ExponentialPlusPiecewisePolynomial< T > Class Template Reference

Detailed Description

template<typename T>
class drake::trajectories::ExponentialPlusPiecewisePolynomial< T >

Represents a piecewise-trajectory with piece \(j\) given by:

\[ x(t) = K e^{A (t - t_j)} \alpha_j + \sum_{i=0}^k \beta_{j,i}(t-t_j)^i, \]

where \(k\) is the order of the piecewise_polynomial_part and \(t_j\) is the start time of the \(j\)-th segment.

This particular form can represent the solution to a linear dynamical system driven by a piecewise-polynomial input:

\[ \dot{x}(t) = A x(t) + B u(t), \]

where the input \( u(t) \) is a piecewise-polynomial function of time. See [1] for details and a motivating use case.

[1] R. Tedrake, S. Kuindersma, R. Deits and K. Miura, "A closed-form solution for real-time ZMP gait generation and feedback stabilization," 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), Seoul, 2015, pp. 936-940.

Template Parameters

T	The scalar type, which must be double.

#include <drake/common/trajectories/exponential_plus_piecewise_polynomial.h>

Public Member Functions
	ExponentialPlusPiecewisePolynomial ()=default
template<typename DerivedK , typename DerivedA , typename DerivedAlpha >
	ExponentialPlusPiecewisePolynomial (const Eigen::MatrixBase< DerivedK > &K, const Eigen::MatrixBase< DerivedA > &A, const Eigen::MatrixBase< DerivedAlpha > &alpha, const PiecewisePolynomial< T > &piecewise_polynomial_part)
	ExponentialPlusPiecewisePolynomial (const PiecewisePolynomial< T > &piecewise_polynomial_part)
	~ExponentialPlusPiecewisePolynomial () override
std::unique_ptr< Trajectory< T > >	Clone () const override
MatrixX< T >	value (const T &t) const override
	Evaluates the trajectory at the given time t. More...
ExponentialPlusPiecewisePolynomial	derivative (int derivative_order=1) const
Eigen::Index	rows () const override
Eigen::Index	cols () const override
void	shiftRight (double offset)
Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable
	ExponentialPlusPiecewisePolynomial (const ExponentialPlusPiecewisePolynomial &)=default
ExponentialPlusPiecewisePolynomial &	operator= (const ExponentialPlusPiecewisePolynomial &)=default
	ExponentialPlusPiecewisePolynomial (ExponentialPlusPiecewisePolynomial &&)=default
ExponentialPlusPiecewisePolynomial &	operator= (ExponentialPlusPiecewisePolynomial &&)=default
Public Member Functions inherited from PiecewiseTrajectory< T >
	~PiecewiseTrajectory () override
int	get_number_of_segments () const
T	start_time (int segment_number) const
T	end_time (int segment_number) const
T	duration (int segment_number) const
T	start_time () const override
T	end_time () const override
boolean< T >	is_time_in_range (const T &t) const
	Returns true iff t >= getStartTime() && t <= getEndTime(). More...
int	get_segment_index (const T &t) const
const std::vector< T > &	get_segment_times () const
void	segment_number_range_check (int segment_number) const
Public Member Functions inherited from Trajectory< T >
virtual	~Trajectory ()
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
Static Public Member Functions inherited from PiecewiseTrajectory< T >
static std::vector< T >	RandomSegmentTimes (int num_segments, std::default_random_engine &generator)
Static Public Attributes inherited from PiecewiseTrajectory< T >
static constexpr double	kEpsilonTime = std::numeric_limits<double>::epsilon()
	Minimum delta quantity used for comparing time. More...
Protected Member Functions inherited from PiecewiseTrajectory< T >
	PiecewiseTrajectory ()=default
	PiecewiseTrajectory (const std::vector< T > &breaks)
	breaks increments must be greater or equal to kEpsilonTime. More...
bool	SegmentTimesEqual (const PiecewiseTrajectory &b, double tol=kEpsilonTime) const
const std::vector< T > &	breaks () const
std::vector< T > &	get_mutable_breaks ()
	PiecewiseTrajectory (const PiecewiseTrajectory &)=default
PiecewiseTrajectory &	operator= (const PiecewiseTrajectory &)=default
	PiecewiseTrajectory (PiecewiseTrajectory &&)=default
PiecewiseTrajectory &	operator= (PiecewiseTrajectory &&)=default
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
	Trajectory (const Trajectory &)=default
Trajectory &	operator= (const Trajectory &)=default
	Trajectory (Trajectory &&)=default
Trajectory &	operator= (Trajectory &&)=default

Constructor & Destructor Documentation

ExponentialPlusPiecewisePolynomial() [1/5]

ExponentialPlusPiecewisePolynomial ( const ExponentialPlusPiecewisePolynomial< T > &  )

default

ExponentialPlusPiecewisePolynomial() [2/5]

ExponentialPlusPiecewisePolynomial ( ExponentialPlusPiecewisePolynomial< T > &&  )

default

ExponentialPlusPiecewisePolynomial() [3/5]

ExponentialPlusPiecewisePolynomial ( )

default

ExponentialPlusPiecewisePolynomial() [4/5]

ExponentialPlusPiecewisePolynomial	(	const Eigen::MatrixBase< DerivedK > &	K,
		const Eigen::MatrixBase< DerivedA > &	A,
		const Eigen::MatrixBase< DerivedAlpha > &	alpha,
		const PiecewisePolynomial< T > &	piecewise_polynomial_part
	)

ExponentialPlusPiecewisePolynomial() [5/5]

ExponentialPlusPiecewisePolynomial

(

const PiecewisePolynomial< T > &

piecewise_polynomial_part

)

~ExponentialPlusPiecewisePolynomial()

~ExponentialPlusPiecewisePolynomial ( )

override

Member Function Documentation

Clone()

std::unique_ptr<Trajectory<T> > Clone ( ) const

overridevirtual

Returns

A deep copy of this Trajectory.

Implements Trajectory< T >.

cols()

Eigen::Index cols ( ) const

overridevirtual

Returns

The number of columns in the matrix returned by value().

Implements Trajectory< T >.

derivative()

ExponentialPlusPiecewisePolynomial derivative

(

int

derivative_order = 1

)

const

operator=() [1/2]

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

default

operator=() [2/2]

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

default

rows()

Eigen::Index rows ( ) const

overridevirtual

Returns

The number of rows in the matrix returned by value().

Implements Trajectory< T >.

shiftRight()

void shiftRight

(

double

offset

)

value()

MatrixX<T> value ( const T &  t ) const

overridevirtual

Evaluates the trajectory at the given time t.

Parameters

t	The time at which to evaluate the trajectory.

Returns

The matrix of evaluated values.

Implements Trajectory< T >.

---

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

• drake/common/trajectories/exponential_plus_piecewise_polynomial.h