Quaternion class for attitude representation. More...

#include <Quaternion.h>

Inheritance diagram for clockwerk::Quaternion:

[legend]

Public Member Functions
	Quaternion ()
	Default constructor generates Quaternion sequence as zero rotation – 1 0 0 0.
	Quaternion (const floating_point(&initial)[QUATERNION_NUM_ELEMENTS])
	Quaternion (const Quaternion &initial)
	Quaternion (const std::array< floating_point, QUATERNION_NUM_ELEMENTS > &initial)
	~Quaternion ()
Quaternion &	operator= (const Quaternion &other)
	Equals operator overload for quaternion.
Quaternion	operator* (const Quaternion &other) const
	Multiplication operator overload for quaternion to quaternion multiplication.
CartesianVector< 3 >	operator* (const CartesianVector< 3 > &vec__f2) const
	Multiplication operator overload for rotating a vector in frame 2 by a quat_f1_f2.
void	rate (const CartesianVector< 3 > &omega_f1_f2__f1, Matrix< QUATERNION_NUM_ELEMENTS, 1 > &quatdot_f1_f2) const
	Function to calculate the rate of change in the current representation based on the omega vector.
void	rate (const Matrix< 3, 1 > &omega_f1_f2__f1, Matrix< QUATERNION_NUM_ELEMENTS, 1 > &quatdot_f1_f2) const
void	toDCM (DCM &dcm_f1_f2) const
	Function to convert current attitude to DCM.
DCM	toDCM () const
void	toMRP (MRP &mrp_f1_f2) const
	Function to convert current attitude to MRP.
MRP	toMRP () const
int16	rotationAngle (floating_point &val) const
	Calculate the rotation angle represented by the quaternion.
floating_point	rotationAngle () const
void	inverse (Quaternion &quat_f2_f1) const
	Function to convert quaternion rotation to inverse quaternion (assumes unit quaternion and outputs its conjugate).
Quaternion	inverse () const
void	dRate_dOmega (Matrix< QUATERNION_NUM_ELEMENTS, 3 > &jacobian) const
	Function to compute the partial derivative of dq/dt (Quaternion::rate) with respect to omega_f1_f2__f1.
Matrix< QUATERNION_NUM_ELEMENTS, 3 >	dRate_dOmega () const
void	dRate_dQuat (const CartesianVector< 3 > &omega_f1_f2__f1, Matrix< QUATERNION_NUM_ELEMENTS, QUATERNION_NUM_ELEMENTS > &jacobian) const
	Function to compute the partial derivative of dq/dt (Quaternion::rate) with respect to quat_f1_f2.
Matrix< QUATERNION_NUM_ELEMENTS, QUATERNION_NUM_ELEMENTS >	dRate_dQuat (const CartesianVector< 3 > &omega_f1_f2__f1) const
void	dRotatedVec_dQuat (const CartesianVector< 3 > &vec__f2, Matrix< 3, QUATERNION_NUM_ELEMENTS > &jacobian) const
	Function to compute the partial derivative of quat_f1_f2*vec__f2 with respect to quat_f1_f2.
Matrix< 3, QUATERNION_NUM_ELEMENTS >	dRotatedVec_dQuat (const CartesianVector< 3 > &vec__f2) const
void	dInvRotatedVec_dQuat (const CartesianVector< 3 > &vec__f1, Matrix< 3, QUATERNION_NUM_ELEMENTS > &jacobian) const
	Function to compute the partial derivative of quat_f2_f1*vec__f1 with respect to quat_f1_f2 (note the inverse quaternion).
Matrix< 3, QUATERNION_NUM_ELEMENTS >	dInvRotatedVec_dQuat (const CartesianVector< 3 > &vec__f1) const
Public Member Functions inherited from clockwerk::CartesianVector< QUATERNION_NUM_ELEMENTS >
	CartesianVector ()
	~CartesianVector ()
floating_point &	operator[] (uint32 idx)
	Function to return a vector value.
int	set (uint32 idx, floating_point value)
	Setter specific to the vector class.
int	get (uint32 idx, floating_point &result) const
	Getter specific to the vector class.
int16	norm (floating_point &result) const
	Function to take the norm of a vector.
int16	normSquared (floating_point &result) const
	Function to take the squared norm of a vector.
int16	unit (CartesianVector< L > &result) const
	Function to return the unitized version of the vector.
int16	unitize ()
	Function to unitize the current vector.
int16	normalize ()
	Function to unitize the current vector.
Public Member Functions inherited from clockwerk::Matrix< L, 1 >
	Matrix ()
	Default constructor to initialize a matrix to all zeroes for ease of use.
	~Matrix ()
int16	str (char *output, size_t size) const
	Function to dump information on matrix.
int16	fromStr (const char *val)
	Set value of matrix from string in same format as str().
int16	set (uint32 row, uint32 col, const floating_point &value)
	Function to set a single value in the matrix.
int16	get (uint32 row, uint32 col, floating_point &result) const
	Function to get a single value in the matrix.
void	setFromArray (const floating_point *start_ptr, bool column_major=false)
	Function to set the values of the matrix row-wise.
void	getAsArray (floating_point *start_ptr, bool column_major=false) const
	Function to get the values of the matrix row-wise.
void	getCopy (Matrix< R, C > &result) const
	Function to get a copy of the matrix.
Matrix< R, C > &	operator= (const Matrix< R, C > &other)
	Equals operator overload for matrix.
floating_point *	operator[] (uint32 idx)
	Function to return a matrix row or vector value.
std::pair< uint32, uint32 >	size () const
	Function to get the size of the matrix.
void	max (floating_point &result, std::pair< uint32, uint32 > &index) const
	Function to return the maximum value in the matrix.
void	min (floating_point &result, std::pair< uint32, uint32 > &index) const
	Function to return the minimum value in the matrix.
int16	det (floating_point &result) const
	Function to return the determinant of the matrix.
int16	chol (Matrix< R, C > &retval) const
	Take the cholesky decomposition of this matrix.
int16	inverse (Matrix< R, C > &result) const
	Function to return the inverse of the matrix.
int16	pseudoinverse (Matrix< C, R > &result) const
void	transpose (Matrix< C, R > &result) const
	Function to return the transpose of the matrix.
int16	trace (floating_point &result) const
	Function to return the trace of the matrix.
void	setToZeros ()
	Function to set all elements of the matrix to zero.
int16	identity ()
	Function to set matrix to identity, if it is a square matrix.
int16	eye ()

