The two-dimensional special Euclidean group SE(2), i.e. More...

#include <aikido/statespace/SE2.hpp>

Inheritance diagram for aikido::statespace::SE2:

Classes
class	State

Public Types
using	StateHandle = SE2StateHandle< State >

using	StateHandleConst = SE2StateHandle< const State >

using	ScopedState = statespace::ScopedState< StateHandle >

using	ScopedStateConst = statespace::ScopedState< StateHandleConst >

using	Isometry2d = State::Isometry2d

Public Types inherited from aikido::statespace::StateSpace
using	StateHandle = statespace::StateHandle< StateSpace, State >

using	StateHandleConst = statespace::StateHandle< StateSpace, const State >

using	ScopedState = statespace::ScopedState< StateHandle >

using	ScopedStateConst = statespace::ScopedState< StateHandleConst >

Public Member Functions
	SE2 ()=default
	Constructs a state space representing SE(2). More...

ScopedState	createState () const
	Helper function to create a `ScopedState`. More...

ScopedState	cloneState (const StateSpace::State *stateIn) const
	Creates an identical clone of `stateIn`. More...

const Isometry2d &	getIsometry (const State *_state) const
	Gets value as an Eigen transformation object. More...

void	setIsometry (State *_state, const Isometry2d &_transform) const
	Sets value to an Eigen transfomation object. More...

std::size_t	getStateSizeInBytes () const override
	Gets the size of a State, in bytes. More...

StateSpace::State *	allocateStateInBuffer (void *_buffer) const override
	Create a new state in a pre-allocated buffer. More...

void	freeStateInBuffer (StateSpace::State *_state) const override
	Free a state previously created by `allocateStateInBuffer`. More...

void	compose (const StateSpace::State _state1, const StateSpace::State _state2, StateSpace::State *_out) const override
	Lie group operation for this StateSpace. More...

void	getIdentity (StateSpace::State *_out) const override
	Gets the identity element for this Lie group, such that: More...

void	getInverse (const StateSpace::State _in, StateSpace::State _out) const override
	Gets the inverse of `_in` in this Lie group, such that: More...

std::size_t	getDimension () const override
	Get the dimension of this Lie group. More...

void	copyState (const StateSpace::State _source, StateSpace::State _destination) const override
	Copy a state. More...

void	expMap (const Eigen::VectorXd &_tangent, StateSpace::State *_out) const override
	Exponential mapping of Lie algebra element to a Lie group element. More...

void	logMap (const StateSpace::State *_state, Eigen::VectorXd &_tangent) const override
	Log mapping of Lie group element to a Lie algebra element. More...

void	print (const StateSpace::State *_state, std::ostream &_os) const override
	Print the state. Format: [x, y, theta]. More...

virtual void	compose (const State _state1, const State _state2, State *_out) const=0
	Lie group operation for this StateSpace. More...

virtual void	compose (State _state1, const State _state2) const
	Lie group operation for this StateSpace. More...

Public Member Functions inherited from aikido::statespace::StateSpace
virtual	~StateSpace ()=default

ScopedState	createState () const
	Helper function to create a `ScopedState`. More...

ScopedState	cloneState (const State *stateIn) const
	Creates an identical clone of `stateIn`. More...

virtual State *	allocateState () const
	Allocate a new state. More...

virtual void	freeState (State *_state) const
	Free a state previously created by `allocateState`. More...

virtual void	compose (State _state1, const State _state2) const
	Lie group operation for this StateSpace. More...

virtual void	getInverse (State *_state) const
	Gets the inverse of `_in` in this Lie group. More...

Detailed Description

The two-dimensional special Euclidean group SE(2), i.e.

the space of planar rigid body transformations. Note that the group operation for SE(2) differs from the group operation of the Cartesian product space R^2 x SO(2) because it is constructed through the semi-direct product.

Member Typedef Documentation

◆ Isometry2d

using aikido::statespace::SE2::Isometry2d = State::Isometry2d

◆ ScopedState

using aikido::statespace::SE2::ScopedState = statespace::ScopedState<StateHandle>

◆ ScopedStateConst

using aikido::statespace::SE2::ScopedStateConst = statespace::ScopedState<StateHandleConst>

◆ StateHandle

using aikido::statespace::SE2::StateHandle = SE2StateHandle<State>

◆ StateHandleConst

using aikido::statespace::SE2::StateHandleConst = SE2StateHandle<const State>

Constructor & Destructor Documentation

◆ SE2()

aikido::statespace::SE2::SE2 ( )

default

Constructs a state space representing SE(2).

Member Function Documentation

◆ allocateStateInBuffer()

StateSpace::State* aikido::statespace::SE2::allocateStateInBuffer ( void * _buffer ) const

overridevirtual

Create a new state in a pre-allocated buffer.

The input argument must contain at least getStateSizeInBytes() bytes of memory. This state must be freed with freeStateInBuffer before freeing _buffer.

Parameters

_buffer memory used to store the returned state

Returns: state object allocated in _buffer

Implements aikido::statespace::StateSpace.

◆ cloneState()

ScopedState aikido::statespace::SE2::cloneState ( const StateSpace::State * stateIn ) const

Creates an identical clone of stateIn.

