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 StateAbstractTpl< Scalar >	StateAbstract

typedef MathBase::VectorXs	VectorXs

Public Member Functions
	ActionModelNumDiffTpl (boost::shared_ptr< Base > model, bool with_gauss_approx=false)
	Initialize the numdiff action model. More...

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

virtual void	calc (const boost::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &u)
	Compute the next state and cost value. More...

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

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

virtual boost::shared_ptr< ActionDataAbstract >	createData ()
	Create the action data. More...

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

const boost::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
	Print relevant information of the diff-action numdiff model. More...

virtual void	quasiStatic (const boost::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))
	Computes the quasic static commands. More...

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

Public Member Functions inherited from ActionModelAbstractTpl< _Scalar >
	ActionModelAbstractTpl (boost::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)
	Initialize the action model. More...

virtual bool	checkData (const boost::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_nh () const
	Return the number of equality 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 boost::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 boost::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

boost::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	nh_
	Number of equality constraints.

std::size_t	nr_
	Dimension of the cost residual.

std::size_t	nu_
	Control dimension.

boost::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 46 of file action.hpp.

Constructor & Destructor Documentation

◆ ActionModelNumDiffTpl()

ActionModelNumDiffTpl	(	boost::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]

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

virtual

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]

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

virtual

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]

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

virtual

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]

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

virtual

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()

virtual boost::shared_ptr<ActionDataAbstract> createData ( )

virtual

Create the action data.

Returns: the action data

Reimplemented from ActionModelAbstractTpl< _Scalar >.

◆ quasiStatic()

virtual void quasiStatic	(	const boost::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)`
	)

virtual

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 >.

◆ print()

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

virtual

Print relevant information of the diff-action numdiff model.

Parameters

[out] os Output stream object

Reimplemented from ActionModelAbstractTpl< _Scalar >.

Member Data Documentation

◆ has_control_limits_

bool has_control_limits_

protected

Indicates whether any of the control limits is finite

Definition at line 315 of file action-base.hpp.

◆ nr_

std::size_t nr_

protected

< Indicates whether any of the control limits

Definition at line 306 of file 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/action.hpp

Public Types

Public Member Functions

Public Attributes

Protected Attributes

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

◆ ActionModelNumDiffTpl()

Member Function Documentation

◆ calc() [1/2]

◆ calc() [2/2]

◆ calcDiff() [1/2]

◆ calcDiff() [2/2]

◆ createData()

◆ quasiStatic()

◆ print()

Member Data Documentation

◆ has_control_limits_

◆ nr_

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