Symplectic Euler integrator. More...

#include <euler.hpp>

Inheritance diagram for IntegratedActionModelEulerTpl< _Scalar >:

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 Types inherited from IntegratedActionModelAbstractTpl< _Scalar >
typedef ActionDataAbstractTpl< Scalar >	ActionDataAbstract

typedef ActionModelAbstractTpl< Scalar >	Base

typedef ControlParametrizationModelAbstractTpl< Scalar >	ControlParametrizationModelAbstract

typedef IntegratedActionDataAbstractTpl< Scalar >	Data

typedef DifferentialActionModelAbstractTpl< Scalar >	DifferentialActionModelAbstract

typedef MathBaseTpl< Scalar >	MathBase

typedef MathBase::MatrixXs	MatrixXs

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

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

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

virtual void	calcDiff (const std::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 std::shared_ptr< ActionDataAbstract > &data)
	Checks that a specific data belongs to this model.

virtual std::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 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))
	Computes the quasic static commands. More...

Public Member Functions inherited from IntegratedActionModelAbstractTpl< _Scalar >
	IntegratedActionModelAbstractTpl (std::shared_ptr< DifferentialActionModelAbstract > model, const Scalar time_step=Scalar(1e-3), const bool with_cost_residual=true)
	Initialize the integrator. More...

	IntegratedActionModelAbstractTpl (std::shared_ptr< DifferentialActionModelAbstract > model, std::shared_ptr< ControlParametrizationModelAbstract > control, const Scalar time_step=Scalar(1e-3), const bool with_cost_residual=true)
	Initialize the integrator. More...

	DEPRECATED ("The DifferentialActionModel should be set at construction time", void set_differential(std::shared_ptr< DifferentialActionModelAbstract > model))

const std::shared_ptr< ControlParametrizationModelAbstract > &	get_control () const
	Return the control parametrization model associated to this integrated action model.

const std::shared_ptr< DifferentialActionModelAbstract > &	get_differential () const
	Return the differential action model associated to this integrated action model.

const Scalar	get_dt () const
	Return the time step used for the integration.

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.

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.

void	set_dt (const Scalar dt)
	Set the time step for the integration.

Public Member Functions inherited from ActionModelAbstractTpl< _Scalar >
	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. More...

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

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 IntegratedActionModelAbstractTpl< _Scalar >
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef _Scalar	Scalar

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

Protected Attributes
std::size_t	ng_
	< Differential action model

std::size_t	nh_
	< Number of inequality constraints

std::size_t	nu_
	< Number of equality constraints

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

Protected Attributes inherited from IntegratedActionModelAbstractTpl< _Scalar >
std::shared_ptr< ControlParametrizationModelAbstract >	control_
	Model of the control parametrization.

std::shared_ptr< DifferentialActionModelAbstract >	differential_
	Differential action model that is integrated.

bool	has_control_limits_

std::size_t	nr_

std::size_t	nu_
	< Dimension of the cost residual

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

Scalar	time_step2_
	Square of the time step used for integration.

Scalar	time_step_
	Time step used for integration.

VectorXs	u_lb_
	< Model of the state

VectorXs	u_ub_
	< Lower control limits

bool	with_cost_residual_
	Flag indicating whether a cost residual is used.

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 IntegratedActionModelAbstractTpl< _Scalar >
void	init ()
	< Upper control limits

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::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 37 of file euler.hpp.

Constructor & Destructor Documentation

◆ IntegratedActionModelEulerTpl() [1/2]

IntegratedActionModelEulerTpl	(	std::shared_ptr< DifferentialActionModelAbstract >	model,
		std::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	(	std::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 std::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 \(\mathbf{u}\in\mathbb{R}^{nu}\)

Implements ActionModelAbstractTpl< _Scalar >.

◆ calc() [2/2]

virtual void calc	(	const std::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 \(\mathbf{x}\in\mathbb{R}^{ndx}\)

Reimplemented from ActionModelAbstractTpl< _Scalar >.

◆ calcDiff() [1/2]

virtual void calcDiff	(	const std::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 \(\mathbf{u}\in\mathbb{R}^{nu}\)

Implements ActionModelAbstractTpl< _Scalar >.

◆ calcDiff() [2/2]

virtual void calcDiff	(	const std::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 \(\mathbf{x}\in\mathbb{R}^{ndx}\)

Reimplemented from ActionModelAbstractTpl< _Scalar >.

◆ createData()

virtual std::shared_ptr<ActionDataAbstract> createData ( )

virtual

Create the symplectic Euler data.

Returns: the symplectic Euler data

Reimplemented from IntegratedActionModelAbstractTpl< _Scalar >.

◆ quasiStatic()

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)`
	)

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

Reimplemented from ActionModelAbstractTpl< _Scalar >.

◆ print()

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

virtual

Print relevant information of the Euler integrator model.

Parameters

[out] os Output stream object

Reimplemented from ActionModelAbstractTpl< _Scalar >.

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/integrator/euler.hpp

Public Types

Public Member Functions

Public Attributes

Protected Attributes

Additional Inherited Members

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 >