Interface for numerical integrators (explicit and implicit) More...

#include <integrator_interface.h>

Inheritance diagram for corbo::NumericalIntegratorExplicitInterface:

[legend]

Public Types
using	Ptr = std::shared_ptr< NumericalIntegratorExplicitInterface >

using	UnaryFunction = const std::function< void(const Eigen::VectorXd &, Eigen::Ref< Eigen::VectorXd >)>

using	UPtr = std::unique_ptr< NumericalIntegratorExplicitInterface >

Public Types inherited from corbo::DynamicsEvalInterface
using	InputVector = Eigen::VectorXd

using	Ptr = std::shared_ptr< DynamicsEvalInterface >

using	StateVector = Eigen::VectorXd

using	UPtr = std::unique_ptr< DynamicsEvalInterface >

Public Member Functions
void	computeEqualityConstraint (const StateVector &x1, const InputVector &u1, const StateVector &x2, double dt, const SystemDynamicsInterface &system, Eigen::Ref< Eigen::VectorXd > error) override
	Compute error between two consecutive (discrete) states. More...

void	computeEqualityConstraint (const Eigen::Ref< const Eigen::VectorXd > &x1, const Eigen::Ref< const Eigen::VectorXd > &x2, double dt, const UnaryFunction &fun, Eigen::Ref< Eigen::VectorXd > error)

virtual int	getConvergenceOrder () const =0
	Return the convergence order. More...

DynamicsEvalInterface::Ptr	getInstance () const override=0
	Return a newly created shared instance of the implemented class. More...

virtual void	initialize (int state_dim)
	Allocate memory for a given state dimension. More...

bool	interpolate (const Eigen::Ref< const Eigen::VectorXd > &x1, const Eigen::Ref< const Eigen::VectorXd > &u1, const Eigen::Ref< const Eigen::VectorXd > &, const Eigen::Ref< const Eigen::VectorXd > &, double dt, const SystemDynamicsInterface &system, const Range &range, std::vector< Eigen::VectorXd > &states, std::vector< Eigen::VectorXd > &controls) override

virtual void	solveIVP (const Eigen::VectorXd &x1, double dt, const UnaryFunction &fun, Eigen::Ref< Eigen::VectorXd > x2)=0
	Solution of the initial value problem. More...

virtual void	solveIVP (const StateVector &x1, const InputVector &u1, double dt, const SystemDynamicsInterface &system, Eigen::Ref< Eigen::VectorXd > x2)=0
	Solution of the initial value problem. More...

virtual	~NumericalIntegratorExplicitInterface ()
	Virtual destructor. More...

Public Member Functions inherited from corbo::DynamicsEvalInterface
virtual bool	interpolate (const std::vector< const Eigen::VectorXd > &x, const std::vector< const Eigen::VectorXd > &u, double dt, const SystemDynamicsInterface &system, const Range &range, std::vector< Eigen::VectorXd > &states, std::vector< Eigen::VectorXd > &controls)

virtual	~DynamicsEvalInterface ()
	Virtual destructor. More...

Additional Inherited Members
Static Public Member Functions inherited from corbo::DynamicsEvalInterface
static Factory< DynamicsEvalInterface > &	getFactory ()
	Get access to the accociated factory. More...

Detailed Description

Interface for numerical integrators (explicit and implicit)

Explicit numerical integrators in the context of ordinary or partial differential equations determine the integral value only based on the previous or current time instance, e.g.:

$// * x(t_0 + \Delta t) = \int_{t_0}^{t_0+\Delta T} f(x(t_0), t) dt // *$

.

Implicit methods require the solution of a (nonlinear) equation, since
they also depend on the solution itself:

$// * x(t_0 + \Delta t) = \int_{t_0}^{t_0+\Delta T} f(x(t_0+ \Delta T), x(t_0), t) dt // *$

.

This generic interface mainly provides access to the underlying quadrature rules.
These might be used as part of an optimization or might be solved via root-finding directly.
For a direct use of integrators you might refer to the subclass NumericalIntegratorExplicitInterface.

@remark This interface is provided with factory support.

@see NumericalIntegratorExplicitInterface FiniteDifferencesInterface

@author Christoph Rösmann (christoph.roesmann@tu-dortmund.de)

Todo:: This interface is not yet completed (messages, subclasses, ...)

Allocate memory for a given state dimension

Remarks: This method is optional and not guaranteed to be called, but if so this might speed up computation.

Parameters

[in] state_dim Expected dimension of the state vector Compute equality constraint containing the implicit quadrature/interpolation formula (system dynamics specialization)

$// * e = \int_{t=0}^{t=\Delta T} f(x(t), u_1) dt - x_2 = 0 // *$

.

