Midpoint integration rule. More...

#include <aligator/modelling/dynamics/integrator-midpoint.hpp>

Inheritance diagram for aligator::dynamics::IntegratorMidpointTpl< _Scalar >:

Collaboration diagram for aligator::dynamics::IntegratorMidpointTpl< _Scalar >:

Public Types
using	Scalar = _Scalar

using	Base = IntegratorAbstractTpl<Scalar>

using	ContinuousDynamics = ContinuousDynamicsAbstractTpl<Scalar>

using	Manifold = ManifoldAbstractTpl<Scalar>

using	Data = IntegratorMidpointDataTpl<Scalar>

Public Types inherited from aligator::dynamics::IntegratorAbstractTpl< _Scalar >
using	Scalar = _Scalar

using	Base = DynamicsModelTpl<Scalar>

using	BaseData = DynamicsDataTpl<Scalar>

using	ContinuousDynamics = ContinuousDynamicsAbstractTpl<Scalar>

Public Types inherited from aligator::DynamicsModelTpl< _Scalar >
using	Scalar = _Scalar

using	Base = StageFunctionTpl<Scalar>

using	Data = DynamicsDataTpl<Scalar>

using	Manifold = ManifoldAbstractTpl<Scalar>

using	ManifoldPtr = shared_ptr<Manifold>

Public Types inherited from aligator::StageFunctionTpl< _Scalar >
using	Scalar = _Scalar

using	Data = StageFunctionDataTpl<Scalar>

Public Member Functions
	ALIGATOR_DYNAMIC_TYPEDEFS (Scalar)

	IntegratorMidpointTpl (const shared_ptr< ContinuousDynamics > &cont_dynamics, const Scalar timestep)

void	evaluate (const ConstVectorRef &x, const ConstVectorRef &u, const ConstVectorRef &y, DynamicsDataTpl< Scalar > &data) const

void	computeJacobians (const ConstVectorRef &x, const ConstVectorRef &u, const ConstVectorRef &y, DynamicsDataTpl< Scalar > &data) const

shared_ptr< DynamicsDataTpl< Scalar > >	createData () const
	Instantiate a Data object.

Public Member Functions inherited from aligator::dynamics::IntegratorAbstractTpl< _Scalar >
	IntegratorAbstractTpl (const shared_ptr< ContinuousDynamics > &cont_dynamics)
	Constructor from instances of DynamicsType.

virtual	~IntegratorAbstractTpl ()=default

Public Member Functions inherited from aligator::DynamicsModelTpl< _Scalar >
	ALIGATOR_DYNAMIC_TYPEDEFS (Scalar)

const Manifold &	space () const
	State space for the input.

const Manifold &	space_next () const
	State space for the output of this dynamics model.

virtual bool	is_explicit () const
	Check if this dynamics model is implicit or explicit.

int	nx1 () const

int	nx2 () const

	DynamicsModelTpl (ManifoldPtr space, const int nu)
	Constructor for dynamics.

	DynamicsModelTpl (ManifoldPtr space, const int nu, ManifoldPtr space2)
	Constructor for dynamics. This constructor assumes same dimension for the current and next state.

Public Member Functions inherited from aligator::StageFunctionTpl< _Scalar >
	ALIGATOR_DYNAMIC_TYPEDEFS (Scalar)

	StageFunctionTpl (const int ndx1, const int nu, const int ndx2, const int nr)

	StageFunctionTpl (const int ndx, const int nu, const int nr)
	Constructor where ndx2 = ndx1.

virtual void	evaluate (const ConstVectorRef &x, const ConstVectorRef &u, const ConstVectorRef &y, Data &data) const =0
	Evaluate the function.

virtual void	computeJacobians (const ConstVectorRef &x, const ConstVectorRef &u, const ConstVectorRef &y, Data &data) const =0
	Compute Jacobians of this function.

virtual void	computeVectorHessianProducts (const ConstVectorRef &x, const ConstVectorRef &u, const ConstVectorRef &y, const ConstVectorRef &lbda, Data &data) const
	Compute the vector-hessian products of this function.

virtual	~StageFunctionTpl ()=default

Public Attributes
Scalar	timestep_

Public Attributes inherited from aligator::dynamics::IntegratorAbstractTpl< _Scalar >
shared_ptr< ContinuousDynamics >	continuous_dynamics_
	The underlying continuous dynamics.

Public Attributes inherited from aligator::DynamicsModelTpl< _Scalar >
ManifoldPtr	space_
	State space for the input.

ManifoldPtr	space_next_
	State space for the output of this dynamics model.

