ActionModelNumDiffTpl< _Scalar > Class Template Reference

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

#include <crocoddyl/core/numdiff/action.hpp>

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 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)
	Compute the total cost value for nodes that depends only on the state. More...
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 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.
void	set_disturbance (const Scalar disturbance)
	Modify the disturbance used in the numerical differentiation routine.

Public Attributes
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar	Scalar

Protected Attributes
bool	has_control_limits_
	Indicates whether any of the control limits is finite.
std::size_t	nr_
	< Indicates whether any of the control limits
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
VectorXs	unone_
	< Upper control limits

Detailed Description

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

This class computes the numerical differentiation of an action model.

It computes 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 215 of file fwd.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 \(\mathbf{u}\in\mathbb{R}^{nu}\)

calc() [2/2]

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

virtual

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 \(\mathbf{x}\in\mathbb{R}^{ndx}\)

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 \(\mathbf{u}\in\mathbb{R}^{nu}\)

calcDiff() [2/2]

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

virtual

createData()

virtual boost::shared_ptr<ActionDataAbstract> createData ( )

virtual

Create the action data.

Returns

the action data

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

• include/crocoddyl/core/fwd.hpp
• include/crocoddyl/core/numdiff/action.hpp