This class computes the numerical differentiation of a differential action model. More...

#include <diff-action.hpp>

Inheritance diagram for DifferentialActionModelNumDiffTpl< _Scalar >:

Public Types
typedef DifferentialActionModelAbstractTpl< Scalar >	Base

typedef DifferentialActionDataNumDiffTpl< Scalar >	Data

typedef DifferentialActionDataAbstractTpl< Scalar >	DifferentialActionDataAbstract

typedef MathBaseTpl< Scalar >	MathBase

typedef MathBase::MatrixXs	MatrixXs

typedef MathBase::VectorXs	VectorXs

Public Types inherited from DifferentialActionModelAbstractTpl< _Scalar >
typedef DifferentialActionDataAbstractTpl< Scalar >	DifferentialActionDataAbstract

typedef MathBaseTpl< Scalar >	MathBase

typedef MathBase::MatrixXs	MatrixXs

typedef ScalarSelector< Scalar >::type	ScalarType

typedef StateAbstractTpl< Scalar >	StateAbstract

typedef MathBase::VectorXs	VectorXs

Public Member Functions
	DifferentialActionModelNumDiffTpl (std::shared_ptr< Base > model, const bool with_gauss_approx=false)
	Initialize the numdiff differential action model.

virtual void	calc (const std::shared_ptr< DifferentialActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x) override

virtual void	calc (const std::shared_ptr< DifferentialActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &u) override
	Compute the system acceleration and cost value.

virtual void	calcDiff (const std::shared_ptr< DifferentialActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x) override

virtual void	calcDiff (const std::shared_ptr< DifferentialActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &u) override
	Compute the derivatives of the dynamics and cost functions.

template<typename NewScalar >
DifferentialActionModelNumDiffTpl< NewScalar >	cast () const
	Cast the diff-action numdiff model to a different scalar type.

virtual std::shared_ptr< DifferentialActionDataAbstract >	createData () override
	Create the differential action data.

EIGEN_MAKE_ALIGNED_OPERATOR_NEW	CROCODDYL_DERIVED_CAST (DifferentialActionModelBase, DifferentialActionModelNumDiffTpl) typedef _Scalar Scalar

const Scalar	get_disturbance () const
	Return the disturbance constant used in the numerical differentiation routine.

const std::shared_ptr< Base > &	get_model () const
	Return the differential acton model that we use to numerical differentiate.

bool	get_with_gauss_approx ()
	Identify if the Gauss approximation is going to be used or not.

virtual void	print (std::ostream &os) const override
	Print relevant information of the action numdiff model.

virtual void	quasiStatic (const std::shared_ptr< DifferentialActionDataAbstract > &data, Eigen::Ref< VectorXs > u, const Eigen::Ref< const VectorXs > &x, const std::size_t maxiter=100, const Scalar tol=Scalar(1e-9)) override
	Computes the quasic static commands.

void	set_disturbance (const Scalar disturbance)
	Modify the disturbance constant used in the numerical differentiation routine.

Public Member Functions inherited from DifferentialActionModelAbstractTpl< _Scalar >
	DifferentialActionModelAbstractTpl (std::shared_ptr< StateAbstract > state, const std::size_t nu, const std::size_t nr=0, const std::size_t ng=0, const std::size_t nh=0, const std::size_t ng_T=0, const std::size_t nh_T=0)
	Initialize the differential action model.

virtual bool	checkData (const std::shared_ptr< DifferentialActionDataAbstract > &data)
	Checks that a specific data belongs to this model.

virtual const VectorXs &	get_g_lb () const
	Return the lower bound of the inequality constraints.

virtual const VectorXs &	get_g_ub () const
	Return the upper bound of the inequality constraints.

bool	get_has_control_limits () const
	Indicates if there are defined control limits.

virtual std::size_t	get_ng () const
	Return the number of inequality constraints.

virtual std::size_t	get_ng_T () const
	Return the number of inequality terminal constraints.

virtual std::size_t	get_nh () const
	Return the number of equality constraints.

virtual std::size_t	get_nh_T () const
	Return the number of equality terminal constraints.

std::size_t	get_nr () const
	Return the dimension of the cost-residual vector.

std::size_t	get_nu () const
	Return the dimension of the control input.

const std::shared_ptr< StateAbstract > &	get_state () const
	Return the state.

const VectorXs &	get_u_lb () const
	Return the control lower bound.

const VectorXs &	get_u_ub () const
	Return the control upper bound.

VectorXs	quasiStatic_x (const std::shared_ptr< DifferentialActionDataAbstract > &data, const VectorXs &x, const std::size_t maxiter=100, const Scalar tol=Scalar(1e-9))

void	set_g_lb (const VectorXs &g_lb)
	Modify the lower bound of the inequality constraints.

void	set_g_ub (const VectorXs &g_ub)
	Modify the upper bound of the inequality constraints.

void	set_u_lb (const VectorXs &u_lb)
	Modify the control lower bounds.

void	set_u_ub (const VectorXs &u_ub)
	Modify the control upper bounds.

