Abstract class for the state representation. More...

#include <state-base.hpp>

Inheritance diagram for StateAbstractTpl< _Scalar >:

Public Types
typedef MathBaseTpl< Scalar >	MathBase
typedef MathBase::MatrixXs	MatrixXs
typedef MathBase::VectorXs	VectorXs

Public Member Functions
	StateAbstractTpl (const std::size_t nx, const std::size_t ndx)
	Initialize the state dimensions.
virtual void	diff (const Eigen::Ref< const VectorXs > &x0, const Eigen::Ref< const VectorXs > &x1, Eigen::Ref< VectorXs > dxout) const =0
	Compute the state manifold differentiation.
VectorXs	diff_dx (const Eigen::Ref< const VectorXs > &x0, const Eigen::Ref< const VectorXs > &x1)
	Compute the state manifold differentiation.
bool	get_has_limits () const
	Indicate if the state has defined limits.
const VectorXs &	get_lb () const
	Return the state lower bound.
std::size_t	get_ndx () const
	Return the dimension of the tangent space of the state manifold.
std::size_t	get_nq () const
	Return the dimension of the configuration tuple.
std::size_t	get_nv () const
	Return the dimension of tangent space of the configuration manifold.
std::size_t	get_nx () const
	Return the dimension of the state tuple.
const VectorXs &	get_ub () const
	Return the state upper bound.
virtual void	integrate (const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &dx, Eigen::Ref< VectorXs > xout) const =0
	Compute the state manifold integration.
VectorXs	integrate_x (const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &dx)
	Compute the state manifold integration.
virtual void	Jdiff (const Eigen::Ref< const VectorXs > &x0, const Eigen::Ref< const VectorXs > &x1, Eigen::Ref< MatrixXs > Jfirst, Eigen::Ref< MatrixXs > Jsecond, const Jcomponent firstsecond=both) const =0
	Compute the Jacobian of the state manifold differentiation.
std::vector< MatrixXs >	Jdiff_Js (const Eigen::Ref< const VectorXs > &x0, const Eigen::Ref< const VectorXs > &x1, const Jcomponent firstsecond=both)
virtual void	Jintegrate (const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &dx, Eigen::Ref< MatrixXs > Jfirst, Eigen::Ref< MatrixXs > Jsecond, const Jcomponent firstsecond=both, const AssignmentOp op=setto) const =0
	Compute the Jacobian of the state manifold integration.
std::vector< MatrixXs >	Jintegrate_Js (const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &dx, const Jcomponent firstsecond=both)
	Compute the Jacobian of the state manifold integration.
virtual void	JintegrateTransport (const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &dx, Eigen::Ref< MatrixXs > Jin, const Jcomponent firstsecond) const =0
	Parallel transport from integrate(x, dx) to x.
virtual void	print (std::ostream &os) const
	Print relevant information of the state model.
virtual VectorXs	rand () const =0
	Generate a random state.
void	set_lb (const VectorXs &lb)
	Modify the state lower bound.
void	set_ub (const VectorXs &ub)
	Modify the state upper bound.
virtual VectorXs	zero () const =0
	Generate a zero state.

Public Attributes
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar	Scalar

Protected Member Functions
void	update_has_limits ()

Protected Attributes
bool	has_limits_
	Indicates whether any of the state limits is finite.
VectorXs	lb_
	Lower state limits.
std::size_t	ndx_
	State rate dimension.
std::size_t	nq_
	Configuration dimension.
std::size_t	nv_
	Velocity dimension.
std::size_t	nx_
	State dimension.
VectorXs	ub_
	Upper state limits.

Friends
template<class Scalar>
std::ostream &	operator<< (std::ostream &os, const ActionModelAbstractTpl< Scalar > &model)
	Print information on the state model.

Detailed Description

template<typename _Scalar>
class crocoddyl::StateAbstractTpl< _Scalar >

Abstract class for the state representation.

