This class computes the numerical differentiation of an action model. More...

#include <action.hpp>

Inheritance diagram for ActionModelNumDiffTpl< _Scalar >:

Public Types
typedef ActionDataAbstractTpl< Scalar >	ActionDataAbstract
typedef ActionModelAbstractTpl< Scalar >	Base
typedef ActionDataNumDiffTpl< Scalar >	Data
typedef MathBaseTpl< Scalar >	MathBase
typedef MathBaseTpl< Scalar >::MatrixXs	MatrixXs
typedef MathBaseTpl< Scalar >::VectorXs	VectorXs
Public Types inherited from ActionModelAbstractTpl< _Scalar >
typedef ActionDataAbstractTpl< Scalar >	ActionDataAbstract
typedef MathBaseTpl< Scalar >	MathBase
typedef ScalarSelector< Scalar >::type	ScalarType
typedef StateAbstractTpl< Scalar >	StateAbstract
typedef MathBase::VectorXs	VectorXs

Public Member Functions
	ActionModelNumDiffTpl (std::shared_ptr< Base > model, bool with_gauss_approx=false)
	Initialize the numdiff action model.
virtual void	calc (const std::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x) override
	Compute the total cost value for nodes that depends only on the state.
virtual void	calc (const std::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &u) override
	Compute the next state and cost value.
virtual void	calcDiff (const std::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x) override
	Compute the derivatives of the cost functions with respect to the state only.
virtual void	calcDiff (const std::shared_ptr< ActionDataAbstract > &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>
ActionModelNumDiffTpl< NewScalar >	cast () const
	Cast the action numdiff model to a different scalar type.
virtual std::shared_ptr< ActionDataAbstract >	createData () override
	Create the action data.
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 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 diff-action numdiff model.
virtual void	quasiStatic (const std::shared_ptr< ActionDataAbstract > &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 ActionModelAbstractTpl< _Scalar >
	ActionModelAbstractTpl (const ActionModelAbstractTpl< Scalar > &other)
	Copy constructor.
	ActionModelAbstractTpl (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 action model.
virtual bool	checkData (const std::shared_ptr< ActionDataAbstract > &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< ActionDataAbstract > &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.

Public Attributes
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar	Scalar
Public Attributes inherited from ActionModelAbstractTpl< _Scalar >
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar	Scalar

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 ActionModelAbstractTpl< _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
Protected Member Functions inherited from ActionModelAbstractTpl< _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::ActionModelNumDiffTpl< _Scalar >

This class computes the numerical differentiation of an 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: ActionModelAbstractTpl(), calcDiff()

Definition at line 44 of file action.hpp.

Member Typedef Documentation

◆ ActionDataAbstract

template<typename _Scalar>

typedef ActionDataAbstractTpl<Scalar> ActionDataAbstract

Definition at line 50 of file action.hpp.

◆ Base

template<typename _Scalar>

typedef ActionModelAbstractTpl<Scalar> Base

Definition at line 51 of file action.hpp.

◆ Data

template<typename _Scalar>

typedef ActionDataNumDiffTpl<Scalar> Data

Definition at line 52 of file action.hpp.

◆ MathBase

template<typename _Scalar>

typedef MathBaseTpl<Scalar> MathBase

Definition at line 53 of file action.hpp.

◆ VectorXs

template<typename _Scalar>

typedef MathBaseTpl<Scalar>::VectorXs VectorXs

Definition at line 54 of file action.hpp.

◆ MatrixXs

template<typename _Scalar>

typedef MathBaseTpl<Scalar>::MatrixXs MatrixXs

Definition at line 55 of file action.hpp.

Constructor & Destructor Documentation

◆ ActionModelNumDiffTpl()

template<typename _Scalar>

ActionModelNumDiffTpl	(	std::shared_ptr< Base >	model,
		bool	with_gauss_approx = false )

explicit

Initialize the numdiff action model.

Parameters

[in]	model	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< ActionDataAbstract > &	data,
		const Eigen::Ref< const VectorXs > &	x,
		const Eigen::Ref< const VectorXs > &	u )

overridevirtual

Compute the next state and cost value.

Parameters

[in]	data	Action data
[in]	x	State point $\mathbf{x}\in\mathbb{R}^{ndx}$
[in]	u	Control input $\mathbf{u}\in\mathbb{R}^{nu}$

Implements ActionModelAbstractTpl< _Scalar >.

