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 ScalarSelector< Scalar >::type	ScalarType
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.
	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.
virtual void	calc (const std::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x) override
	Integrate the total cost value for nodes that depends only on the state using symplectic Euler scheme.
virtual void	calc (const std::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &u) override
	Integrate the differential action model using symplectic Euler scheme.
virtual void	calcDiff (const std::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x) override
	Compute the partial derivatives of the cost.
virtual void	calcDiff (const std::shared_ptr< ActionDataAbstract > &data, const Eigen::Ref< const VectorXs > &x, const Eigen::Ref< const VectorXs > &u) override
	Compute the partial derivatives of the symplectic Euler integrator.
template<typename NewScalar>
IntegratedActionModelEulerTpl< NewScalar >	cast () const
	Cast the Euler integrated-action model to a different scalar type.
virtual bool	checkData (const std::shared_ptr< ActionDataAbstract > &data) override
	Checks that a specific data belongs to this model.
virtual std::shared_ptr< ActionDataAbstract >	createData () override
	Create the symplectic Euler data.
virtual void	print (std::ostream &os) const override
	Print relevant information of the Euler integrator 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.
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.
	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.
	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 override
	Return the lower bound of the inequality constraints.
virtual const VectorXs &	get_g_ub () const override
	Return the upper bound of the inequality constraints.
virtual std::size_t	get_ng () const override
	Return the number of inequality constraints.
virtual std::size_t	get_ng_T () const override
	Return the number of inequality terminal constraints.
virtual std::size_t	get_nh () const override
	Return the number of equality constraints.
virtual std::size_t	get_nh_T () const override
	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 (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.
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::shared_ptr< ControlParametrizationModelAbstract >	control_
	Model of the control parametrization.
std::shared_ptr< DifferentialActionModelAbstract >	differential_
	< Control parametrization
std::size_t	nu_
	< Number of equality constraints
std::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
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 >
	IntegratedActionModelAbstractTpl ()
	< Upper control limits
void	init ()
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.

Member Typedef Documentation

◆ MathBase

template<typename _Scalar>

typedef MathBaseTpl<Scalar> MathBase

Definition at line 44 of file euler.hpp.

◆ Base

template<typename _Scalar>

typedef IntegratedActionModelAbstractTpl<Scalar> Base

Definition at line 45 of file euler.hpp.

◆ Data

template<typename _Scalar>

typedef IntegratedActionDataEulerTpl<Scalar> Data

Definition at line 46 of file euler.hpp.

◆ ActionDataAbstract

template<typename _Scalar>

typedef ActionDataAbstractTpl<Scalar> ActionDataAbstract

Definition at line 47 of file euler.hpp.

◆ DifferentialActionModelAbstract

template<typename _Scalar>

typedef DifferentialActionModelAbstractTpl<Scalar> DifferentialActionModelAbstract

Definition at line 49 of file euler.hpp.

◆ ControlParametrizationModelAbstract

template<typename _Scalar>

typedef ControlParametrizationModelAbstractTpl<Scalar> ControlParametrizationModelAbstract

Definition at line 51 of file euler.hpp.

◆ ControlParametrizationDataAbstract

template<typename _Scalar>

typedef ControlParametrizationDataAbstractTpl<Scalar> ControlParametrizationDataAbstract

Definition at line 53 of file euler.hpp.

◆ VectorXs

template<typename _Scalar>

typedef MathBase::VectorXs VectorXs

Definition at line 54 of file euler.hpp.

◆ MatrixXs

template<typename _Scalar>

typedef MathBase::MatrixXs MatrixXs

Definition at line 55 of file euler.hpp.

Constructor & Destructor Documentation

◆ IntegratedActionModelEulerTpl() [1/2]

template<typename _Scalar>

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]

template<typename _Scalar>

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]

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

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]

template<typename _Scalar>

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

overridevirtual

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]

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 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]

template<typename _Scalar>

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

overridevirtual

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()

template<typename _Scalar>

virtual std::shared_ptr< ActionDataAbstract > createData ( )

overridevirtual

Create the symplectic Euler data.

Returns: the symplectic Euler data

Reimplemented from IntegratedActionModelAbstractTpl< _Scalar >.

◆ cast()

template<typename _Scalar>

template<typename NewScalar>

IntegratedActionModelEulerTpl< NewScalar > cast ( ) const

Cast the Euler integrated-action 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: IntegratedActionModelEulerTpl<NewScalar> An action model with the new scalar type.

◆ checkData()

template<typename _Scalar>

virtual bool checkData ( const std::shared_ptr< ActionDataAbstract > & data )

overridevirtual

Checks that a specific data belongs to this model.

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	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()

template<typename _Scalar>

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

overridevirtual

Print relevant information of the Euler integrator 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 43 of file euler.hpp.

◆ control_

template<typename _Scalar>

std::shared_ptr<ControlParametrizationModelAbstract> control_

protected

Model of the control parametrization.

Definition at line 173 of file integ-action-base.hpp.

◆ differential_

template<typename _Scalar>

std::shared_ptr<DifferentialActionModelAbstract> differential_

protected

< Control parametrization

Definition at line 171 of file integ-action-base.hpp.

◆ time_step2_

template<typename _Scalar>

Scalar time_step2_

protected

< Model of the state

Definition at line 176 of file integ-action-base.hpp.

◆ time_step_

template<typename _Scalar>

Scalar time_step_

protected

< Square of the time step used for integration

Definition at line 175 of file integ-action-base.hpp.

◆ with_cost_residual_

template<typename _Scalar>

bool with_cost_residual_

protected

< Time step used for integration

Definition at line 178 of file integ-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/integrator/euler.hpp

Public Types

Public Member Functions

Public Attributes

Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ MathBase

◆ Base

◆ Data

◆ ActionDataAbstract

◆ DifferentialActionModelAbstract

◆ ControlParametrizationModelAbstract

◆ ControlParametrizationDataAbstract

◆ VectorXs

◆ MatrixXs

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()

◆ cast()

◆ checkData()

◆ quasiStatic()

◆ print()

Member Data Documentation

◆ Scalar

◆ control_

◆ differential_

◆ time_step2_

◆ time_step_

◆ with_cost_residual_