    @param[in]  x1      Initial state vector [SystemDynamicsInterface::getStateDimension() x 1]
    @param[in]  u1      Constant control input vector [SystemDynamicsInterface::getInputDimension() x 1]
    @param[in]  x2      Final state vector [SystemDynamicsInterface::getStateDimension() x 1]
    @param[in]  dt      Time interval length
    @param[in]  system  System dynamics object
    @param[out] error   Resulting error [SystemDynamicsInterface::getStateDimension() x 1] (must be preallocated)

Compute equality constraint containing the implicit quadrature/interpolation formula (unary function specialization)

$// * e = \int_{t=0}^{t=\Delta T} f(x(t)) dt - x_2 = 0 // *$

.

    @param[in]  x1      Initial function argument
    @param[in]  x2      Final function argument
    @param[in]  dt      Time interval length
    @param[in]  fun     f(x) to be integrated in the interval [0, dt]
    @param[out] error   Resulting error [SystemDynamicsInterface::getStateDimension() x 1] (must be preallocated)

Interface for explicit numerical integrators

Explicit numerical integrators in the context of ordinary or partial differential equations determine the integral value only based on the previous or current time instance, e.g.:

$x(t_0 + \Delta t) = \int_{t_0}^{t_0+\Delta T} f(x(t_0), t) dt$

.

Remarks: This interface is provided with factory support (DynamicsEval).

See also: NumericalIntegratorInterface FiniteDifferencesInterface

Author: Christoph Rösmann (chris.nosp@m.toph.nosp@m..roes.nosp@m.mann.nosp@m.@tu-d.nosp@m.ortm.nosp@m.und.d.nosp@m.e)

Definition at line 158 of file integrator_interface.h.

Member Typedef Documentation

◆ Ptr

using corbo::NumericalIntegratorExplicitInterface::Ptr = std::shared_ptr<NumericalIntegratorExplicitInterface>

Definition at line 161 of file integrator_interface.h.

◆ UnaryFunction

using corbo::NumericalIntegratorExplicitInterface::UnaryFunction = const std::function<void(const Eigen::VectorXd&, Eigen::Ref<Eigen::VectorXd>)>

Definition at line 164 of file integrator_interface.h.

◆ UPtr

using corbo::NumericalIntegratorExplicitInterface::UPtr = std::unique_ptr<NumericalIntegratorExplicitInterface>

Definition at line 162 of file integrator_interface.h.

Constructor & Destructor Documentation

◆ ~NumericalIntegratorExplicitInterface()

virtual corbo::NumericalIntegratorExplicitInterface::~NumericalIntegratorExplicitInterface ( )

inlinevirtual

Virtual destructor.

Definition at line 169 of file integrator_interface.h.

Member Function Documentation

◆ computeEqualityConstraint() [1/2]

void corbo::NumericalIntegratorExplicitInterface::computeEqualityConstraint	(	const StateVector &	x1,
		const InputVector &	u1,
		const StateVector &	x2,
		double	dt,
		const SystemDynamicsInterface &	system,
		Eigen::Ref< Eigen::VectorXd >	error
	)

inlineoverridevirtual

Compute error between two consecutive (discrete) states.

$e = f(x,u,t) - \dot{x}$

.

Remarks: We require no alias between error and all other parameters!

Parameters

[in]	x1	Initial state vector [SystemDynamicsInterface::getStateDimension() x 1]
[in]	u1	Constant control input vector [SystemDynamicsInterface::getInputDimension() x 1]
[in]	x2	Final state vector [SystemDynamicsInterface::getStateDimension() x 1]
[in]	dt	Time interval length
[in]	system	System dynamics object
[out]	error	Resulting error [SystemDynamicsInterface::getStateDimension() x 1] (must be preallocated)

Implements corbo::DynamicsEvalInterface.

Definition at line 217 of file integrator_interface.h.

◆ computeEqualityConstraint() [2/2]

void corbo::NumericalIntegratorExplicitInterface::computeEqualityConstraint	(	const Eigen::Ref< const Eigen::VectorXd > &	x1,
		const Eigen::Ref< const Eigen::VectorXd > &	x2,
		double	dt,
		const UnaryFunction &	fun,
		Eigen::Ref< Eigen::VectorXd >	error
	)

inline

Definition at line 224 of file integrator_interface.h.

◆ getConvergenceOrder()

virtual int corbo::NumericalIntegratorExplicitInterface::getConvergenceOrder ( ) const

pure virtual

Return the convergence order.

Implemented in corbo::IntegratorMultiStageScaled, corbo::IntegratorMultiStageFixedStep, corbo::IntegratorAdaptiveStepSize, corbo::IntegratorExplicitRungeKutta7, corbo::IntegratorExplicitRungeKutta6, corbo::IntegratorExplicitRungeKutta5, corbo::IntegratorExplicitRungeKutta4, corbo::IntegratorExplicitRungeKutta3, corbo::IntegratorExplicitRungeKutta2, and corbo::IntegratorExplicitEuler.

◆ getInstance()

DynamicsEvalInterface::Ptr corbo::NumericalIntegratorExplicitInterface::getInstance ( ) const

overridepure virtual

Return a newly created shared instance of the implemented class.