A state is represented by its operators: difference, integrates, transport and their derivatives. The difference operator returns the value of $\mathbf{x}_{1}\ominus\mathbf{x}_{0}$ operation. Instead the integrate operator returns the value of $\mathbf{x}\oplus\delta\mathbf{x}$ . These operators are used to compared two points on the state manifold $\mathcal{M}$ or to advance the state given a tangential velocity ( $T_\mathbf{x} \mathcal{M}$ ). Therefore the points $\mathbf{x}$ , $\mathbf{x}_{0}$ and $\mathbf{x}_{1}$ belong to the manifold $\mathcal{M}$ ; and $\delta\mathbf{x}$ or $\mathbf{x}_{1}\ominus\mathbf{x}_{0}$ lie on its tangential space.

See also: diff(), integrate(), Jdiff(), Jintegrate() and JintegrateTransport()

Definition at line 48 of file state-base.hpp.

Member Typedef Documentation

◆ MathBase

template<typename _Scalar>

typedef MathBaseTpl<Scalar> MathBase

Definition at line 53 of file state-base.hpp.

◆ VectorXs

template<typename _Scalar>

typedef MathBase::VectorXs VectorXs

Definition at line 54 of file state-base.hpp.

◆ MatrixXs

template<typename _Scalar>

typedef MathBase::MatrixXs MatrixXs

Definition at line 55 of file state-base.hpp.

Constructor & Destructor Documentation

◆ StateAbstractTpl()

template<typename _Scalar>

StateAbstractTpl	(	const std::size_t	nx,
		const std::size_t	ndx )

Initialize the state dimensions.

Parameters

[in]	nx	Dimension of state configuration tuple
[in]	ndx	Dimension of state tangent vector

Member Function Documentation

◆ zero()

template<typename _Scalar>

virtual VectorXs zero ( ) const

pure virtual

Generate a zero state.

Implemented in StateMultibodyTpl< _Scalar >, StateMultibodyTpl< double >, StateMultibodyTpl< Scalar >, StateNumDiffTpl< _Scalar >, StateNumDiffTpl< double >, StateVectorTpl< _Scalar >, StateVectorTpl< double >, and StateVectorTpl< Scalar >.

◆ rand()

template<typename _Scalar>

virtual VectorXs rand ( ) const

pure virtual

Generate a random state.

Implemented in StateMultibodyTpl< _Scalar >, StateMultibodyTpl< double >, StateMultibodyTpl< Scalar >, StateNumDiffTpl< _Scalar >, StateNumDiffTpl< double >, StateVectorTpl< _Scalar >, StateVectorTpl< double >, and StateVectorTpl< Scalar >.

◆ diff()

template<typename _Scalar>

virtual void diff	(	const Eigen::Ref< const VectorXs > &	x0,
		const Eigen::Ref< const VectorXs > &	x1,
		Eigen::Ref< VectorXs >	dxout ) const

pure virtual

Compute the state manifold differentiation.

The state differentiation is defined as:

$\begin{equation*} \delta\mathbf{x} = \mathbf{x}_{1} \ominus \mathbf{x}_{0}, \end{equation*}$

where $\mathbf{x}_{1}$ , $\mathbf{x}_{0}$ are the current and previous state which lie in a manifold $\mathcal{M}$ , and $\delta\mathbf{x} \in T_\mathbf{x} \mathcal{M}$ is the rate of change in the state in the tangent space of the manifold.

Parameters

[in]	x0	Previous state point (size nx)
[in]	x1	Current state point (size nx)
[out]	dxout	Difference between the current and previous state points (size ndx)

Implemented in StateMultibodyTpl< _Scalar >, StateMultibodyTpl< double >, StateMultibodyTpl< Scalar >, StateNumDiffTpl< _Scalar >, StateNumDiffTpl< double >, StateVectorTpl< _Scalar >, StateVectorTpl< double >, and StateVectorTpl< Scalar >.

◆ integrate()

template<typename _Scalar>

virtual void integrate	(	const Eigen::Ref< const VectorXs > &	x,
		const Eigen::Ref< const VectorXs > &	dx,
		Eigen::Ref< VectorXs >	xout ) const

pure virtual

Compute the state manifold integration.