◆ compose() [1/3]

virtual void aikido::statespace::StateSpace::compose

Lie group operation for this StateSpace.

It is not acceptable for _out to share memory with _state1 or _state2.

Parameters

	_state1	left input state
	_state2	right input state
[out]	_out	output state

◆ compose() [2/3]

void aikido::statespace::SE2::compose	(	const StateSpace::State *	_state1,
		const StateSpace::State *	_state2,
		StateSpace::State *	_out
	)		const

overridevirtual

Lie group operation for this StateSpace.

It is not acceptable for _out to share memory with _state1 or _state2.

Parameters

	_state1	left input state
	_state2	right input state
[out]	_out	output state

Implements aikido::statespace::StateSpace.

◆ compose() [3/3]

virtual void aikido::statespace::StateSpace::compose

Lie group operation for this StateSpace.

This is an in-place version of the three argument compose member function that computes:

_state1 = _state1 * _state2.

Parameters

[in,out]	_state1	left input state, overwritten by output
	_state2	right input state

◆ copyState()

void aikido::statespace::SE2::copyState	(	const StateSpace::State *	_source,
		StateSpace::State *	_destination
	)		const

overridevirtual

Copy a state.

Parameters

	_source	input state
[out]	_destination	output state

Implements aikido::statespace::StateSpace.

◆ createState()

ScopedState aikido::statespace::SE2::createState ( ) const

Helper function to create a ScopedState.

Returns: new ScopedState

◆ expMap()

void aikido::statespace::SE2::expMap	(	const Eigen::VectorXd &	_tangent,
		StateSpace::State *	_out
	)		const

overridevirtual

Exponential mapping of Lie algebra element to a Lie group element.

The tangent space is parameterized a planar twist of the form (translation, translation, rotation).

Parameters

	_tangent	element of the tangent space
[out]	_out	corresponding element of the Lie group

Implements aikido::statespace::StateSpace.

◆ freeStateInBuffer()

void aikido::statespace::SE2::freeStateInBuffer ( StateSpace::State * _state ) const

overridevirtual

Free a state previously created by allocateStateInBuffer.

It is undefined behavior to access _state after calling this function.

Parameters

_state state to free

Implements aikido::statespace::StateSpace.

◆ getDimension()

std::size_t aikido::statespace::SE2::getDimension ( ) const

overridevirtual

Get the dimension of this Lie group.

This is also the dimension of the tangent space, i.e. the Lie algebra, associated with this group.

Returns: dimension of this state space

Implements aikido::statespace::StateSpace.

◆ getIdentity()

void aikido::statespace::SE2::getIdentity ( StateSpace::State * _out ) const

overridevirtual

Gets the identity element for this Lie group, such that:

compose(state, identity) = state

Parameters

[out] _out output state

Implements aikido::statespace::StateSpace.

◆ getInverse()

void aikido::statespace::SE2::getInverse	(	const StateSpace::State *	_state,
		StateSpace::State *	_out
	)		const

overridevirtual

Gets the inverse of _in in this Lie group, such that:

compose(state, inverse(state)) = identity

It is not acceptable for _in to share memory with _out.

Parameters

	_state	input state
[out]	_out	output state

Implements aikido::statespace::StateSpace.

◆ getIsometry()

const Isometry2d& aikido::statespace::SE2::getIsometry ( const State * _state ) const

Gets value as an Eigen transformation object.

Parameters

_state a State in this state space

Returns: Eigen transformation

◆ getStateSizeInBytes()

std::size_t aikido::statespace::SE2::getStateSizeInBytes ( ) const

overridevirtual

Gets the size of a State, in bytes.

Returns: size, in bytes, requires to store a State

Implements aikido::statespace::StateSpace.

◆ logMap()

void aikido::statespace::SE2::logMap	(	const StateSpace::State *	_state,
		Eigen::VectorXd &	_tangent
	)		const

overridevirtual

Log mapping of Lie group element to a Lie algebra element.

The tangent space is parameterized as a planar twist of the form (translation, translation, rotation).

Parameters

	_state	element of this Lie group
[out]	_tangent	corresponding element of the tangent space

Implements aikido::statespace::StateSpace.

◆ print()

void aikido::statespace::SE2::print	(	const StateSpace::State *	_state,
		std::ostream &	_os
	)		const

overridevirtual

Print the state. Format: [x, y, theta].

Implements aikido::statespace::StateSpace.

◆ setIsometry()

void aikido::statespace::SE2::setIsometry	(	State *	_state,
		const Isometry2d &	_transform
	)		const

Sets value to an Eigen transfomation object.

Parameters

_state	a `State` in this state space
_transform	Eigen transformation

Classes

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ Isometry2d

◆ ScopedState

◆ ScopedStateConst

◆ StateHandle

◆ StateHandleConst

Constructor & Destructor Documentation

◆ SE2()

Member Function Documentation

◆ allocateStateInBuffer()

◆ cloneState()

◆ compose() [1/3]

◆ compose() [2/3]

◆ compose() [3/3]

◆ copyState()

◆ createState()

◆ expMap()

◆ freeStateInBuffer()

◆ getDimension()

◆ getIdentity()

◆ getInverse()

◆ getIsometry()

◆ getStateSizeInBytes()

◆ logMap()

◆ print()

◆ setIsometry()