Protected Attributes
bool	has_control_limits_

std::size_t	nr_

std::size_t	nu_
	< Dimension of the cost residual

std::shared_ptr< StateAbstract >	state_
	< Control dimension

VectorXs	u_lb_
	< Model of the state

VectorXs	u_ub_
	< Lower control limits

Protected Attributes inherited from DifferentialActionModelAbstractTpl< _Scalar >
VectorXs	g_lb_
	Lower bound of the inequality constraints.

VectorXs	g_ub_
	Lower bound of the inequality constraints.

bool	has_control_limits_

std::size_t	ng_
	Number of inequality constraints.

std::size_t	ng_T_
	Number of inequality terminal constraints.

std::size_t	nh_
	Number of equality constraints.

std::size_t	nh_T_
	Number of equality terminal constraints.

std::size_t	nr_
	Dimension of the cost residual.

std::size_t	nu_
	Control dimension.

std::shared_ptr< StateAbstract >	state_
	Model of the state.

VectorXs	u_lb_
	Lower control limits.

VectorXs	u_ub_
	Upper control limits.

VectorXs	unone_
	Neutral state.

Additional Inherited Members
Public Attributes inherited from DifferentialActionModelAbstractTpl< _Scalar >
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar	Scalar

Protected Member Functions inherited from DifferentialActionModelAbstractTpl< _Scalar >
void	update_has_control_limits ()
	Update the status of the control limits (i.e. if there are defined limits)

Detailed Description

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

This class computes the numerical differentiation of a differential action model.

It computes the Jacobian of the cost, its residual and dynamics via numerical differentiation. It considers that the action model owns a cost residual and the cost is the square of this residual, i.e., \(\ell(\mathbf{x},\mathbf{u})=\frac{1}{2}\|\mathbf{r}(\mathbf{x},\mathbf{u})\|^2\), where \(\mathbf{r}(\mathbf{x},\mathbf{u})\) is the residual vector. The Hessian is computed only through the Gauss-Newton approximation, i.e.,

\begin{eqnarray*} \mathbf{\ell}_\mathbf{xx} &=& \mathbf{R_x}^T\mathbf{R_x} \\ \mathbf{\ell}_\mathbf{uu} &=& \mathbf{R_u}^T\mathbf{R_u} \\ \mathbf{\ell}_\mathbf{xu} &=& \mathbf{R_x}^T\mathbf{R_u} \end{eqnarray*}

where the Jacobians of the cost residuals are denoted by \(\mathbf{R_x}\) and \(\mathbf{R_u}\). Note that this approximation ignores the tensor products (e.g., \(\mathbf{R_{xx}}\mathbf{r}\)).

Finally, in the case that the cost does not have a residual, we set the Hessian to zero, i.e., \(\mathbf{L_{xx}} = \mathbf{L_{xu}} = \mathbf{L_{uu}} = \mathbf{0}\).

See also: DifferentialActionModelAbstractTpl(), calcDiff()

Definition at line 44 of file diff-action.hpp.

Member Typedef Documentation

◆ MathBase

template<typename _Scalar >

typedef MathBaseTpl<Scalar> MathBase

Definition at line 52 of file diff-action.hpp.

◆ Base

template<typename _Scalar >

typedef DifferentialActionModelAbstractTpl<Scalar> Base

Definition at line 53 of file diff-action.hpp.

◆ Data

template<typename _Scalar >

typedef DifferentialActionDataNumDiffTpl<Scalar> Data

Definition at line 54 of file diff-action.hpp.

◆ DifferentialActionDataAbstract

template<typename _Scalar >

typedef DifferentialActionDataAbstractTpl<Scalar> DifferentialActionDataAbstract

Definition at line 56 of file diff-action.hpp.

◆ VectorXs

template<typename _Scalar >

typedef MathBase::VectorXs VectorXs

Definition at line 57 of file diff-action.hpp.

◆ MatrixXs

template<typename _Scalar >

typedef MathBase::MatrixXs MatrixXs

Definition at line 58 of file diff-action.hpp.

Constructor & Destructor Documentation

◆ DifferentialActionModelNumDiffTpl()

template<typename _Scalar >

DifferentialActionModelNumDiffTpl	(	std::shared_ptr< Base >	model,
		const bool	with_gauss_approx = `false`
	)

explicit

Initialize the numdiff differential action model.

Parameters

[in]	model	Differential action model that we want to apply the numerical differentiation
[in]	with_gauss_approx	True if we want to use the Gauss approximation for computing the Hessians

Member Function Documentation

◆ calc() [1/2]

template<typename _Scalar >

virtual void calc	(	const std::shared_ptr< DifferentialActionDataAbstract > &	data,
		const Eigen::Ref< const VectorXs > &	x,
		const Eigen::Ref< const VectorXs > &	u
	)

overridevirtual

Compute the system acceleration and cost value.

Parameters

[in]	data	Differential action data
[in]	x	State point \(\mathbf{x}\in\mathbb{R}^{ndx}\)
[in]	u	Control input \(\mathbf{u}\in\mathbb{R}^{nu}\)

Implements DifferentialActionModelAbstractTpl< _Scalar >.