◆ calc() [2/2]

template<typename _Scalar>

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

overridevirtual

Compute the total cost value for nodes that depends only on the state.

It updates the total cost and the next state is not computed as it is not expected to change. This function is used in the terminal nodes of an optimal control problem.

Parameters

[in]	data	Action data
[in]	x	State point $\mathbf{x}\in\mathbb{R}^{ndx}$

Reimplemented from ActionModelAbstractTpl< _Scalar >.

◆ calcDiff() [1/2]

template<typename _Scalar>

virtual void calcDiff	(	const std::shared_ptr< ActionDataAbstract > &	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 linear-quadratic approximation of the action model (i.e. dynamical system and cost function).

Parameters

[in]	data	Action data
[in]	x	State point $\mathbf{x}\in\mathbb{R}^{ndx}$
[in]	u	Control input $\mathbf{u}\in\mathbb{R}^{nu}$

Implements ActionModelAbstractTpl< _Scalar >.

◆ calcDiff() [2/2]

template<typename _Scalar>

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

overridevirtual

Compute the derivatives of the cost functions with respect to the state only.

It updates the derivatives of the cost function with respect to the state only. This function is used in the terminal nodes of an optimal control problem.

Parameters

[in]	data	Action data
[in]	x	State point $\mathbf{x}\in\mathbb{R}^{ndx}$

Reimplemented from ActionModelAbstractTpl< _Scalar >.

◆ createData()

template<typename _Scalar>

virtual std::shared_ptr< ActionDataAbstract > createData ( )

overridevirtual

Create the action data.

Returns: the action data

Reimplemented from ActionModelAbstractTpl< _Scalar >.

◆ quasiStatic()

template<typename _Scalar>

virtual void quasiStatic	(	const std::shared_ptr< ActionDataAbstract > &	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 $\mathbf{f^q_x}\delta\mathbf{q}+\mathbf{f_u}\delta\mathbf{u}=\mathbf{0}$

Parameters

[in]	data	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 ActionModelAbstractTpl< _Scalar >.

◆ cast()

template<typename _Scalar>

template<typename NewScalar>

ActionModelNumDiffTpl< NewScalar > cast ( ) const

Cast the 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: ActionModelNumDiffTpl<NewScalar> An action model with the new scalar type.

◆ print()

template<typename _Scalar>

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

overridevirtual

Print relevant information of the diff-action numdiff model.

Parameters

[out] os Output stream object

Reimplemented from ActionModelAbstractTpl< _Scalar >.

Member Data Documentation

◆ Scalar

template<typename _Scalar>

EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar Scalar

Definition at line 49 of file action.hpp.

◆ has_control_limits_

template<typename _Scalar>

bool has_control_limits_

protected

Indicates whether any of the control limits is finite

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

◆ nr_

template<typename _Scalar>

std::size_t nr_

protected

< Indicates whether any of the control limits

Definition at line 329 of file action-base.hpp.

◆ nu_

template<typename _Scalar>

std::size_t nu_

protected

< Dimension of the cost residual

Definition at line 328 of file action-base.hpp.

◆ state_

template<typename _Scalar>

std::shared_ptr<StateAbstract> state_

protected

< Control dimension

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

◆ u_lb_

template<typename _Scalar>

VectorXs u_lb_

protected

< Model of the state

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

◆ u_ub_

template<typename _Scalar>

VectorXs u_ub_

protected

< Lower control limits

Definition at line 339 of file action-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/numdiff/action.hpp

Public Types

Public Member Functions

Public Attributes

Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ ActionDataAbstract

◆ Base

◆ Data

◆ MathBase

◆ VectorXs

◆ MatrixXs

Constructor & Destructor Documentation

◆ ActionModelNumDiffTpl()

Member Function Documentation

◆ calc() [1/2]

◆ calc() [2/2]

◆ calcDiff() [1/2]

◆ calcDiff() [2/2]

◆ createData()

◆ quasiStatic()

◆ cast()

◆ print()

Member Data Documentation

◆ Scalar

◆ has_control_limits_

◆ nr_

◆ nu_

◆ state_

◆ u_lb_

◆ u_ub_