Public Attributes inherited from aligator::StageFunctionTpl< _Scalar >
const int	ndx1
	Current state dimension.

const int	nu
	Control dimension.

const int	ndx2
	Next state dimension.

const int	nr
	Function codimension.

Detailed Description

template<typename _Scalar>
struct aligator::dynamics::IntegratorMidpointTpl< _Scalar >

Midpoint integration rule.

The rule is described, for general DAEs, as

\[ \phi(x_k, u_k, x_{k+1}) = g(\hat{x}_0, u_k, \frac{x_{k+1}\ominus x_k}{h}) = 0. \]

where \(\hat{x}_0 = \mathrm{Interp}_{1/2}(x_k, x_{k+1})\). Even for ODEs, it is still an implicit integration rule.

The Jacobians are:

\[ \frac{\partial f}{\partial z} = \frac{\partial g}{\partial \hat{x}_0} \frac{\partial \hat{x}_0}{\partial z} + \frac{\partial g}{\partial z} + \frac{\partial g}{\partial v} \frac{\partial v}{\partial z} \]

Definition at line 28 of file integrator-midpoint.hpp.

Member Typedef Documentation

◆ Scalar

template<typename _Scalar >

using aligator::dynamics::IntegratorMidpointTpl< _Scalar >::Scalar = _Scalar

Definition at line 29 of file integrator-midpoint.hpp.

◆ Base

template<typename _Scalar >

using aligator::dynamics::IntegratorMidpointTpl< _Scalar >::Base = IntegratorAbstractTpl<Scalar>

Definition at line 31 of file integrator-midpoint.hpp.

◆ ContinuousDynamics

template<typename _Scalar >

using aligator::dynamics::IntegratorMidpointTpl< _Scalar >::ContinuousDynamics = ContinuousDynamicsAbstractTpl<Scalar>

Definition at line 32 of file integrator-midpoint.hpp.

◆ Manifold

template<typename _Scalar >

using aligator::dynamics::IntegratorMidpointTpl< _Scalar >::Manifold = ManifoldAbstractTpl<Scalar>

Definition at line 33 of file integrator-midpoint.hpp.

◆ Data

template<typename _Scalar >

using aligator::dynamics::IntegratorMidpointTpl< _Scalar >::Data = IntegratorMidpointDataTpl<Scalar>

Definition at line 34 of file integrator-midpoint.hpp.

Constructor & Destructor Documentation

◆ IntegratorMidpointTpl()

template<typename _Scalar >

aligator::dynamics::IntegratorMidpointTpl< _Scalar >::IntegratorMidpointTpl	(	const shared_ptr< ContinuousDynamics > &	cont_dynamics,
		const Scalar	timestep )

Member Function Documentation

◆ ALIGATOR_DYNAMIC_TYPEDEFS()

template<typename _Scalar >

aligator::dynamics::IntegratorMidpointTpl< _Scalar >::ALIGATOR_DYNAMIC_TYPEDEFS ( Scalar )

◆ evaluate()

template<typename _Scalar >

void aligator::dynamics::IntegratorMidpointTpl< _Scalar >::evaluate	(	const ConstVectorRef &	x,
		const ConstVectorRef &	u,
		const ConstVectorRef &	y,
		DynamicsDataTpl< Scalar > &	data ) const

◆ computeJacobians()

template<typename _Scalar >

void aligator::dynamics::IntegratorMidpointTpl< _Scalar >::computeJacobians	(	const ConstVectorRef &	x,
		const ConstVectorRef &	u,
		const ConstVectorRef &	y,
		DynamicsDataTpl< Scalar > &	data ) const

◆ createData()

template<typename _Scalar >

shared_ptr< DynamicsDataTpl< Scalar > > aligator::dynamics::IntegratorMidpointTpl< _Scalar >::createData ( ) const

virtual

Instantiate a Data object.

Reimplemented from aligator::dynamics::IntegratorAbstractTpl< _Scalar >.

Member Data Documentation

◆ timestep_

template<typename _Scalar >

Scalar aligator::dynamics::IntegratorMidpointTpl< _Scalar >::timestep_

Definition at line 36 of file integrator-midpoint.hpp.

The documentation for this struct was generated from the following file:

include/aligator/modelling/dynamics/integrator-midpoint.hpp

Public Types

Public Member Functions

Public Attributes

Detailed Description

Member Typedef Documentation

◆ Scalar

◆ Base

◆ ContinuousDynamics

◆ Manifold

◆ Data

Constructor & Destructor Documentation

◆ IntegratorMidpointTpl()

Member Function Documentation

◆ ALIGATOR_DYNAMIC_TYPEDEFS()

◆ evaluate()

◆ computeJacobians()

◆ createData()

Member Data Documentation

◆ timestep_