Additional Inherited Members
Public Attributes inherited from clockwerk::Matrix< L, 1 >
std::array< std::array< floating_point, C >, R >	values
Protected Member Functions inherited from clockwerk::Matrix< L, 1 >
int16	_checkLookupBoundaries (uint32 start_r, uint32 end_r, uint32 start_c, uint32 end_c) const
int16	_LUPDecompose (floating_point *A[R], uint32 P[R+1]) const
	Function to take a 2-d matrix represented by A and decompose it into LU form.

Detailed Description

Quaternion class for attitude representation.

This file defines a simple Quaternion attitude representation for cartesian coordinate systems. It is largely the same as the base vector, with the following exceptions:

Set to be 4 elements
Functions defined to convert to other attitude representations
Function defined to calculate rate of change as a function of omega

Naming conventions

All naming conventions and equations are per Analytical Mechanics of Space Systems by Schaub and Junkins
The omega vector is sometimes denoted by w and assumed frame consistent with the attitude representation. For example, if a DCM represents the relative orientation between two frames [BN] the omega vector is assumed to be w_(B/N)
The naming convention for all vectors is: variablename_obj1_obj2__frameN (note the double underscore preceding frame) and reads back as: "variable variablename representing the relationship between obj1 and obj2 represented in frameN"
Unless otherwise noted angles are in RADIANS

NOTE: All attitude representations, including DCMs, are assumed to represent a three dimensional, cartesian coordinate system because that is what they are used, and in many cases defined, for. NOTE: The math in this class assumes a unit quaternion.