Implements corbo::DynamicsEvalInterface.

Implemented in corbo::IntegratorMultiStageScaled, corbo::IntegratorMultiStageFixedStep, corbo::IntegratorAdaptiveStepSize, corbo::IntegratorExplicitRungeKutta7, corbo::IntegratorExplicitRungeKutta6, corbo::IntegratorExplicitRungeKutta5, corbo::IntegratorExplicitRungeKutta4, corbo::IntegratorExplicitRungeKutta3, corbo::IntegratorExplicitRungeKutta2, and corbo::IntegratorExplicitEuler.

◆ initialize()

virtual void corbo::NumericalIntegratorExplicitInterface::initialize ( int state_dim )

inlinevirtual

Allocate memory for a given state dimension.

Remarks: This method is optional and not guaranteed to be called, but if so this might speed up computation.

Parameters

[in] state_dim Expected dimension of the state vector

Reimplemented in corbo::IntegratorAdaptiveStepSize, corbo::IntegratorExplicitRungeKutta7, corbo::IntegratorExplicitRungeKutta6, corbo::IntegratorExplicitRungeKutta5, corbo::IntegratorExplicitRungeKutta4, corbo::IntegratorExplicitRungeKutta3, and corbo::IntegratorExplicitRungeKutta2.

Definition at line 182 of file integrator_interface.h.

◆ interpolate()

bool corbo::NumericalIntegratorExplicitInterface::interpolate	(	const Eigen::Ref< const Eigen::VectorXd > &	x1,
		const Eigen::Ref< const Eigen::VectorXd > &	u1,
		const Eigen::Ref< const Eigen::VectorXd > &	,
		const Eigen::Ref< const Eigen::VectorXd > &	,
		double	dt,
		const SystemDynamicsInterface &	system,
		const Range &	range,
		std::vector< Eigen::VectorXd > &	states,
		std::vector< Eigen::VectorXd > &	controls
	)

inlineoverridevirtual

Implements corbo::DynamicsEvalInterface.

Definition at line 231 of file integrator_interface.h.

◆ solveIVP() [1/2]

virtual void corbo::NumericalIntegratorExplicitInterface::solveIVP	(	const Eigen::VectorXd &	x1,
		double	dt,
		const UnaryFunction &	fun,
		Eigen::Ref< Eigen::VectorXd >	x2
	)

pure virtual

Solution of the initial value problem.

$x(t=\Delta T) = \int_{t=0}^{t=\Delta T} f(x(t)) dt$

with $ x(t=0) = x_1 $.

Parameters

[in]	x1	Initial state vector [SystemDynamicsInterface::getStateDimension() x 1]
[in]	u1	Constant control input vector [SystemDynamicsInterface::getInputDimension() x 1]
[in]	dt	Time interval length
[in]	system	System dynamics object
[out]	x2	Resulting state vector [SystemDynamicsInterface::getStateDimension() x 1] (must be preallocated)

Implemented in corbo::IntegratorMultiStageScaled, and corbo::IntegratorMultiStageFixedStep.

◆ solveIVP() [2/2]

virtual void corbo::NumericalIntegratorExplicitInterface::solveIVP	(	const StateVector &	x1,
		const InputVector &	u1,
		double	dt,
		const SystemDynamicsInterface &	system,
		Eigen::Ref< Eigen::VectorXd >	x2
	)

pure virtual

Solution of the initial value problem.

$x(t=\Delta T) = \int_{t=0}^{t=\Delta T} f(x(t), u_1) dt$

with $ x(t=0) = x_1 $.

Parameters

[in]	x1	Initial state vector [SystemDynamicsInterface::getStateDimension() x 1]
[in]	u1	Constant control input vector [SystemDynamicsInterface::getInputDimension() x 1]
[in]	dt	Time interval length
[in]	system	System dynamics object
[out]	x2	Resulting state vector [SystemDynamicsInterface::getStateDimension() x 1] (must be preallocated)

Implemented in corbo::IntegratorMultiStageScaled, corbo::IntegratorMultiStageFixedStep, corbo::IntegratorAdaptiveStepSize, corbo::IntegratorExplicitRungeKutta7, corbo::IntegratorExplicitRungeKutta6, corbo::IntegratorExplicitRungeKutta5, corbo::IntegratorExplicitRungeKutta4, corbo::IntegratorExplicitRungeKutta3, corbo::IntegratorExplicitRungeKutta2, and corbo::IntegratorExplicitEuler.

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

integrator_interface.h

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Ptr

◆ UnaryFunction

◆ UPtr

Constructor & Destructor Documentation

◆ ~NumericalIntegratorExplicitInterface()

Member Function Documentation

◆ computeEqualityConstraint() [1/2]

◆ computeEqualityConstraint() [2/2]

◆ getConvergenceOrder()

◆ getInstance()

◆ initialize()

◆ interpolate()

◆ solveIVP() [1/2]

◆ solveIVP() [2/2]