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Drake
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Drake
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A DiscreteTimeTrajectory is a Trajectory whose value is only defined at discrete time points.
Calling value() at a time that is not equal to one of those times (up to a tolerance) will throw. This trajectory does not have well-defined time-derivatives.
In some applications, it may be preferable to use PiecewisePolynomial<T>::ZeroOrderHold instead of a DiscreteTimeTrajectory (and we offer a method here to easily convert). Note if the breaks are periodic, then one can also achieve a similar result in a Diagram by using the DiscreteTimeTrajectory in a TrajectorySource and connecting a ZeroOrderHold system to the output port, but remember that this will add discrete state to your diagram.
So why not always use the zero-order hold (ZOH) trajectory? This class forces us to be more precise in our implementations. For instance, consider the case of a solution to a discrete-time finite-horizon linear quadratic regulator (LQR) problem. In this case, the solution to the Riccati equation is a DiscreteTimeTrajectory, K(t). Implementing
x(t) -> MatrixGain(-K(t)) -> u(t)
in a block diagram is perfectly correct, and if the u(t) is only connected to the original system that it was designed for, then K(t) will only get evaluated at the defined sample times, and all is well. But if you wire it up to a continuous-time system, then K(t) may be evaluated at arbitrary times, and may throw. If one wishes to use the K(t) solution on a continuous-time system, then we can use
x(t) -> MatrixGain(-K(t)) -> ZOH -> u(t).
This is different, and more correct than implementing K(t) as a zero-order hold trajectory, because in this version, both K(t) and the inputs x(t) will only be evaluated at the discrete-time input. If t_s was the most recent discrete sample time, then this means u(t) = -K(t_s)*x(t_s) instead of u(t) = -K(t_s)*x(t). Using x(t_s) and having a true zero-order hold on u(t) is the correct model for the discrete-time LQR result.
| T | The scalar type, which must be one of the default scalars. |
#include <drake/common/trajectories/discrete_time_trajectory.h>
Public Member Functions | |
| DiscreteTimeTrajectory ()=default | |
| Default constructor creates the empty trajectory. More... | |
| DiscreteTimeTrajectory (const Eigen::Ref< const VectorX< T >> ×, const Eigen::Ref< const MatrixX< T >> &values, double time_comparison_tolerance=std::numeric_limits< double >::epsilon()) | |
Constructs a trajectory of vector values at the specified times. More... | |
| DiscreteTimeTrajectory (const std::vector< T > ×, const std::vector< MatrixX< T >> &values, double time_comparison_tolerance=std::numeric_limits< double >::epsilon()) | |
Constructs a trajectory of matrix values at the specified times. More... | |
| ~DiscreteTimeTrajectory () final | |
| PiecewisePolynomial< T > | ToZeroOrderHold () const |
| Converts the discrete-time trajectory using PiecewisePolynomial<T>::ZeroOrderHold(). More... | |
| double | time_comparison_tolerance () const |
| The trajectory is only defined at finite sample times. More... | |
| int | num_times () const |
| Returns the number of discrete times where the trajectory value is defined. More... | |
| const std::vector< T > & | get_times () const |
| Returns the times where the trajectory value is defined. More... | |
| MatrixX< T > | value (const T &t) const final |
Returns the value of the trajectory at t. More... | |
| Eigen::Index | rows () const final |
| Returns the number of rows in the MatrixX<T> returned by value(). More... | |
| Eigen::Index | cols () const final |
| Returns the number of cols in the MatrixX<T> returned by value(). More... | |
| T | start_time () const final |
| Returns the minimum value of get_times(). More... | |
| T | end_time () const final |
| Returns the maximum value of get_times(). More... | |
Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable | |
| DiscreteTimeTrajectory (const DiscreteTimeTrajectory &)=default | |
| DiscreteTimeTrajectory & | operator= (const DiscreteTimeTrajectory &)=default |
| DiscreteTimeTrajectory (DiscreteTimeTrajectory &&)=default | |
| DiscreteTimeTrajectory & | operator= (DiscreteTimeTrajectory &&)=default |
 Public Member Functions inherited from Trajectory< T > | |
| virtual | ~Trajectory () |
| virtual std::unique_ptr< Trajectory< T > > | Clone () const |
