LieGroupBase< Derived > Struct Template Reference

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, AssignmentOperatorType op=SETTO) 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 AssignmentOperatorType op=SETTO) 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 AssignmentOperatorType op=SETTO) 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 JacobianIn_t , class JacobianOut_t >
void	dIntegrate_dq (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Tangent_t > &v, const Eigen::MatrixBase< JacobianIn_t > &Jin, int self, const Eigen::MatrixBase< JacobianOut_t > &Jout, const AssignmentOperatorType op=SETTO) const
template<class Config_t , class Tangent_t , class JacobianIn_t , class JacobianOut_t >
void	dIntegrate_dq (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Tangent_t > &v, int self, const Eigen::MatrixBase< JacobianIn_t > &Jin, const Eigen::MatrixBase< JacobianOut_t > &Jout, const AssignmentOperatorType op=SETTO) const
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 AssignmentOperatorType op=SETTO) const
	Computes the Jacobian of a small variation of the tangent vector into tangent space at identity. More...
template<class Config_t , class Tangent_t , class JacobianIn_t , class JacobianOut_t >
void	dIntegrate_dv (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Tangent_t > &v, int self, const Eigen::MatrixBase< JacobianIn_t > &Jin, const Eigen::MatrixBase< JacobianOut_t > &Jout, const AssignmentOperatorType op=SETTO) const
template<class Config_t , class Tangent_t , class JacobianIn_t , class JacobianOut_t >
void	dIntegrate_dv (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Tangent_t > &v, const Eigen::MatrixBase< JacobianIn_t > &Jin, int self, const Eigen::MatrixBase< JacobianOut_t > &Jout, const AssignmentOperatorType op=SETTO) const
template<class Config_t , class Tangent_t , class JacobianIn_t , class JacobianOut_t >
void	dIntegrateTransport (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Tangent_t > &v, const Eigen::MatrixBase< JacobianIn_t > &Jin, const Eigen::MatrixBase< JacobianOut_t > &Jout, const ArgumentPosition arg) const
	Transport a matrix from the terminal to the initial tangent space of the integrate operation, with respect to the configuration or the velocity arguments. More...
template<class Config_t , class Tangent_t , class JacobianIn_t , class JacobianOut_t >
void	dIntegrateTransport_dq (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Tangent_t > &v, const Eigen::MatrixBase< JacobianIn_t > &Jin, const Eigen::MatrixBase< JacobianOut_t > &Jout) const
	Transport a matrix from the terminal to the initial tangent space of the integrate operation, with respect to the configuration argument. More...
template<class Config_t , class Tangent_t , class JacobianIn_t , class JacobianOut_t >
void	dIntegrateTransport_dv (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Tangent_t > &v, const Eigen::MatrixBase< JacobianIn_t > &Jin, const Eigen::MatrixBase< JacobianOut_t > &Jout) const
	Transport a matrix from the terminal to the initial tangent space of the integrate operation, with respect to the velocity argument. More...
template<class Config_t , class Tangent_t , class Jacobian_t >
void	dIntegrateTransport (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Tangent_t > &v, const Eigen::MatrixBase< Jacobian_t > &J, const ArgumentPosition arg) const
	Transport in place a matrix from the terminal to the initial tangent space of the integrate operation, with respect to the configuration or the velocity arguments. More...
template<class Config_t , class Tangent_t , class Jacobian_t >
void	dIntegrateTransport_dq (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Tangent_t > &v, const Eigen::MatrixBase< Jacobian_t > &J) const
	Transport in place a matrix from the terminal to the initial tangent space of the integrate operation, with respect to the configuration argument. More...
template<class Config_t , class Tangent_t , class Jacobian_t >
void	dIntegrateTransport_dv (const Eigen::MatrixBase< Config_t > &q, const Eigen::MatrixBase< Tangent_t > &v, const Eigen::MatrixBase< Jacobian_t > &J) const
	Transport in place a matrix from the terminal to the initial tangent space of the integrate operation, with respect to the velocity argument. 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 >
bool	isNormalized (const Eigen::MatrixBase< Config_t > &qin, const Scalar &prec=Eigen::NumTraits< Scalar >::dummy_precision()) const
	Check whether the input joint configuration is normalized. 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<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 , class JacobianOut_t >
void	dDifference (const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1, const Eigen::MatrixBase< JacobianOut_t > &J, const ArgumentPosition arg) const
	Computes the Jacobian of the difference operation with respect to q0 or q1. More...
template<ArgumentPosition arg, class ConfigL_t , class ConfigR_t , class JacobianIn_t , class JacobianOut_t >
void	dDifference (const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1, const Eigen::MatrixBase< JacobianIn_t > &Jin, int self, const Eigen::MatrixBase< JacobianOut_t > &Jout, const AssignmentOperatorType op=SETTO) const
template<ArgumentPosition arg, class ConfigL_t , class ConfigR_t , class JacobianIn_t , class JacobianOut_t >
void	dDifference (const Eigen::MatrixBase< ConfigL_t > &q0, const Eigen::MatrixBase< ConfigR_t > &q1, int self, const Eigen::MatrixBase< JacobianIn_t > &Jin, const Eigen::MatrixBase< JacobianOut_t > &Jout, const AssignmentOperatorType op=SETTO) const
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...
bool	operator== (const LieGroupBase &other) const
bool	operator!= (const LieGroupBase &other) const
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 Config_t , class Tangent_t , class JacobianIn_t , class JacobianOut_t >
void	dIntegrate_product_impl (const Config_t &q, const Tangent_t &v, const JacobianIn_t &Jin, JacobianOut_t &Jout, bool dIntegrateOnTheLeft, const ArgumentPosition arg, const AssignmentOperatorType op) const
template<ArgumentPosition arg, class ConfigL_t , class ConfigR_t , class JacobianIn_t , class JacobianOut_t >
void	dDifference_product_impl (const ConfigL_t &q0, const ConfigR_t &q1, const JacobianIn_t &Jin, JacobianOut_t &Jout, bool dDifferenceOnTheLeft, const AssignmentOperatorType op) const
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 Config_t >
bool	isNormalized_impl (const Eigen::MatrixBase< Config_t > &qin, const Scalar &prec=Eigen::NumTraits< Scalar >::dummy_precision()) 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
bool	isEqual_impl (const LieGroupBase &) const
	Default equality check. By default, two LieGroupBase of same type are considered equal.
bool	isDifferent_impl (const LieGroupBase &other) 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 &)
LieGroupBase &	operator= (const LieGroupBase &)

