Detailed Description

template<typename T>
class drake::systems::RungeKutta5Integrator< T >

A fifth-order, seven-stage, first-same-as-last (FSAL) Runge Kutta integrator with a fifth order error estimate.

Specifically, this is an explicit Runge-Kutta method of order 5(4), where the higher order estimate is meant to be propagated (unlike the Fehlberg 4(5) method, where the 4th order solution is meant to be propagated).

For a discussion of this Runge-Kutta method, see [Dormand, 1980] and [Hairer, 1993]. The embedded error estimate was derived as described in [Hairer, 1993], where all the coefficients are tabulated.

The Butcher tableau for this integrator follows:

   0 |
 1/5 |        1/5
3/10 |       3/40         9/40
 4/5 |      44/45       -56/15         32/9
 8/9 | 19372/6561   −25360/2187   64448/6561   −212/729
   1 |  9017/3168      −355/33   46732/5247     49/176     −5103/18656
   1 |     35/384            0     500/1113    125/192      −2187/6784      11/84         
---------------------------------------------------------------------------------         
           35/384            0     500/1113    125/192      −2187/6784      11/84      0  
       5179/57600            0   7571/16695    393/640   −92097/339200   187/2100   1/40

where the second to last row is the 5th-order (propagated) solution and the last row gives a 4th-order accurate solution used for error control.

[Dormand, 1980] J. Dormand and P. Prince. "A family of embedded Runge-Kutta formulae", Journal of Computational and Applied Mathematics, 1980, 6(1): 19–26.
[Hairer, 1993] E. Hairer, S. Nørsett, and G. Wanner. Solving ODEs I. 2nd rev. ed. Springer, 1993. pp. 178-9.
[Fehlberg, 1969] E. Fehlberg. Low-order classical Runge-Kutta formulas with stepsize control and their application to some heat transfer problems (Vol. 315). National aeronautics and space administration, 1969.

Template Parameters

T	The scalar type, which must be one of the default nonsymbolic scalars.

#include <drake/systems/analysis/runge_kutta5_integrator.h>

Public Member Functions
	~RungeKutta5Integrator () override

	RungeKutta5Integrator (const System< T > &system, Context< T > *context=nullptr)

bool	supports_error_estimation () const override
	The integrator supports error estimation. More...

int	get_error_estimate_order () const override
	The order of the asymptotic term in the error estimate. More...

Does not allow copy, move, or assignment
	RungeKutta5Integrator (const RungeKutta5Integrator &)=delete

RungeKutta5Integrator &	operator= (const RungeKutta5Integrator &)=delete

	RungeKutta5Integrator (RungeKutta5Integrator &&)=delete

RungeKutta5Integrator &	operator= (RungeKutta5Integrator &&)=delete

Public Member Functions inherited from IntegratorBase< T >
	IntegratorBase (const System< T > &system, Context< T > *context=nullptr)
	Maintains references to the system being integrated and the context used to specify the initial conditions for that system (if any). More...

virtual	~IntegratorBase ()

void	Reset ()
	Resets the integrator to initial values, i.e., default construction values. More...

void	Initialize ()
	An integrator must be initialized before being used. More...

StepResult	IntegrateNoFurtherThanTime (const T &publish_time, const T &update_time, const T &boundary_time)
	(Internal use only) Integrates the system forward in time by a single step with step size subject to integration error tolerances (assuming that the integrator supports error estimation). More...

void	IntegrateWithMultipleStepsToTime (const T &t_final)
	Stepping function for integrators operating outside of Simulator that advances the continuous state exactly to `t_final`. More...

bool	IntegrateWithSingleFixedStepToTime (const T &t_target)
	Stepping function for integrators operating outside of Simulator that advances the continuous state using a single step to `t_target`. More...

const Context< T > &	get_context () const
	Returns a const reference to the internally-maintained Context holding the most recent state in the trajectory. More...

Context< T > *	get_mutable_context ()
	Returns a mutable pointer to the internally-maintained Context holding the most recent state in the trajectory. More...

void	reset_context (Context< T > *context)
	Replace the pointer to the internally-maintained Context with a different one. More...

void	reset_context (std::unique_ptr< Context< T >> context)
	Same as above but allows the integrator to take ownership of the context. More...

const System< T > &	get_system () const
	Gets a constant reference to the system that is being integrated (and was provided to the constructor of the integrator). More...

bool	is_initialized () const
	Indicates whether the integrator has been initialized. More...

const T &	get_previous_integration_step_size () const
	Gets the size of the last (previous) integration step. More...

	IntegratorBase (const IntegratorBase &)=delete

IntegratorBase &	operator= (const IntegratorBase &)=delete

	IntegratorBase (IntegratorBase &&)=delete

IntegratorBase &	operator= (IntegratorBase &&)=delete

void	set_target_accuracy (double accuracy)
	Request that the integrator attempt to achieve a particular accuracy for the continuous portions of the simulation. More...

double	get_target_accuracy () const
	Gets the target accuracy. More...

double	get_accuracy_in_use () const
	Gets the accuracy in use by the integrator. More...

const ContinuousState< T > *	get_error_estimate () const
	Gets the error estimate (used only for integrators that support error estimation). More...

const T &	get_ideal_next_step_size () const
	Return the step size the integrator would like to take next, based primarily on the integrator's accuracy prediction. More...

void	set_fixed_step_mode (bool flag)
	Sets an integrator with error control to fixed step mode. More...

bool	get_fixed_step_mode () const
	Gets whether an integrator is running in fixed step mode. More...

const Eigen::VectorXd &	get_generalized_state_weight_vector () const
	Gets the weighting vector (equivalent to a diagonal matrix) applied to weighting both generalized coordinate and velocity state variable errors, as described in the group documentation. More...

Eigen::VectorBlock< Eigen::VectorXd >	get_mutable_generalized_state_weight_vector ()
	Gets a mutable weighting vector (equivalent to a diagonal matrix) applied to weighting both generalized coordinate and velocity state variable errors, as described in the group documentation. More...

const Eigen::VectorXd &	get_misc_state_weight_vector () const
	Gets the weighting vector (equivalent to a diagonal matrix) for weighting errors in miscellaneous continuous state variables `z`. More...

Eigen::VectorBlock< Eigen::VectorXd >	get_mutable_misc_state_weight_vector ()
	Gets a mutable weighting vector (equivalent to a diagonal matrix) for weighting errors in miscellaneous continuous state variables `z`. More...

void	request_initial_step_size_target (const T &step_size)
	Request that the first attempted integration step have a particular size. More...

const T &	get_initial_step_size_target () const
	Gets the target size of the first integration step. More...

void	set_maximum_step_size (const T &max_step_size)
	Sets the maximum step size that may be taken by this integrator. More...

const T &	get_maximum_step_size () const
	Gets the maximum step size that may be taken by this integrator. More...

double	get_stretch_factor () const
	Gets the stretch factor (> 1), which is multiplied by the maximum (typically user-designated) integration step size to obtain the amount that the integrator is able to stretch the maximum time step toward hitting an upcoming publish or update event in IntegrateNoFurtherThanTime(). More...

void	set_requested_minimum_step_size (const T &min_step_size)
	Sets the requested minimum step size `h_min` that may be taken by this integrator. More...

const T &	get_requested_minimum_step_size () const
	Gets the requested minimum step size `h_min` for this integrator. More...

void	set_throw_on_minimum_step_size_violation (bool throws)
	Sets whether the integrator should throw a std::exception when the integrator's step size selection algorithm determines that it must take a step smaller than the minimum step size (for, e.g., purposes of error control). More...

bool	get_throw_on_minimum_step_size_violation () const
	Reports the current setting of the throw_on_minimum_step_size_violation flag. More...

T	get_working_minimum_step_size () const
	Gets the current value of the working minimum step size `h_work(t)` for this integrator, which may vary with the current time t as stored in the integrator's context. More...

void	ResetStatistics ()
	Forget accumulated statistics. More...

int64_t	get_num_substep_failures () const
	Gets the number of failed sub-steps (implying one or more step size reductions was required to permit solving the necessary nonlinear system of equations). More...

int64_t	get_num_step_shrinkages_from_substep_failures () const
	Gets the number of step size shrinkages due to sub-step failures (e.g., integrator convergence failures) since the last call to ResetStatistics() or Initialize(). More...

int64_t	get_num_step_shrinkages_from_error_control () const
	Gets the number of step size shrinkages due to failure to meet targeted error tolerances, since the last call to ResetStatistics or Initialize(). More...

int64_t	get_num_derivative_evaluations () const
	Returns the number of ODE function evaluations (calls to CalcTimeDerivatives()) since the last call to ResetStatistics() or Initialize(). More...

const T &	get_actual_initial_step_size_taken () const
	The actual size of the successful first step. More...

const T &	get_smallest_adapted_step_size_taken () const
	The size of the smallest step taken as the result of a controlled integration step adjustment since the last Initialize() or ResetStatistics() call. More...

const T &	get_largest_step_size_taken () const
	The size of the largest step taken since the last Initialize() or ResetStatistics() call. More...

int64_t	get_num_steps_taken () const
	The number of integration steps taken since the last Initialize() or ResetStatistics() call. More...

void	add_derivative_evaluations (double evals)
	Manually increments the statistic for the number of ODE evaluations. More...

void	StartDenseIntegration ()
	Starts dense integration, allocating a new dense output for this integrator to use. More...

const trajectories::PiecewisePolynomial< T > *	get_dense_output () const
	Returns a const pointer to the integrator's current PiecewisePolynomial instance, holding a representation of the continuous state trajectory since the last StartDenseIntegration() call. More...

std::unique_ptr< trajectories::PiecewisePolynomial< T > >	StopDenseIntegration ()
	Stops dense integration, yielding ownership of the current dense output to the caller. More...

std::unique_ptr< IntegratorBase< T > >	Clone () const
	Returns a copy of this integrator with reset statistics, reinitialized internal integrator states, and a cloned system context. More...