| MatrixX< T > | vector_values (const std::vector< T > &t) const |
If cols()==1, then evaluates the trajectory at each time t, and returns the results as a Matrix with the ith column corresponding to the ith time. More... | |
| MatrixX< T > | vector_values (const Eigen::Ref< const VectorX< T >> &t) const |
If cols()==1, then evaluates the trajectory at each time t, and returns the results as a Matrix with the ith column corresponding to the ith time. More... | |
| bool | has_derivative () const |
| Returns true iff the Trajectory provides and implementation for EvalDerivative() and MakeDerivative(). More... | |
| MatrixX< T > | EvalDerivative (const T &t, int derivative_order=1) const |
Evaluates the derivative of this at the given time t. More... | |
| std::unique_ptr< Trajectory< T > > | MakeDerivative (int derivative_order=1) const |
| Takes the derivative of this Trajectory. More... | |
Additional Inherited Members | |
| Protected Member Functions inherited from Trajectory< T > | |
| Trajectory ()=default | |
| virtual bool | do_has_derivative () const |
| virtual MatrixX< T > | DoEvalDerivative (const T &t, int derivative_order) const |
| virtual std::unique_ptr< Trajectory< T > > | DoMakeDerivative (int derivative_order) const |
| Trajectory (const Trajectory &)=default | |
| Trajectory & | operator= (const Trajectory &)=default |
| Trajectory (Trajectory &&)=default | |
| Trajectory & | operator= (Trajectory &&)=default |
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default |
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default |
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default |
Default constructor creates the empty trajectory.
| DiscreteTimeTrajectory | ( | const Eigen::Ref< const VectorX< T >> & | times, |
| const Eigen::Ref< const MatrixX< T >> & | values, | ||
| double | time_comparison_tolerance = std::numeric_limits< double >::epsilon() |
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| ) |
Constructs a trajectory of vector values at the specified times.
times must differ by more than time_comparison_tolerance and be monotonically increasing. values must have times.size() columns. time_comparison_tolerance must be >= 0. | if | T=symbolic:Expression and times are not constants. |
| DiscreteTimeTrajectory | ( | const std::vector< T > & | times, |
| const std::vector< MatrixX< T >> & | values, | ||
| double | time_comparison_tolerance = std::numeric_limits< double >::epsilon() |
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| ) |
Constructs a trajectory of matrix values at the specified times.
times should differ by more than time_comparison_tolerance and be monotonically increasing. values must have times.size() elements, each with the same number of rows and columns. time_comparison_tolerance must be >= 0. | if | T=symbolic:Expression and times are not constants. |
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final |
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finalvirtual |
Returns the number of cols in the MatrixX<T> returned by value().
Reimplemented from Trajectory< T >.
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finalvirtual |
Returns the maximum value of get_times().
Reimplemented from Trajectory< T >.
| const std::vector<T>& get_times | ( | ) | const |
Returns the times where the trajectory value is defined.
| int num_times | ( | ) | const |
Returns the number of discrete times where the trajectory value is defined.
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default |
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default |
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finalvirtual |
Returns the number of rows in the MatrixX<T> returned by value().
Reimplemented from Trajectory< T >.
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finalvirtual |
Returns the minimum value of get_times().
Reimplemented from Trajectory< T >.
| double time_comparison_tolerance | ( | ) | const |
The trajectory is only defined at finite sample times.
This method returns the tolerance used determine which time sample (if any) matches a query time on calls to value(t).
| PiecewisePolynomial<T> ToZeroOrderHold | ( | ) | const |
Converts the discrete-time trajectory using PiecewisePolynomial<T>::ZeroOrderHold().
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finalvirtual |
Returns the value of the trajectory at t.
| std::exception | if t is not within tolerance of one of the sample times. |
Reimplemented from Trajectory< T >.