Detailed Description

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

Definition at line 44 of file liegroup-base.hpp.

Constructor & Destructor Documentation

LieGroupBase() [1/2]

LieGroupBase ( )

inlineprotected

Default constructor.

Prevent the construction of derived class.

Definition at line 722 of file liegroup-base.hpp.

LieGroupBase() [2/2]

LieGroupBase ( const LieGroupBase< Derived > &  )

inlineprotected

Copy constructor

Prevent the copy of derived class.

Definition at line 729 of file liegroup-base.hpp.

Member Function Documentation

dDifference() [1/2]

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.

Template Parameters

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

Parameters

[in]	q0	the initial configuration vector.
[in]	q1	the terminal configuration vector.
[out]	J	the Jacobian of the difference operation.

Warning

because \( q_1 \ominus q_0 = - \left( q_0 \ominus q_1 \right) \), you may be tempted to write \( \frac{\partial\ominus}{\partial q_1} = - \frac{\partial\ominus}{\partial q_0} \). This is false in the general case because \( \frac{\partial\ominus}{\partial q_i} \) expects an input velocity relative to frame i. See SpecialEuclideanOperationTpl<3,_Scalar,_Options>::dDifference_impl.

Remarkable identity:

\( \frac{\partial\ominus}{\partial q_1} \frac{\partial\oplus}{\partial v} = I \)

dDifference() [2/2]

void dDifference	(	const Eigen::MatrixBase< ConfigL_t > &	q0,
		const Eigen::MatrixBase< ConfigR_t > &	q1,
		const Eigen::MatrixBase< JacobianOut_t > &	J,
		const ArgumentPosition	arg
	)		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.
[in]	arg	ARG0 (resp. ARG1) to get the Jacobian with respect to q0 (resp. q1).
[out]	J	the Jacobian of the difference operation.

difference()

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.

Note

Both inputs must be well-formed configuration vectors. The output of this function is unspecified if inputs contain NaNs or extremal values for the underlying scalar type.

Remarkable identity:

\( q_1 \ominus q_0 = - \left( q_0 \ominus q_1 \right) \)

dIntegrate() [1/2]

void dIntegrate ( const Eigen::MatrixBase< Config_t > &  q, const Eigen::MatrixBase< Tangent_t > &  v, const Eigen::MatrixBase< JacobianOut_t > &  J, AssignmentOperatorType  op = SETTO  ) 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.
[in]	op	assignment operator (SETTO, ADDTO or RMTO).

