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Drake
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Drake
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A StepwiseDenseOutput class implementation using Hermitian interpolators, and therefore a continuous extension of the solution 𝐱(t) (see [Engquist, 2105]).
This concept can be recast as a type of dense output that is continuous.
Updates take the form of integration steps, for which state 𝐱 and state time derivative d𝐱/dt are known at least at both ends of the step. Hermite cubic polynomials are then constructed upon consolidation, yielding a C1 extension of the solution 𝐱(t).
Hermitian continuous extensions exhibit the same truncation error as that of the integration scheme being used for up to 3rd order schemes (see [Hairer, 1993]).
From a performance standpoint, memory footprint and evaluation overhead (i.e. the computational cost of an evaluation) increase linearly and logarithmically with the amount of steps taken, respectively.
| T | The scalar type, which must be one of the default scalars. |
#include <drake/systems/analysis/hermitian_dense_output.h>
Classes | |
| class | IntegrationStep |
| An integration step representation class, holding just enough for Hermitian interpolation: three (3) related sets containing step times {t₀, ..., tᵢ₋₁, tᵢ} where tᵢ ∈ ℝ, step states {𝐱₀, ..., 𝐱ᵢ₋₁, 𝐱ᵢ} where 𝐱ᵢ ∈ ℝⁿ, and state derivatives {d𝐱/dt₀, ..., d𝐱/dtᵢ₋₁, d𝐱/dtᵢ} where d𝐱/dtᵢ ∈ ℝⁿ. More... | |
Public Member Functions | |
| HermitianDenseOutput ()=default | |
| HermitianDenseOutput (const trajectories::PiecewisePolynomial< T > &trajectory) | |
| Initialize the DenseOutput with an existing trajectory. More... | |
| void | Update (IntegrationStep step) |
Update output with the given step. More... | |
| void | Rollback () override |
| Rolls back (drops) the last update. More... | |
| void | Consolidate () override |
| Consolidates latest updates. More... | |
Does not allow copy, move, or assignment | |
| HermitianDenseOutput (const HermitianDenseOutput &)=delete | |
| HermitianDenseOutput & | operator= (const HermitianDenseOutput &)=delete |
| HermitianDenseOutput (HermitianDenseOutput &&)=delete | |
| HermitianDenseOutput & | operator= (HermitianDenseOutput &&)=delete |
 Public Member Functions inherited from StepwiseDenseOutput< T > | |
| ~StepwiseDenseOutput () override=default | |
| StepwiseDenseOutput (const StepwiseDenseOutput &)=delete | |
| StepwiseDenseOutput & | operator= (const StepwiseDenseOutput &)=delete |
| StepwiseDenseOutput (StepwiseDenseOutput &&)=delete | |
| StepwiseDenseOutput & | operator= (StepwiseDenseOutput &&)=delete |
| Public Member Functions inherited from DenseOutput< T > | |
| virtual | ~DenseOutput ()=default |
| VectorX< T > | Evaluate (const T &t) const |
Evaluates the output at the given time t. More... | |
| T | EvaluateNth (const T &t, int n) const |
Evaluates the output value's nth scalar element (0-indexed) at the given time t. More... | |
| int | size () const |
| Returns the output size (i.e. More... | |
| bool | is_empty () const |
| Checks whether the output is empty or not. More... | |
| const T & | start_time () const |
Returns output's start time, or in other words, the oldest time t that it can be evaluated at e.g. More... | |
| const T & | end_time () const |
Returns output's end time, or in other words, the newest time t that it can be evaluated at e.g. More... | |
| DenseOutput (const DenseOutput &)=delete | |
| DenseOutput & | operator= (const DenseOutput &)=delete |
| DenseOutput (DenseOutput &&)=delete | |
| DenseOutput & | operator= (DenseOutput &&)=delete |
Protected Member Functions | |
| VectorX< T > | DoEvaluate (const T &t) const override |
| T | DoEvaluateNth (const T &t, const int n) const override |
| bool | do_is_empty () const override |
| int | do_size () const override |
| const T & | do_end_time () const override |
| const T & | do_start_time () const override |
| Protected Member Functions inherited from StepwiseDenseOutput< T > | |
| StepwiseDenseOutput ()=default | |
| Protected Member Functions inherited from DenseOutput< T > | |
| DenseOutput ()=default | |
| void | ThrowIfOutputIsEmpty (const char *func_name) const |
| void | ThrowIfNthElementIsInvalid (const char *func_name, int n) const |
| void | ThrowIfTimeIsInvalid (const char *func_name, const T &t) const |
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delete |
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delete |
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default |
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explicit |
Initialize the DenseOutput with an existing trajectory.
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overridevirtual |
Consolidates latest updates.
All updates since last call or construction are put into a form that is suitable for evaluation.
| std::exception | if any of the preconditions is not met. |
Implements StepwiseDenseOutput< T >.
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overrideprotectedvirtual |
Implements DenseOutput< T >.
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overrideprotectedvirtual |
Implements DenseOutput< T >.
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overrideprotectedvirtual |
Implements DenseOutput< T >.
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overrideprotectedvirtual |
Implements DenseOutput< T >.
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overrideprotectedvirtual |
Implements DenseOutput< T >.
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overrideprotectedvirtual |
Reimplemented from DenseOutput< T >.
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delete |
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delete |
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overridevirtual |
Rolls back (drops) the last update.
| std::exception | if any of the preconditions is not met. |
Implements StepwiseDenseOutput< T >.
| void Update | ( | IntegrationStep | step | ) |
Update output with the given step.
Provided step is queued for later consolidation. Note that the time the step extends cannot be readily evaluated (see StepwiseDenseOutput class documentation).
| step | Integration step to update this output with. |
| std::exception | if given step has zero length.if given step does not ensure C1 continuity at the end of this dense output.if given step dimensions does not match this dense output dimensions. |