PiecewiseQuaternionSlerp< T > Class Template Reference

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 () final
Quaternion< T >	orientation (const T &time) const
	Interpolates orientation. 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
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
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 ()
std::unique_ptr< Trajectory< T > >	Clone () const
MatrixX< T >	value (const T &t) const
	Evaluates the trajectory at the given time t. More...
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...
Eigen::Index	rows () const
Eigen::Index	cols () const
T	start_time () const
T	end_time () const

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...
T	do_start_time () const override
T	do_end_time () const override
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 ( )

final

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.

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= ( const PiecewiseQuaternionSlerp< T > &  )

default

operator=() [2/2]

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

default

orientation()

Quaternion<T> orientation

(

const T &

time

)

const

Interpolates orientation.

Parameters

time	Time for interpolation.

Returns

The interpolated quaternion at time.

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

• drake/common/trajectories/piecewise_quaternion.h