Additional Inherited Members
Public Types inherited from IntegratorBase< T >
enum	StepResult { kReachedPublishTime = 1, kReachedZeroCrossing = 2, kReachedUpdateTime = 3, kTimeHasAdvanced = 4, kReachedBoundaryTime = 5, kReachedStepLimit = 6 }
	Status returned by IntegrateNoFurtherThanTime(). More...

Protected Member Functions inherited from IntegratorBase< T >
virtual void	DoResetStatistics ()
	Resets any statistics particular to a specific integrator. More...

const ContinuousState< T > &	EvalTimeDerivatives (const Context< T > &context)
	Evaluates the derivative function and updates call statistics. More...

template<typename U >
const ContinuousState< U > &	EvalTimeDerivatives (const System< U > &system, const Context< U > &context)
	Evaluates the derivative function (and updates call statistics). More...

void	set_accuracy_in_use (double accuracy)
	Sets the working ("in use") accuracy for this integrator. More...

bool	StepOnceErrorControlledAtMost (const T &h_max)
	Default code for advancing the continuous state of the system by a single step of `h_max` (or smaller, depending on error control). More...

T	CalcStateChangeNorm (const ContinuousState< T > &dx_state) const
	Computes the infinity norm of a change in continuous state. More...

std::pair< bool, T >	CalcAdjustedStepSize (const T &err, const T &attempted_step_size, bool *at_minimum_step_size) const
	Calculates adjusted integrator step sizes toward keeping state variables within error bounds on the next integration step. More...

virtual void	DoReset ()
	Derived classes can override this method to perform routines when Reset() is called. More...

trajectories::PiecewisePolynomial< T > *	get_mutable_dense_output ()
	Returns a mutable pointer to the internally-maintained PiecewisePolynomial instance, holding a representation of the continuous state trajectory since the last time StartDenseIntegration() was called. More...

bool	DoDenseStep (const T &h)
	Calls DoStep(h) while recording the resulting step in the dense output. More...

ContinuousState< T > *	get_mutable_error_estimate ()
	Gets an error estimate of the state variables recorded by the last call to StepOnceFixedSize(). More...

void	set_actual_initial_step_size_taken (const T &h)

void	set_smallest_adapted_step_size_taken (const T &h)
	Sets the size of the smallest-step-taken statistic as the result of a controlled integration step adjustment. More...

void	set_largest_step_size_taken (const T &h)

void	set_ideal_next_step_size (const T &h)

Constructor & Destructor Documentation

◆ RungeKutta5Integrator() [1/3]

RungeKutta5Integrator ( const RungeKutta5Integrator< T > & )

delete

◆ RungeKutta5Integrator() [2/3]

RungeKutta5Integrator ( RungeKutta5Integrator< T > && )

delete

◆ ~RungeKutta5Integrator()

~RungeKutta5Integrator ( )

override

◆ RungeKutta5Integrator() [3/3]

RungeKutta5Integrator	(	const System< T > &	system,
		Context< T > *	context = `nullptr`
	)

explicit

Member Function Documentation

◆ get_error_estimate_order()

int get_error_estimate_order ( ) const

overridevirtual

The order of the asymptotic term in the error estimate.

Implements IntegratorBase< T >.

◆ operator=() [1/2]

RungeKutta5Integrator& operator= ( RungeKutta5Integrator< T > && )

delete

◆ operator=() [2/2]

RungeKutta5Integrator& operator= ( const RungeKutta5Integrator< T > & )

delete

◆ supports_error_estimation()

bool supports_error_estimation ( ) const

overridevirtual

The integrator supports error estimation.

Implements IntegratorBase< T >.

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

drake/systems/analysis/runge_kutta5_integrator.h

Detailed Description

template<typename T> class drake::systems::RungeKutta5Integrator< T >

Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ RungeKutta5Integrator() [1/3]

◆ RungeKutta5Integrator() [2/3]

◆ ~RungeKutta5Integrator()

◆ RungeKutta5Integrator() [3/3]

Member Function Documentation

◆ get_error_estimate_order()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ supports_error_estimation()

template<typename T>
class drake::systems::RungeKutta5Integrator< T >