#include <manifold.h>

Collaboration diagram for gcop::Manifold< T, _n >:

Public Types
typedef Matrix< double, _n, 1 >	Vectornd
typedef Matrix< double, _n, _n >	Matrixnd
Public Member Functions
	Manifold (int n=_n)
virtual void	Lift (Vectornd &v, const T &xa, const T &xb)=0
virtual void	Retract (T &xb, const T &xa, const Vectornd &v)=0
virtual void	dtau (Matrixnd &M, const Vectornd &v)
virtual void	Adtau (Matrixnd &M, const Vectornd &v)
Public Attributes
int	n
	dimension
bool	bnd
	is the space bounded (false by default). Bounds are defined below: these "box" bounds make sense when there is a natural ordering on the manifold, e.g. of the natural numbers)
T	lb
	lower bound (-inf by default)
T	ub
	upper bound (inf by default)

Detailed Description

template<typename T, int _n = Dynamic>
class gcop::Manifold< T, _n >

Homogeneous manifold

Author: Marin Kobilarov marin(at)jhu.edu

Member Typedef Documentation

template<typename T, int _n = Dynamic>

typedef Matrix<double, _n, _n> gcop::Manifold< T, _n >::Matrixnd

template<typename T, int _n = Dynamic>

typedef Matrix<double, _n, 1> gcop::Manifold< T, _n >::Vectornd

Constructor & Destructor Documentation

template<typename T , int _n>

gcop::Manifold< T, _n >::Manifold ( int n = _n )

Create a manifold of dimension n. For fixed-size use default constructor Manifold<T,n>() For dynamic-size use Manifold<T>(n).

Parameters:

n	manifold dimension

Member Function Documentation

template<typename T, int _n = Dynamic>

virtual void gcop::Manifold< T, _n >::Adtau	(	Matrixnd &	M,
		const Vectornd &	v
	)		`[inline, virtual]`

Adjoint map of the retraction, i.e. Ad((v))

Parameters:

M	resulting matrix operator
v	Lie algebra element

Reimplemented in gcop::Group< 6, 4 >, gcop::Group< 3, 3 >, gcop::Rn< _n >, gcop::Rn< Dynamic >, gcop::Rn< _np >, and gcop::Rn< _nu >.

template<typename T, int _n = Dynamic>

virtual void gcop::Manifold< T, _n >::dtau	(	Matrixnd &	M,
		const Vectornd &	v
	)		`[inline, virtual]`

Right-trivialized derivative of the retraction map dtau(v)

Parameters:

M	matrix operator
v	Lie algebra element

Reimplemented in gcop::Group< 6, 4 >, gcop::Group< 3, 3 >, gcop::Rn< _n >, gcop::Rn< Dynamic >, gcop::Rn< _np >, and gcop::Rn< _nu >.

template<typename T, int _n = Dynamic>

virtual void gcop::Manifold< T, _n >::Lift	(	Vectornd &	v,
		const T &	xa,
		const T &	xb
	)		`[pure virtual]`

Compute a lie algebra element corresponding to a group action between two given states on a manifold. This operation geometrically means that the curve from xa to xb is "lifted" to the tangent space of the manifold to a vector represented by the lie algebra element.

The element can also be regarded as a difference between the two states xa and xb. On a vector space this is v = xb - xa. On homogeneous manifolds v is a Lie algebra element corresponding to an action taking xa to xb.

Parameters:

v	Lie algebra element (regarded as difference between xb and xa)
xa	starting state
xb	ending state

Implemented in gcop::Group< 6, 4 >, gcop::Group< 3, 3 >, gcop::Rn< _n >, gcop::Rn< Dynamic >, gcop::Rn< _np >, gcop::Rn< _nu >, and gcop::MbsCspace.

template<typename T, int _n = Dynamic>

virtual void gcop::Manifold< T, _n >::Retract	(	T &	xb,
		const T &	xa,
		const Vectornd &	v
	)		`[pure virtual]`

Retracts a tangent vector on a manifold at state xa to produce a new state xb. The vector is represented using a Lie algebra element.

The operation can also be regarded as a way to perform addition on manifolds, i.e. to increment a given state xa by v to get a new state xb. On a vector space this is xb = xa + v. On homogeneous manifolds v is a Lie algebra element corresponding to an action taking xa to xb.

Parameters:

xb	ending state
xa	starting state
v	Lie algebra element (regarded as difference between xb and xa)

Implemented in gcop::Group< 6, 4 >, gcop::Group< 3, 3 >, gcop::Rn< _n >, gcop::Rn< Dynamic >, gcop::Rn< _np >, and gcop::Rn< _nu >.

Member Data Documentation

template<typename T, int _n = Dynamic>

bool gcop::Manifold< T, _n >::bnd

is the space bounded (false by default). Bounds are defined below: these "box" bounds make sense when there is a natural ordering on the manifold, e.g. of the natural numbers)

Referenced by gcop::Airbot::Airbot(), gcop::Bulletrccar::Bulletrccar(), gcop::Bulletrccar1::Bulletrccar1(), gcop::Chain::Chain(), gcop::Rccar::Rccar(), and gcop::Rccar1::Rccar1().

template<typename T, int _n = Dynamic>

T gcop::Manifold< T, _n >::lb

lower bound (-inf by default)

Referenced by gcop::Airbot::Airbot(), gcop::Bulletrccar::Bulletrccar(), gcop::Bulletrccar1::Bulletrccar1(), gcop::Chain::Chain(), gcop::Mbs::CheckLimits(), gcop::Mbs::ClampPose(), gcop::Mbs::ClampVelocity(), gcop::Mbs::Force(), gcop::Mbs::GetImpulse(), gcop::Rccar::Rccar(), and gcop::Rccar1::Rccar1().