The state integration is defined as:

$\begin{equation*} \mathbf{x}_{next} = \mathbf{x} \oplus \delta\mathbf{x}, \end{equation*}$

where $\mathbf{x}$ , $\mathbf{x}_{next}$ are the current and next state which lie in a manifold $\mathcal{M}$ , and $\delta\mathbf{x} \in T_\mathbf{x} \mathcal{M}$ is the rate of change in the state in the tangent space of the manifold.

Parameters

[in]	x	State point (size nx)
[in]	dx	Velocity vector (size ndx)
[out]	xout	Next state point (size nx)

Implemented in StateMultibodyTpl< _Scalar >, StateMultibodyTpl< double >, StateMultibodyTpl< Scalar >, StateNumDiffTpl< _Scalar >, StateNumDiffTpl< double >, StateVectorTpl< _Scalar >, StateVectorTpl< double >, and StateVectorTpl< Scalar >.

◆ Jdiff()

template<typename _Scalar>

virtual void Jdiff	(	const Eigen::Ref< const VectorXs > &	x0,
		const Eigen::Ref< const VectorXs > &	x1,
		Eigen::Ref< MatrixXs >	Jfirst,
		Eigen::Ref< MatrixXs >	Jsecond,
		const Jcomponent	firstsecond = both ) const

pure virtual

Compute the Jacobian of the state manifold differentiation.

The state differentiation is defined as:

$\begin{equation*} \delta\mathbf{x} = \mathbf{x}_{1} \ominus \mathbf{x}_{0}, \end{equation*}$

where $\mathbf{x}_{1}$ , $\mathbf{x}_{0}$ are the current and previous state which lie in a manifold $\mathcal{M}$ , and $\delta\mathbf{x} \in T_\mathbf{x} \mathcal{M}$ is the rate of change in the state in the tangent space of the manifold.

The Jacobians lie in the tangent space of manifold, i.e. $\mathbb{R}^{\textrm{ndx}\times\textrm{ndx}}$ . Note that the state is represented as a tuple of nx values and its dimension is ndx. Calling $\boldsymbol{\Delta}(\mathbf{x}_{0}, \mathbf{x}_{1})$ , the difference function, these Jacobians satisfy the following relationships:

$\boldsymbol{\Delta}(\mathbf{x}_{0},\mathbf{x}_{0}\oplus\delta\mathbf{y}) - \boldsymbol{\Delta}(\mathbf{x}_{0},\mathbf{x}_{1}) = \mathbf{J}_{\mathbf{x}_{1}}\delta\mathbf{y} + \mathbf{o}(\mathbf{x}_{0})$ .
$\boldsymbol{\Delta}(\mathbf{x}_{0}\oplus\delta\mathbf{y},\mathbf{x}_{1}) - \boldsymbol{\Delta}(\mathbf{x}_{0},\mathbf{x}_{1}) = \mathbf{J}_{\mathbf{x}_{0}}\delta\mathbf{y} + \mathbf{o}(\mathbf{x}_{0})$ ,

where $\mathbf{J}_{\mathbf{x}_{1}}$ and $\mathbf{J}_{\mathbf{x}_{0}}$ are the Jacobian with respect to the current and previous state, respectively.

Parameters

[in]	x0	Previous state point (size nx)
[in]	x1	Current state point (size nx)
[out]	Jfirst	Jacobian of the difference operation relative to the previous state point (size ndx $\times$ ndx)
[out]	Jsecond	Jacobian of the difference operation relative to the current state point (size ndx $\times$ ndx)
[in]	firstsecond	Argument (either x0 and / or x1) with respect to which the differentiation is performed.

Implemented in StateMultibodyTpl< _Scalar >, StateMultibodyTpl< double >, StateMultibodyTpl< Scalar >, StateNumDiffTpl< _Scalar >, StateNumDiffTpl< double >, StateVectorTpl< _Scalar >, StateVectorTpl< double >, and StateVectorTpl< Scalar >.

◆ Jintegrate()

template<typename _Scalar>

virtual void Jintegrate	(	const Eigen::Ref< const VectorXs > &	x,
		const Eigen::Ref< const VectorXs > &	dx,
		Eigen::Ref< MatrixXs >	Jfirst,
		Eigen::Ref< MatrixXs >	Jsecond,
		const Jcomponent	firstsecond = both,
		const AssignmentOp	op = setto ) const

pure virtual

Compute the Jacobian of the state manifold integration.

The state integration is defined as:

$\begin{equation*} \mathbf{x}_{next} = \mathbf{x} \oplus \delta\mathbf{x}, \end{equation*}$

where $\mathbf{x}$ , $\mathbf{x}_{next}$ are the current and next state which lie in a manifold $\mathcal{M}$ , and $\delta\mathbf{x} \in T_\mathbf{x} \mathcal{M}$ is the rate of change in the state in the tangent space of the manifold.

The Jacobians lie in the tangent space of manifold, i.e. $\mathbb{R}^{\textrm{ndx}\times\textrm{ndx}}$ . Note that the state is represented as a tuple of nx values and its dimension is ndx. Calling $\mathbf{f}(\mathbf{x}, \delta\mathbf{x})$ , the integrate function, these Jacobians satisfy the following relationships:

$\mathbf{f}(\mathbf{x}\oplus\delta\mathbf{y},\delta\mathbf{x})\ominus\mathbf{f}(\mathbf{x},\delta\mathbf{x}) = \mathbf{J}_\mathbf{x}\delta\mathbf{y} + \mathbf{o}(\delta\mathbf{x})$ .
$\mathbf{f}(\mathbf{x},\delta\mathbf{x}+\delta\mathbf{y})\ominus\mathbf{f}(\mathbf{x},\delta\mathbf{x}) = \mathbf{J}_{\delta\mathbf{x}}\delta\mathbf{y} + \mathbf{o}(\delta\mathbf{x})$ ,

where $\mathbf{J}_{\delta\mathbf{x}}$ and $\mathbf{J}_{\mathbf{x}}$ are the Jacobian with respect to the state and velocity, respectively.

Parameters

[in]	x	State point (size nx)
[in]	dx	Velocity vector (size ndx)
[out]	Jfirst	Jacobian of the integration operation relative to the state point (size ndx $\times$ ndx)
[out]	Jsecond	Jacobian of the integration operation relative to the velocity vector (size ndx $\times$ ndx)
[in]	firstsecond	Argument (either x and / or dx) with respect to which the differentiation is performed
[in]	op	Assignment operator which sets, adds, or removes the given Jacobian matrix

Implemented in StateMultibodyTpl< _Scalar >, StateMultibodyTpl< double >, StateMultibodyTpl< Scalar >, StateNumDiffTpl< _Scalar >, StateNumDiffTpl< double >, StateVectorTpl< _Scalar >, StateVectorTpl< double >, and StateVectorTpl< Scalar >.

◆ JintegrateTransport()

template<typename _Scalar>

virtual void JintegrateTransport	(	const Eigen::Ref< const VectorXs > &	x,
		const Eigen::Ref< const VectorXs > &	dx,
		Eigen::Ref< MatrixXs >	Jin,
		const Jcomponent	firstsecond ) const

pure virtual

Parallel transport from integrate(x, dx) to x.

This function performs the parallel transportation of an input matrix whose columns are expressed in the tangent space at $\mathbf{x}\oplus\delta\mathbf{x}$ to the tangent space at $\mathbf{x}$ point.

Parameters

[in]	x	State point (size nx).
[in]	dx	Velocity vector (size ndx)
[out]	Jin	Input matrix (number of rows = nv).
[in]	firstsecond	Argument (either x or dx) with respect to which the differentiation of Jintegrate is performed.

Implemented in StateMultibodyTpl< _Scalar >, StateMultibodyTpl< double >, StateMultibodyTpl< Scalar >, StateNumDiffTpl< _Scalar >, StateNumDiffTpl< double >, StateVectorTpl< _Scalar >, StateVectorTpl< double >, and StateVectorTpl< Scalar >.