◆ calc() [2/2]

template<typename _Scalar >

virtual void calc	(	const std::shared_ptr< DifferentialActionDataAbstract > &	data,
		const Eigen::Ref< const VectorXs > &	x
	)

overridevirtual

Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.

◆ calcDiff() [1/2]

template<typename _Scalar >

virtual void calcDiff	(	const std::shared_ptr< DifferentialActionDataAbstract > &	data,
		const Eigen::Ref< const VectorXs > &	x,
		const Eigen::Ref< const VectorXs > &	u
	)

overridevirtual

Compute the derivatives of the dynamics and cost functions.

It computes the partial derivatives of the dynamical system and the cost function. It assumes that calc() has been run first. This function builds a quadratic approximation of the time-continuous action model (i.e. dynamical system and cost function).

Parameters

[in]	data	Differential action data
[in]	x	State point \(\mathbf{x}\in\mathbb{R}^{ndx}\)
[in]	u	Control input \(\mathbf{u}\in\mathbb{R}^{nu}\)

Implements DifferentialActionModelAbstractTpl< _Scalar >.

◆ calcDiff() [2/2]

template<typename _Scalar >

virtual void calcDiff	(	const std::shared_ptr< DifferentialActionDataAbstract > &	data,
		const Eigen::Ref< const VectorXs > &	x
	)

overridevirtual

Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.

◆ createData()

template<typename _Scalar >

virtual std::shared_ptr< DifferentialActionDataAbstract > createData ( )

overridevirtual

Create the differential action data.

Returns: the differential action data

Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.

◆ cast()

template<typename _Scalar >

template<typename NewScalar >

DifferentialActionModelNumDiffTpl< NewScalar > cast ( ) const

Cast the diff-action numdiff model to a different scalar type.

It is useful for operations requiring different precision or scalar types.

Template Parameters

NewScalar The new scalar type to cast to.

Returns: DifferentialActionModelNumDiffTpl<NewScalar> A differential-action model with the new scalar type.

◆ quasiStatic()

template<typename _Scalar >

virtual void quasiStatic	(	const std::shared_ptr< DifferentialActionDataAbstract > &	data,
		Eigen::Ref< VectorXs >	u,
		const Eigen::Ref< const VectorXs > &	x,
		const std::size_t	maxiter = `100`,
		const Scalar	tol = `Scalar(1e-9)`
	)

overridevirtual

Computes the quasic static commands.

The quasic static commands are the ones produced for a the reference posture as an equilibrium point, i.e. for \(\mathbf{f}(\mathbf{q},\mathbf{v}=\mathbf{0},\mathbf{u})=\mathbf{0}\)

Parameters

[in]	data	Differential action data
[out]	u	Quasic static commands
[in]	x	State point (velocity has to be zero)
[in]	maxiter	Maximum allowed number of iterations
[in]	tol	Tolerance

Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.

◆ print()

template<typename _Scalar >

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

overridevirtual

Print relevant information of the action numdiff model.

Parameters

[out] os Output stream object

Reimplemented from DifferentialActionModelAbstractTpl< _Scalar >.

Member Data Documentation

◆ has_control_limits_

template<typename _Scalar >

bool has_control_limits_

protected

Indicates whether any of the control limits is finite

Definition at line 373 of file diff-action-base.hpp.

◆ nr_

template<typename _Scalar >

std::size_t nr_

protected

< Indicates whether any of the control limits

Definition at line 362 of file diff-action-base.hpp.

◆ nu_

template<typename _Scalar >

std::size_t nu_

protected

< Dimension of the cost residual

Definition at line 361 of file diff-action-base.hpp.

◆ state_

template<typename _Scalar >

std::shared_ptr<StateAbstract> state_

protected

< Control dimension

Definition at line 367 of file diff-action-base.hpp.

◆ u_lb_

template<typename _Scalar >

VectorXs u_lb_

protected

< Model of the state

Definition at line 371 of file diff-action-base.hpp.

◆ u_ub_

template<typename _Scalar >

VectorXs u_ub_

protected

< Lower control limits

Definition at line 372 of file diff-action-base.hpp.

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

/root/robotpkg/optimization/py-crocoddyl/work/crocoddyl-2.1.0/include/crocoddyl/core/fwd.hpp
/root/robotpkg/optimization/py-crocoddyl/work/crocoddyl-2.1.0/include/crocoddyl/core/numdiff/diff-action.hpp

Public Types

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ MathBase

◆ Base

◆ Data

◆ DifferentialActionDataAbstract

◆ VectorXs

◆ MatrixXs

Constructor & Destructor Documentation

◆ DifferentialActionModelNumDiffTpl()

Member Function Documentation

◆ calc() [1/2]

◆ calc() [2/2]

◆ calcDiff() [1/2]

◆ calcDiff() [2/2]

◆ createData()

◆ cast()

◆ quasiStatic()

◆ print()

Member Data Documentation

◆ has_control_limits_

◆ nr_

◆ nu_

◆ state_

◆ u_lb_

◆ u_ub_