aikido::statespace::GeodesicInterpolator Class Reference

Interpolate by parallel transport along a geodesic between two states in a Lie group with an affine connection. More...

#include <aikido/statespace/GeodesicInterpolator.hpp>

Inheritance diagram for aikido::statespace::GeodesicInterpolator:

Public Member Functions
	GeodesicInterpolator (statespace::ConstStateSpacePtr _stateSpace)
	Constructs a GeodesicInterpolator for _stateSpace. More...
virtual	~GeodesicInterpolator ()=default
ConstStateSpacePtr	getStateSpace () const override
	Gets the StateSpace on which this Interpolator operates. More...
std::size_t	getNumDerivatives () const override
	Upper bound on the number of non-zero derivatives. More...
Eigen::VectorXd	getTangentVector (const statespace::StateSpace::State *_from, const statespace::StateSpace::State *_to) const
	Gets the tangent vector that defines the geodesic, scaled such that: More...
void	interpolate (const statespace::StateSpace::State *_from, const statespace::StateSpace::State *_to, double _alpha, statespace::StateSpace::State *_state) const override
	Computes the state that lies at path parameter _alpha along the path that connects _from to _to. More...
void	getDerivative (const statespace::StateSpace::State *_from, const statespace::StateSpace::State *_to, std::size_t _derivative, double _alpha, Eigen::VectorXd &_tangentVector) const override
	Computes the _derivative-th derivative of the path at path parameter _alpha between _from and _to. More...
Public Member Functions inherited from aikido::statespace::Interpolator
virtual	~Interpolator ()=default

Private Attributes
statespace::ConstStateSpacePtr	mStateSpace

Detailed Description

Interpolate by parallel transport along a geodesic between two states in a Lie group with an affine connection.

The geodesic is defined by a single tangent vector that remains constant during interpolation.

Constructor & Destructor Documentation

GeodesicInterpolator()

aikido::statespace::GeodesicInterpolator::GeodesicInterpolator ( statespace::ConstStateSpacePtr  _stateSpace )

explicit

Constructs a GeodesicInterpolator for _stateSpace.

Parameters

_stateSpace

used for interpolation

~GeodesicInterpolator()

virtual aikido::statespace::GeodesicInterpolator::~GeodesicInterpolator ( )

virtualdefault

Member Function Documentation

getDerivative()

void aikido::statespace::GeodesicInterpolator::getDerivative ( const statespace::StateSpace::State *  _from, const statespace::StateSpace::State *  _to, std::size_t  _derivative, double  _alpha, Eigen::VectorXd &  _tangentVector  ) const

overridevirtual

Computes the _derivative-th derivative of the path at path parameter _alpha between _from and _to.

The output is an element of the tangent space in the local (i.e. "body") frame.

Parameters

	_from	start state in getStateSpace()
	_to	end state in getStateSpace()
	_derivative	order of the derivative to compute
	_alpha	path parameter in the range [0, 1]
[out]	_tangentVector	output element of the tangent space

Implements aikido::statespace::Interpolator.

getNumDerivatives()

std::size_t aikido::statespace::GeodesicInterpolator::getNumDerivatives ( ) const

overridevirtual

Upper bound on the number of non-zero derivatives.

Implements aikido::statespace::Interpolator.

getStateSpace()

ConstStateSpacePtr aikido::statespace::GeodesicInterpolator::getStateSpace ( ) const

overridevirtual

Gets the StateSpace on which this Interpolator operates.

Implements aikido::statespace::Interpolator.

getTangentVector()

Eigen::VectorXd aikido::statespace::GeodesicInterpolator::getTangentVector	(	const statespace::StateSpace::State *	_from,
		const statespace::StateSpace::State *	_to
	)		const

Gets the tangent vector that defines the geodesic, scaled such that:

interpolate(alpha) = _from * expMap(alpha * tangentVector)

Parameters

_from	start state in getStateSpace()
_to	goal state in getStateSpace()

Returns

tangent vector that defines the geodesic

interpolate()

void aikido::statespace::GeodesicInterpolator::interpolate ( const statespace::StateSpace::State *  _from, const statespace::StateSpace::State *  _to, double  _alpha, statespace::StateSpace::State *  _state  ) const

overridevirtual

Computes the state that lies at path parameter _alpha along the path that connects _from to _to.

By definition interpolate(0) is _from and interpolate(1) is _to. The memory location of _state must differ from the memory locations of _from and _to.

Parameters

	_from	start state in getStateSpace()
	_to	end state in getStateSpace()
	_alpha	path parameter in the range [0, 1]
[out]	_state	output interpolated state

Implements aikido::statespace::Interpolator.

Member Data Documentation

mStateSpace

statespace::ConstStateSpacePtr aikido::statespace::GeodesicInterpolator::mStateSpace

private