◆ diff_dx()

template<typename _Scalar>

VectorXs diff_dx	(	const Eigen::Ref< const VectorXs > &	x0,
		const Eigen::Ref< const VectorXs > &	x1 )

Compute the state manifold differentiation.

Parameters

[in]	x0	Previous state point (size nx)
[in]	x1	Current state point (size nx)

Returns: Difference between the current and previous state points (size ndx)

◆ integrate_x()

template<typename _Scalar>

VectorXs integrate_x	(	const Eigen::Ref< const VectorXs > &	x,
		const Eigen::Ref< const VectorXs > &	dx )

Compute the state manifold integration.

Parameters

[in]	x	State point (size nx)
[in]	dx	Velocity vector (size ndx)

Returns: Next state point (size nx)

◆ Jdiff_Js()

template<typename _Scalar>

std::vector< MatrixXs > Jdiff_Js	(	const Eigen::Ref< const VectorXs > &	x0,
		const Eigen::Ref< const VectorXs > &	x1,
		const Jcomponent	firstsecond = both )

Parameters

[in]	x0	Previous state point (size nx)
[in]	x1	Current state point (size nx)

Returns: Jacobians

◆ Jintegrate_Js()

template<typename _Scalar>

std::vector< MatrixXs > Jintegrate_Js	(	const Eigen::Ref< const VectorXs > &	x,
		const Eigen::Ref< const VectorXs > &	dx,
		const Jcomponent	firstsecond = both )

Compute the Jacobian of the state manifold integration.

Parameters

[in]	x	State point (size nx)
[in]	dx	Velocity vector (size ndx)

Returns: Jacobians

◆ print()

template<typename _Scalar>

virtual void print ( std::ostream & os ) const

virtual

Print relevant information of the state model.

Parameters

[out] os Output stream object

Reimplemented in StateMultibodyTpl< _Scalar >, StateMultibodyTpl< double >, StateMultibodyTpl< Scalar >, StateNumDiffTpl< _Scalar >, StateNumDiffTpl< double >, StateVectorTpl< _Scalar >, StateVectorTpl< double >, and StateVectorTpl< Scalar >.

Member Data Documentation

◆ Scalar

template<typename _Scalar>

EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar Scalar

Definition at line 52 of file state-base.hpp.

◆ nx_

template<typename _Scalar>

std::size_t nx_

protected

State dimension.

Definition at line 334 of file state-base.hpp.

◆ ndx_

template<typename _Scalar>

std::size_t ndx_

protected

State rate dimension.

Definition at line 335 of file state-base.hpp.

◆ nq_

template<typename _Scalar>

std::size_t nq_

protected

Configuration dimension.

Definition at line 336 of file state-base.hpp.

◆ nv_

template<typename _Scalar>

std::size_t nv_

protected

Velocity dimension.

Definition at line 337 of file state-base.hpp.

◆ lb_

template<typename _Scalar>

VectorXs lb_

protected

Lower state limits.

Definition at line 338 of file state-base.hpp.

◆ ub_

template<typename _Scalar>

VectorXs ub_

protected

Upper state limits.

Definition at line 339 of file state-base.hpp.

◆ has_limits_

template<typename _Scalar>

bool has_limits_

protected

Indicates whether any of the state limits is finite.

Definition at line 340 of file state-base.hpp.

The documentation for this class was generated from the following files:

/build/source/include/crocoddyl/core/fwd.hpp
/build/source/include/crocoddyl/core/state-base.hpp

Public Types

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ MathBase

◆ VectorXs

◆ MatrixXs

Constructor & Destructor Documentation

◆ StateAbstractTpl()

Member Function Documentation

◆ zero()

◆ rand()

◆ diff()

◆ integrate()

◆ Jdiff()

◆ Jintegrate()

◆ JintegrateTransport()

◆ diff_dx()

◆ integrate_x()

◆ Jdiff_Js()

◆ Jintegrate_Js()

◆ print()

Member Data Documentation

◆ Scalar

◆ nx_

◆ ndx_

◆ nq_

◆ nv_

◆ lb_

◆ ub_

◆ has_limits_