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 112 of file liegroup-base.hpp.

dIntegrate() [2/2]

void dIntegrate	(	const Eigen::MatrixBase< Config_t > &	q,
		const Eigen::MatrixBase< Tangent_t > &	v,
		const Eigen::MatrixBase< JacobianOut_t > &	J,
		const ArgumentPosition	arg,
		const AssignmentOperatorType	op = SETTO
	)		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).
[in]	op	assignment operator (SETTO, ADDTO and RMTO).
[out]	J	the Jacobian of the Integrate operation w.r.t. the argument arg.

dIntegrate_dq()

void dIntegrate_dq	(	const Eigen::MatrixBase< Config_t > &	q,
		const Eigen::MatrixBase< Tangent_t > &	v,
		const Eigen::MatrixBase< JacobianOut_t > &	J,
		const AssignmentOperatorType	op = SETTO
	)		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.
[in]	op	assignment operator (SETTO, ADDTO or RMTO).
[out]	J	the Jacobian of the Integrate operation w.r.t. the configuration vector q.

dIntegrate_dv()

void dIntegrate_dv	(	const Eigen::MatrixBase< Config_t > &	q,
		const Eigen::MatrixBase< Tangent_t > &	v,
		const Eigen::MatrixBase< JacobianOut_t > &	J,
		const AssignmentOperatorType	op = SETTO
	)		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.
[in]	op	assignment operator (SETTO, ADDTO or RMTO).
[out]	J	the Jacobian of the Integrate operation w.r.t. the tangent vector v.

dIntegrateTransport() [1/2]

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

Transport in place a matrix from the terminal to the initial tangent space of the integrate operation, with respect to the configuration or the velocity arguments.

This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \( q \oplus v \), to the tangent space at \( q \). In other words, this functions transforms a tangent vector expressed at \( q \oplus v \) to a tangent vector expressed at \( q \), considering that the change of configuration between \( q \oplus v \) and \( q \) may alter the value of this tangent vector. A typical example of parallel transportation is the action operated by a rigid transformation \( M \in \text{SE}(3)\) on a spatial velocity \( v \in \text{se}(3)\). In the context of configuration spaces assimilated to vector spaces, this operation corresponds to Identity. For Lie groups, its corresponds to the canonical vector field transportation.

Parameters

[in]	q	configuration vector.
[in]	v	tangent vector
[in,out]	J	the inplace matrix
[in]	arg	argument with respect to which the differentiation is performed (ARG0 corresponding to q, and ARG1 to v)

dIntegrateTransport() [2/2]

void dIntegrateTransport	(	const Eigen::MatrixBase< Config_t > &	q,
		const Eigen::MatrixBase< Tangent_t > &	v,
		const Eigen::MatrixBase< JacobianIn_t > &	Jin,
		const Eigen::MatrixBase< JacobianOut_t > &	Jout,
		const ArgumentPosition	arg
	)		const

Transport a matrix from the terminal to the initial tangent space of the integrate operation, with respect to the configuration or the velocity arguments.

This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \( q \oplus v \), to the tangent space at \( q \). In other words, this functions transforms a tangent vector expressed at \( q \oplus v \) to a tangent vector expressed at \( q \), considering that the change of configuration between \( q \oplus v \) and \( q \) may alter the value of this tangent vector. A typical example of parallel transportation is the action operated by a rigid transformation \( M \in \text{SE}(3)\) on a spatial velocity \( v \in \text{se}(3)\). In the context of configuration spaces assimilated to vector spaces, this operation corresponds to Identity. For Lie groups, its corresponds to the canonical vector field transportation.

Parameters

[in]	q	configuration vector.
[in]	v	tangent vector
[in]	Jin	the input matrix
[in]	arg	argument with respect to which the differentiation is performed (ARG0 corresponding to q, and ARG1 to v)
[out]	Jout	Transported matrix

dIntegrateTransport_dq() [1/2]

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

Transport in place a matrix from the terminal to the initial tangent space of the integrate operation, with respect to the configuration argument.

This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \( q \oplus v \), to the tangent space at \( q \). In other words, this functions transforms a tangent vector expressed at \( q \oplus v \) to a tangent vector expressed at \( q \), considering that the change of configuration between \( q \oplus v \) and \( q \) may alter the value of this tangent vector. A typical example of parallel transportation is the action operated by a rigid transformation \( M \in \text{SE}(3)\) on a spatial velocity \( v \in \text{se}(3)\). In the context of configuration spaces assimilated to vector spaces, this operation corresponds to Identity. For Lie groups, its corresponds to the canonical vector field transportation.

