Symplectic Euler integrator. More...

#include <crocoddyl/core/integrator/euler.hpp>

Public Types
typedef ActionDataAbstractTpl< Scalar >	ActionDataAbstract

typedef IntegratedActionModelAbstractTpl< Scalar >	Base

typedef ControlParametrizationDataAbstractTpl< Scalar >	ControlParametrizationDataAbstract

typedef ControlParametrizationModelAbstractTpl< Scalar >	ControlParametrizationModelAbstract

typedef IntegratedActionDataEulerTpl< Scalar >	Data

typedef DifferentialActionModelAbstractTpl< Scalar >	DifferentialActionModelAbstract

typedef MathBaseTpl< Scalar >	MathBase

typedef MathBase::MatrixXs	MatrixXs

typedef MathBase::VectorXs	VectorXs

Public Member Functions
	IntegratedActionModelEulerTpl (boost::shared_ptr< DifferentialActionModelAbstract > model, boost::shared_ptr< ControlParametrizationModelAbstract > control, const Scalar time_step=Scalar(1e-3), const bool with_cost_residual=true)
	Initialize the symplectic Euler integrator. More...

	IntegratedActionModelEulerTpl (boost::shared_ptr< DifferentialActionModelAbstract > model, const Scalar time_step=Scalar(1e-3), const bool with_cost_residual=true)
	Initialize the symplectic Euler integrator. More...

virtual void	calc (const boost::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x)
	Integrate the total cost value for nodes that depends only on the state using symplectic Euler scheme. More...

virtual void	calc (const boost::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &u)
	Integrate the differential action model using symplectic Euler scheme. More...

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

virtual void	calcDiff (const boost::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &u)
	Compute the partial derivatives of the symplectic Euler integrator. More...

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

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

virtual void	print (std::ostream &os) const
	Print relevant information of the Euler integrator 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...

Public Attributes
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar	Scalar

Protected Attributes
boost::shared_ptr< ControlParametrizationModelAbstract >	control_
	Model of the control parametrization.

boost::shared_ptr< DifferentialActionModelAbstract >	differential_
	< Control parametrization

std::size_t	nu_
	< Differential action model

boost::shared_ptr< StateAbstract >	state_
	< Dimension of the control

Scalar	time_step2_
	< Model of the state

Scalar	time_step_
	< Square of the time step used for integration

bool	with_cost_residual_
	< Time step used for integration

Detailed Description

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

Symplectic Euler integrator.

It applies a symplectic Euler integration scheme to a differential (i.e., continuous time) action model.

This symplectic Euler scheme introduces also the possibility to parametrize the control trajectory inside an integration step, for instance using polynomials. This requires introducing some notation to clarify the difference between the control inputs of the differential model and the control inputs to the integrated model. We have decided to use \(\mathbf{w}\) to refer to the control inputs of the differential model and \(\mathbf{u}\) for the control inputs of the integrated action model. Note that the zero-order (e.g., ControlParametrizationModelPolyZeroTpl) are the only ones that make sense to use within this integrator.

See also: calc(), calcDiff(), createData()

Definition at line 60 of file fwd.hpp.

Constructor & Destructor Documentation

◆ IntegratedActionModelEulerTpl() [1/2]

IntegratedActionModelEulerTpl	(	boost::shared_ptr< DifferentialActionModelAbstract >	model,
		boost::shared_ptr< ControlParametrizationModelAbstract >	control,
		const Scalar	time_step = `Scalar(1e-3)`,
		const bool	with_cost_residual = `true`
	)

Initialize the symplectic Euler integrator.

Parameters

[in]	model	Differential action model
[in]	control	Control parametrization
[in]	time_step	Step time (default 1e-3)
[in]	with_cost_residual	Compute cost residual (default true)

◆ IntegratedActionModelEulerTpl() [2/2]

IntegratedActionModelEulerTpl	(	boost::shared_ptr< DifferentialActionModelAbstract >	model,
		const Scalar	time_step = `Scalar(1e-3)`,
		const bool	with_cost_residual = `true`
	)

Initialize the symplectic Euler integrator.

This initialization uses ControlParametrizationPolyZeroTpl for the control parametrization.

Parameters

[in]	model	Differential action model
[in]	time_step	Step time (default 1e-3)
[in]	with_cost_residual	Compute cost residual (default true)

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

Integrate the differential action model using symplectic Euler scheme.

Parameters

[in]	data	Symplectic Euler 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

Integrate the total cost value for nodes that depends only on the state using symplectic Euler scheme.

It computes the total cost and defines the next state as the current one. This function is used in the terminal nodes of an optimal control problem.

Parameters

[in]	data	Symplectic Euler 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 partial derivatives of the symplectic Euler integrator.

Parameters

[in]	data	Symplectic Euler 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

Compute the partial derivatives of the cost.

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	Symplectic Euler data
[in]	x	State point \(\mathbf{x}\in\mathbb{R}^{ndx}\)

◆ createData()

virtual boost::shared_ptr<ActionDataAbstract> createData ( )

virtual

Create the symplectic Euler data.

Returns: the symplectic Euler data

◆ 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	Symplectic Euler 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

◆ print()

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

virtual

Print relevant information of the Euler integrator model.

Parameters

[out] os Output stream object

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

include/crocoddyl/core/fwd.hpp
include/crocoddyl/core/integrator/euler.hpp

Public Types

Public Member Functions

Public Attributes

Protected Attributes

Detailed Description

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

Constructor & Destructor Documentation

◆ IntegratedActionModelEulerTpl() [1/2]

◆ IntegratedActionModelEulerTpl() [2/2]

Member Function Documentation

◆ calc() [1/2]

◆ calc() [2/2]

◆ calcDiff() [1/2]

◆ calcDiff() [2/2]

◆ createData()

◆ quasiStatic()

◆ print()

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