Constructor & Destructor Documentation

◆ Quaternion() [1/4]

clockwerk::Quaternion::Quaternion ( )

Default constructor generates Quaternion sequence as zero rotation – 1 0 0 0.

◆ Quaternion() [2/4]

clockwerk::Quaternion::Quaternion ( const floating_point(&) initial[QUATERNION_NUM_ELEMENTS] )

Constructor for Matrix class with initialization. Initializes matrix to values passed in via array

◆ Quaternion() [3/4]

clockwerk::Quaternion::Quaternion ( const Quaternion & initial )

Copy constructor for Quaternion class. Copies data from Quaternion object to the current instance

◆ Quaternion() [4/4]

clockwerk::Quaternion::Quaternion ( const std::array< floating_point, QUATERNION_NUM_ELEMENTS > & initial )

Constructor for Matrix class with initialization. Initializes matrix to values passed in via array

◆ ~Quaternion()

clockwerk::Quaternion::~Quaternion ( )

inline

Destructor – doesn't do anything because we don't dynamically allocate

Member Function Documentation

◆ dInvRotatedVec_dQuat() [1/2]

Matrix< 3, QUATERNION_NUM_ELEMENTS > clockwerk::Quaternion::dInvRotatedVec_dQuat ( const CartesianVector< 3 > & vec__f1 ) const

◆ dInvRotatedVec_dQuat() [2/2]

void clockwerk::Quaternion::dInvRotatedVec_dQuat	(	const CartesianVector< 3 > &	vec__f1,
		Matrix< 3, QUATERNION_NUM_ELEMENTS > &	jacobian ) const

Function to compute the partial derivative of quat_f2_f1*vec__f1 with respect to quat_f1_f2 (note the inverse quaternion).

Parameters

vec__f1	Vector that would be rotated by the inverse quaternion
jacobian	Implicif return of the partial derivative

Returns: Error code corresponding to success/failure

◆ dRate_dOmega() [1/2]

Matrix< QUATERNION_NUM_ELEMENTS, 3 > clockwerk::Quaternion::dRate_dOmega ( ) const

◆ dRate_dOmega() [2/2]

void clockwerk::Quaternion::dRate_dOmega ( Matrix< QUATERNION_NUM_ELEMENTS, 3 > & jacobian ) const

Function to compute the partial derivative of dq/dt (Quaternion::rate) with respect to omega_f1_f2__f1.

Parameters

jacobian Implicit return of the matrix function denoted as E^T in section 1.5.3 of "Quaternions and Dynamics" by Basile Graf

Returns: Error code corresponding to success/failure

◆ dRate_dQuat() [1/2]

Matrix< QUATERNION_NUM_ELEMENTS, QUATERNION_NUM_ELEMENTS > clockwerk::Quaternion::dRate_dQuat ( const CartesianVector< 3 > & omega_f1_f2__f1 ) const

◆ dRate_dQuat() [2/2]

void clockwerk::Quaternion::dRate_dQuat	(	const CartesianVector< 3 > &	omega_f1_f2__f1,
		Matrix< QUATERNION_NUM_ELEMENTS, QUATERNION_NUM_ELEMENTS > &	jacobian ) const

Function to compute the partial derivative of dq/dt (Quaternion::rate) with respect to quat_f1_f2.

Parameters

omega_f1_f2__f1	Angular velocity for the attitude representation - omega of frame 1 wrt frame 2 expressed in frame 1
jacobian	Implicit return of the matrix function denoted as G^T in section 1.5.4 of "Quaternions and Dynamics" by Basile Graf

Returns: Error code corresponding to success/failure

◆ dRotatedVec_dQuat() [1/2]

Matrix< 3, QUATERNION_NUM_ELEMENTS > clockwerk::Quaternion::dRotatedVec_dQuat ( const CartesianVector< 3 > & vec__f2 ) const

◆ dRotatedVec_dQuat() [2/2]

void clockwerk::Quaternion::dRotatedVec_dQuat	(	const CartesianVector< 3 > &	vec__f2,
		Matrix< 3, QUATERNION_NUM_ELEMENTS > &	jacobian ) const

Function to compute the partial derivative of quat_f1_f2*vec__f2 with respect to quat_f1_f2.