Parameters

[in]	q	configuration vector.
[in]	v	tangent vector
[in,out]	Jin	the inplace matrix

dIntegrateTransport_dq() [2/2]

void dIntegrateTransport_dq	(	const Eigen::MatrixBase< Config_t > &	q,
		const Eigen::MatrixBase< Tangent_t > &	v,
		const Eigen::MatrixBase< JacobianIn_t > &	Jin,
		const Eigen::MatrixBase< JacobianOut_t > &	Jout
	)		const

Transport a matrix from the terminal to the initial tangent space of the integrate operation, with respect to the configuration argument.

This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \( q \oplus v \), to the tangent space at \( q \). In other words, this functions transforms a tangent vector expressed at \( q \oplus v \) to a tangent vector expressed at \( q \), considering that the change of configuration between \( q \oplus v \) and \( q \) may alter the value of this tangent vector. A typical example of parallel transportation is the action operated by a rigid transformation \( M \in \text{SE}(3)\) on a spatial velocity \( v \in \text{se}(3)\). In the context of configuration spaces assimilated to vector spaces, this operation corresponds to Identity. For Lie groups, its corresponds to the canonical vector field transportation.

Parameters

[in]	q	configuration vector.
[in]	v	tangent vector
[in]	Jin	the input matrix
[out]	Jout	Transported matrix

dIntegrateTransport_dv() [1/2]

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

Transport in place a matrix from the terminal to the initial tangent space of the integrate operation, with respect to the velocity argument.

This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \( q \oplus v \), to the tangent space at \( q \). In other words, this functions transforms a tangent vector expressed at \( q \oplus v \) to a tangent vector expressed at \( q \), considering that the change of configuration between \( q \oplus v \) and \( q \) may alter the value of this tangent vector. A typical example of parallel transportation is the action operated by a rigid transformation \( M \in \text{SE}(3)\) on a spatial velocity \( v \in \text{se}(3)\). In the context of configuration spaces assimilated to vector spaces, this operation corresponds to Identity. For Lie groups, its corresponds to the canonical vector field transportation.

Parameters

[in]	q	configuration vector.
[in]	v	tangent vector
[in,out]	J	the inplace matrix

dIntegrateTransport_dv() [2/2]

void dIntegrateTransport_dv	(	const Eigen::MatrixBase< Config_t > &	q,
		const Eigen::MatrixBase< Tangent_t > &	v,
		const Eigen::MatrixBase< JacobianIn_t > &	Jin,
		const Eigen::MatrixBase< JacobianOut_t > &	Jout
	)		const

Transport a matrix from the terminal to the initial tangent space of the integrate operation, with respect to the velocity argument.

This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space of the integrated element \( q \oplus v \), to the tangent space at \( q \). In other words, this functions transforms a tangent vector expressed at \( q \oplus v \) to a tangent vector expressed at \( q \), considering that the change of configuration between \( q \oplus v \) and \( q \) may alter the value of this tangent vector. A typical example of parallel transportation is the action operated by a rigid transformation \( M \in \text{SE}(3)\) on a spatial velocity \( v \in \text{se}(3)\). In the context of configuration spaces assimilated to vector spaces, this operation corresponds to Identity. For Lie groups, its corresponds to the canonical vector field transportation.

Parameters

[in]	q	configuration vector.
[in]	v	tangent vector
[in]	Jin	the input matrix
[out]	Jout	Transported matrix

distance()

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.

integrate()

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.

integrateCoeffWiseJacobian()

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.

interpolate()

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)

isNormalized()

bool isNormalized	(	const Eigen::MatrixBase< Config_t > &	qin,
		const Scalar &	prec = Eigen::NumTraits< Scalar >::dummy_precision()
	)		const

Check whether the input joint configuration is normalized. For instance, the quaternion must be unitary.

Parameters

[in]

qin

The joint configuration to check.

Returns

true if the input vector is normalized, false otherwise.

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

Remarkable identity:

\( q_1 \equiv q_0 \oplus \left( q_1 \ominus q_0 \right) \) ( \(\equiv\) means equivalent, not equal).

normalize()

void normalize

(

const Eigen::MatrixBase< Config_t > &

qout

)

const

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

Note

If the input vector is too small (i.e., qout.norm()==0), then it is left unchanged. It is therefore possible that after this method is called isNormalized(qout) is still false.

Parameters

[in,out]

qout

the normalized joint configuration.

nq()

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.

operator=()

LieGroupBase& operator= ( const LieGroupBase< Derived > &  )

inlineprotected

Copy assignment operator

Prevent the copy of derived class.

Definition at line 736 of file liegroup-base.hpp.

random()

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.

randomConfiguration()

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.

squaredDistance()

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.

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

• include/pinocchio/multibody/liegroup/liegroup-base.hpp