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Drake C++ Documentation
RungeKutta5Integrator< T > Class Template Referencefinal

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 fourth order error estimate.

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.
Template Parameters
TThe scalar type, which must be one of the default nonsymbolic scalars.

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

Public Member Functions

 ~RungeKutta5Integrator () override=default
 
 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
 
RungeKutta5Integratoroperator= (const RungeKutta5Integrator &)=delete
 
 RungeKutta5Integrator (RungeKutta5Integrator &&)=delete
 
RungeKutta5Integratoroperator= (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 ()=default
 
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...
 
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
 
IntegratorBaseoperator= (const IntegratorBase &)=delete
 
 IntegratorBase (IntegratorBase &&)=delete
 
IntegratorBaseoperator= (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...
 
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...
 

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...
 
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 ( )
overridedefault

◆ 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: