Detailed Description

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

A class representing a trajectory for quaternions that are interpolated using piecewise slerp (spherical linear interpolation).

All the orientation samples are expected to be with respect to the same parent reference frame, i.e. q_i represents the rotation R_PBi for the orientation of frame B at the ith sample in a fixed parent frame P. The world frame is a common choice for the parent frame. The angular velocity and acceleration are also relative to the parent frame and expressed in the parent frame. Since there is a sign ambiguity when using quaternions to represent orientation, namely q and -q represent the same orientation, the internal quaternion representations ensure that q_n.dot(q_{n+1}) >= 0. Another intuitive way to think about this is that consecutive quaternions have the shortest geodesic distance on the unit sphere. Note that the quarternion value is in w, x, y, z order when represented as a Vector4.

Template Parameters

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

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

Public Member Functions
	PiecewiseQuaternionSlerp ()=default
	Builds an empty PiecewiseQuaternionSlerp. More...

	PiecewiseQuaternionSlerp (const std::vector< T > &breaks, const std::vector< Quaternion< T >> &quaternions)
	Builds a PiecewiseQuaternionSlerp. More...

	PiecewiseQuaternionSlerp (const std::vector< T > &breaks, const std::vector< Matrix3< T >> &rotation_matrices)
	Builds a PiecewiseQuaternionSlerp. More...

	PiecewiseQuaternionSlerp (const std::vector< T > &breaks, const std::vector< math::RotationMatrix< T >> &rotation_matrices)
	Builds a PiecewiseQuaternionSlerp. More...

	PiecewiseQuaternionSlerp (const std::vector< T > &breaks, const std::vector< AngleAxis< T >> &angle_axes)
	Builds a PiecewiseQuaternionSlerp. More...

	~PiecewiseQuaternionSlerp () override=default

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

Eigen::Index	rows () const override

Eigen::Index	cols () const override

Quaternion< T >	orientation (const T &time) const
	Interpolates orientation. More...

MatrixX< T >	value (const T &time) const override
	Evaluates the trajectory at the given time `t`. More...

Vector3< T >	angular_velocity (const T &time) const
	Interpolates angular velocity. More...

Vector3< T >	angular_acceleration (const T &time) const
	Interpolates angular acceleration. More...

const std::vector< Quaternion< T > > &	get_quaternion_samples () const
	Getter for the internal quaternion samples. More...

bool	is_approx (const PiecewiseQuaternionSlerp< T > &other, double tol) const
	Returns true if all the corresponding segment times are within `tol` seconds, and the angle difference between the corresponding quaternion sample points are within `tol` (using `ExtractDoubleOrThrow`). More...

void	Append (const T &time, const Quaternion< T > &quaternion)
	Given a new Quaternion, this method adds one segment to the end of `this`. More...

void	Append (const T &time, const math::RotationMatrix< T > &rotation_matrix)
	Given a new RotationMatrix, this method adds one segment to the end of `this`. More...

void	Append (const T &time, const AngleAxis< T > &angle_axis)
	Given a new AngleAxis, this method adds one segment to the end of `this`. More...

Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable
	PiecewiseQuaternionSlerp (const PiecewiseQuaternionSlerp &)=default

PiecewiseQuaternionSlerp &	operator= (const PiecewiseQuaternionSlerp &)=default

	PiecewiseQuaternionSlerp (PiecewiseQuaternionSlerp &&)=default

PiecewiseQuaternionSlerp &	operator= (PiecewiseQuaternionSlerp &&)=default

Public Member Functions inherited from PiecewiseTrajectory< T >
	~PiecewiseTrajectory () override=default

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 ()=default

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

	Trajectory (const Trajectory &)=default

Trajectory &	operator= (const Trajectory &)=default

	Trajectory (Trajectory &&)=default

Trajectory &	operator= (Trajectory &&)=default

Constructor & Destructor Documentation

◆ PiecewiseQuaternionSlerp() [1/7]

PiecewiseQuaternionSlerp ( const PiecewiseQuaternionSlerp< T > & )

default

◆ PiecewiseQuaternionSlerp() [2/7]

PiecewiseQuaternionSlerp ( PiecewiseQuaternionSlerp< T > && )

default

◆ PiecewiseQuaternionSlerp() [3/7]

PiecewiseQuaternionSlerp ( )

default

Builds an empty PiecewiseQuaternionSlerp.

◆ PiecewiseQuaternionSlerp() [4/7]

PiecewiseQuaternionSlerp	(	const std::vector< T > &	breaks,
		const std::vector< Quaternion< T >> &	quaternions
	)

Builds a PiecewiseQuaternionSlerp.

Exceptions

std::exception if breaks and quaternions have different length, or breaks have length < 2.

◆ PiecewiseQuaternionSlerp() [5/7]

PiecewiseQuaternionSlerp	(	const std::vector< T > &	breaks,
		const std::vector< Matrix3< T >> &	rotation_matrices
	)

Builds a PiecewiseQuaternionSlerp.

Exceptions

std::exception if breaks and rot_matrices have different length, or breaks have length < 2.

◆ PiecewiseQuaternionSlerp() [6/7]

PiecewiseQuaternionSlerp	(	const std::vector< T > &	breaks,
		const std::vector< math::RotationMatrix< T >> &	rotation_matrices
	)

Builds a PiecewiseQuaternionSlerp.

Exceptions

std::exception if breaks and rot_matrices have different length, or breaks have length < 2.

◆ PiecewiseQuaternionSlerp() [7/7]

PiecewiseQuaternionSlerp	(	const std::vector< T > &	breaks,
		const std::vector< AngleAxis< T >> &	angle_axes
	)

Builds a PiecewiseQuaternionSlerp.

Exceptions

std::exception if breaks and ang_axes have different length, or breaks have length < 2.

◆ ~PiecewiseQuaternionSlerp()

~PiecewiseQuaternionSlerp ( )

overridedefault

Member Function Documentation

◆ angular_acceleration()

Vector3<T> angular_acceleration ( const T & time ) const

Interpolates angular acceleration.

Parameters

time	Time for interpolation.

Returns: The interpolated angular acceleration at time, which is always zero for slerp.

◆ angular_velocity()

Vector3<T> angular_velocity ( const T & time ) const

Interpolates angular velocity.

Parameters

time	Time for interpolation.

Returns: The interpolated angular velocity at time, which is constant per segment.

◆ Append() [1/3]

void Append	(	const T &	time,
		const Quaternion< T > &	quaternion
	)

Given a new Quaternion, this method adds one segment to the end of this.

◆ Append() [2/3]

void Append	(	const T &	time,
		const math::RotationMatrix< T > &	rotation_matrix
	)

Given a new RotationMatrix, this method adds one segment to the end of this.

◆ Append() [3/3]

void Append	(	const T &	time,
		const AngleAxis< T > &	angle_axis
	)

Given a new AngleAxis, this method adds one segment to the end of this.

◆ 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 >.

◆ get_quaternion_samples()

const std::vector<Quaternion<T> >& get_quaternion_samples ( ) const

Getter for the internal quaternion samples.

Note: The returned quaternions might be different from the ones used for construction because the internal representations are set to always be the "closest" w.r.t to the previous one.

Returns: the internal sample points.

◆ is_approx()

bool is_approx	(	const PiecewiseQuaternionSlerp< T > &	other,
		double	tol
	)		const

Returns true if all the corresponding segment times are within tol seconds, and the angle difference between the corresponding quaternion sample points are within tol (using ExtractDoubleOrThrow).

◆ operator=() [1/2]

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

default

◆ operator=() [2/2]

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

default

◆ orientation()

Quaternion<T> orientation ( const T & time ) const

Interpolates orientation.

Parameters

time	Time for interpolation.

Returns: The interpolated quaternion at time.

◆ rows()

Eigen::Index rows ( ) const

overridevirtual

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

Implements Trajectory< T >.

◆ 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/piecewise_quaternion.h

Detailed Description

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

Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ PiecewiseQuaternionSlerp() [1/7]

◆ PiecewiseQuaternionSlerp() [2/7]

◆ PiecewiseQuaternionSlerp() [3/7]

◆ PiecewiseQuaternionSlerp() [4/7]

◆ PiecewiseQuaternionSlerp() [5/7]

◆ PiecewiseQuaternionSlerp() [6/7]

◆ PiecewiseQuaternionSlerp() [7/7]

◆ ~PiecewiseQuaternionSlerp()

Member Function Documentation

◆ angular_acceleration()

◆ angular_velocity()

◆ Append() [1/3]

◆ Append() [2/3]

◆ Append() [3/3]

◆ Clone()

◆ cols()

◆ get_quaternion_samples()

◆ is_approx()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ orientation()

◆ rows()

◆ value()

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