r.t. the argument arg.

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 a small variation of the configuration vector into tangent space at identity.

This Jacobian corresponds to the Jacobian of \( (\mathbf{q} \oplus \delta \mathbf{q}) \oplus \mathbf{v} \) with \( \delta \mathbf{q} \rightarrow 0 \).

Parameters

[in]	q	configuration vector.
[in]	v	tangent vector.
[out]	J	the Jacobian of the Integrate operation w.r.t. the configuration vector q.

Referenced by LieGroupBase< CartesianProductOperation< LieGroup1, LieGroup2 > >::dIntegrate().

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 a small variation of the tangent vector into tangent space at identity.

This Jacobian corresponds to the Jacobian of \( \mathbf{q} \oplus (\mathbf{v} + \delta \mathbf{v}) \) with \( \delta \mathbf{v} \rightarrow 0 \).

Parameters

[in]	q	configuration vector.
[in]	v	tangent vector.
[out]	J	the Jacobian of the Integrate operation w.r.t. the tangent vector v.

Referenced by LieGroupBase< CartesianProductOperation< LieGroup1, LieGroup2 > >::dIntegrate().

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.

Referenced by LieGroupBase< CartesianProductOperation< LieGroup1, LieGroup2 > >::dIntegrate().

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.

Referenced by LieGroupBase< CartesianProductOperation< LieGroup1, LieGroup2 > >::dIntegrate().

void integrateCoeffWiseJacobian	(	const Eigen::MatrixBase< Config_t > &	q,
		const Eigen::MatrixBase< Jacobian_t > &	J
	)		const

Computes the Jacobian of the integrate operator around zero.

This function computes the Jacobian of the configuration vector variation (component-vise) with respect to a small variation in the tangent.

Parameters

[in]	q	configuration vector.
[out]	J	the Jacobian of the log of the Integrate operation w.r.t. the configuration vector q.

Remarks: This function might be useful for instance when using google-ceres to compute the Jacobian of the integrate operation.

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)

Referenced by LieGroupBase< CartesianProductOperation< LieGroup1, LieGroup2 > >::dIntegrate().

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

Referenced by LieGroupBase< CartesianProductOperation< LieGroup1, LieGroup2 > >::dIntegrate().

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.

Referenced by LieGroupBase< CartesianProductOperation< LieGroup1, LieGroup2 > >::dIntegrate().

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.

Referenced by LieGroupBase< CartesianProductOperation< LieGroup1, LieGroup2 > >::dIntegrate().

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.

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.

Referenced by LieGroupBase< CartesianProductOperation< LieGroup1, LieGroup2 > >::dIntegrate().

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.

Referenced by LieGroupBase< CartesianProductOperation< LieGroup1, LieGroup2 > >::dIntegrate().

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

liegroup-base.hpp

Public Types

Public Member Functions

Protected Member Functions

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

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