Lie group

Classes
class	hpp::pinocchio::LiegroupElementConstBase< vector_type >
class	hpp::pinocchio::LiegroupElementBase< vector_type >
class	hpp::pinocchio::LiegroupSpace

Typedefs
typedef ABoostVariant	hpp::pinocchio::LiegroupType

Enumerations
enum	hpp::pinocchio::DerivativeProduct { hpp::pinocchio::DerivativeTimesInput , hpp::pinocchio::InputTimesDerivative }

Functions
template<typename vector_type >
LiegroupElement	hpp::pinocchio::operator+ (const LiegroupElementConstBase< vector_type > &e, vectorIn_t v)
template<typename vector_type1 , typename vector_type2 >
vector_t	hpp::pinocchio::operator- (const LiegroupElementConstBase< vector_type1 > &e1, const LiegroupElementConstBase< vector_type2 > &e2)
template<typename vector_type >
bool	hpp::pinocchio::checkNormalized (const LiegroupElementConstBase< vector_type > &e1, const value_type &eps=PINOCCHIO_DEFAULT_QUATERNION_NORM_TOLERANCE_VALUE)
std::ostream &	hpp::pinocchio::operator<< (std::ostream &os, const LiegroupSpace &space)
	Writing in a stream. More...
hpp::pinocchio::LiegroupSpacePtr_t	std::operator* (const hpp::pinocchio::LiegroupSpaceConstPtr_t &sp1, const hpp::pinocchio::LiegroupSpaceConstPtr_t &sp2)
	Cartesian product between Lie groups. More...
hpp::pinocchio::LiegroupSpacePtr_t	std::operator^ (const hpp::pinocchio::LiegroupSpaceConstPtr_t &sp, hpp::pinocchio::size_type n)
	Cartesian power by an integer. More...

Detailed Description

Configurations of robots, as well as some values like the position of a robot joint with respect to a fixed frame belong to differential manifolds that have the structure of Lie groups. These manifolds are the cartesian products of the following elementary Lie groups

• \(\mathbf{R}^n\),
• \(SO(2)\) the group of rotations in the plane represented by a vector of dimension 2 \((\cos \theta, \sin \theta)\) for a rotation of angle \(\theta\),
• \(SO(3)\)the group of rotations in the 3d space represented by a quaternion \(Xi + Yj + Zk + W\) (ie a vector of dimension 4),
• \(SE(2)\) the group of rigid-body motions in the plane, represented by a vector of dimention 4 \((x,y,\cos\theta,\sin\theta)\),
• \(SE(3)\), the group of rigid-body motion in 3d space, represented by a vector of dimension 7 \((x,y,z,X,Y,Z,W)\).

Typedef Documentation

LiegroupType

typedef ABoostVariant hpp::pinocchio::LiegroupType

Elementary Lie groups A boost variant with the following classes:

• \(\mathbf{R}^n\), where \(n\) is either 1, 2, 3 or dynamic,
• \(\mathbf{R}^n \times SO(n) \), where \(n\) is either 2 or 3,
• \(SO(n) \), where \(n\) is either 2 or 3,
• \(SE(n) \), where \(n\) is either 2 or 3.

  See also

  hpp::pinocchio::liegroup::VectorSpaceOperation, hpp::pinocchio::liegroup::CartesianProductOperation, hpp::pinocchio::liegroup::SpecialOrthogonalOperation, hpp::pinocchio::liegroup::SpecialEuclideanOperation,

Enumeration Type Documentation

DerivativeProduct

enum hpp::pinocchio::DerivativeProduct

Enumerator
DerivativeTimesInput
InputTimesDerivative

Function Documentation

checkNormalized()

template<typename vector_type >

bool hpp::pinocchio::checkNormalized	(	const LiegroupElementConstBase< vector_type > &	e1,
		const value_type &	eps = PINOCCHIO_DEFAULT_QUATERNION_NORM_TOLERANCE_VALUE
	)

Check if a configuration is normalized

Parameters

e1	configuration to be checked
eps	the error threshold

Returns

whether the configuration is normalized

operator*()

hpp::pinocchio::LiegroupSpacePtr_t std::operator*	(	const hpp::pinocchio::LiegroupSpaceConstPtr_t &	sp1,
		const hpp::pinocchio::LiegroupSpaceConstPtr_t &	sp2
	)

Cartesian product between Lie groups.

operator+()

template<typename vector_type >

LiegroupElement hpp::pinocchio::operator+	(	const LiegroupElementConstBase< vector_type > &	e,
		vectorIn_t	v
	)

Integration of a velocity vector from a configuration

Parameters

e	element of the Lie group,
v	element of the tangent space of the Lie group.

Returns

the element of the Lie group resulting from the integration

By extension of the vector space case, we represent the integration of a constant velocity during unit time by an addition

operator-()

template<typename vector_type1 , typename vector_type2 >

vector_t hpp::pinocchio::operator-	(	const LiegroupElementConstBase< vector_type1 > &	e1,
		const LiegroupElementConstBase< vector_type2 > &	e2
	)

Difference between two configurations

Parameters

e1,e2

elements of the Lie group,

Returns

the velocity that integrated from e2 yields e1

By extension of the vector space case, we represent the integration of a constant velocity during unit time by an addition

operator<<()

std::ostream& hpp::pinocchio::operator<< ( std::ostream &  os, const LiegroupSpace &  space  )

inline

Writing in a stream.

operator^()

hpp::pinocchio::LiegroupSpacePtr_t std::operator^	(	const hpp::pinocchio::LiegroupSpaceConstPtr_t &	sp,
		hpp::pinocchio::size_type	n
	)

Cartesian power by an integer.