Parameters

vec__f2	Vector that would be rotated by the quaternion
jacobian	Implicit return of the partial derivative

Returns: Error code corresponding to success/failure

◆ inverse() [1/2]

Quaternion clockwerk::Quaternion::inverse ( ) const

◆ inverse() [2/2]

void clockwerk::Quaternion::inverse ( Quaternion & quat_f2_f1 ) const

Function to convert quaternion rotation to inverse quaternion (assumes unit quaternion and outputs its conjugate).

Quaternion Conversions

Parameters

quat_f2_f1 return of quaternion representation of the inverse rotation of current quaternion

Returns: Integer error code corresponding to errors in clockwerkerrors.h

Warning: This function is only valid for unit quaternions, make sure to unitize before use

◆ operator*() [1/2]

CartesianVector< 3 > clockwerk::Quaternion::operator* ( const CartesianVector< 3 > & vec__f2 ) const

Multiplication operator overload for rotating a vector in frame 2 by a quat_f1_f2.

Parameters

vec__f2 Vector to be rotated expressed in frame 2

Returns: Vector after rotatin expressed in frame 1

◆ operator*() [2/2]

Quaternion clockwerk::Quaternion::operator* ( const Quaternion & other ) const

Multiplication operator overload for quaternion to quaternion multiplication.

Parameters

other Quaternion to multiply with

Returns: Quaternion mutiplication result

◆ operator=()

Quaternion & clockwerk::Quaternion::operator= ( const Quaternion & other )

Equals operator overload for quaternion.

◆ rate() [1/2]

void clockwerk::Quaternion::rate	(	const CartesianVector< 3 > &	omega_f1_f2__f1,
		Matrix< QUATERNION_NUM_ELEMENTS, 1 > &	quatdot_f1_f2 ) const

Function to calculate the rate of change in the current representation based on the omega vector.

Dynamics and kinematics functions

Parameters

omega_f1_f2__f1	Angular velocity vector for the attitude representation - omega of frame 1 wrt frame 2 expressed in frame 1
quatdot_f1_f2	Rate of change in the current Quaternion

◆ rate() [2/2]

void clockwerk::Quaternion::rate	(	const Matrix< 3, 1 > &	omega_f1_f2__f1,
		Matrix< QUATERNION_NUM_ELEMENTS, 1 > &	quatdot_f1_f2 ) const

◆ rotationAngle() [1/2]

floating_point clockwerk::Quaternion::rotationAngle ( ) const

◆ rotationAngle() [2/2]

int16 clockwerk::Quaternion::rotationAngle ( floating_point & val ) const

Calculate the rotation angle represented by the quaternion.

Parameters

val	Implicit return of rotation angle

Returns: Error code corresponding to success/failure

◆ toDCM() [1/2]

DCM clockwerk::Quaternion::toDCM ( ) const

◆ toDCM() [2/2]

void clockwerk::Quaternion::toDCM ( DCM & dcm_f1_f2 ) const

Function to convert current attitude to DCM.

Conversions to other attitude representations

Parameters

PBR	return of DCM in PBR case

Returns: Integer error code corresponding to errors in clockwerkerrors.h

◆ toMRP() [1/2]

MRP clockwerk::Quaternion::toMRP ( ) const

◆ toMRP() [2/2]

void clockwerk::Quaternion::toMRP ( MRP & mrp_f1_f2 ) const

Function to convert current attitude to MRP.

Parameters

PBR	return of MRP in PBR case

Returns: Integer error code corresponding to errors in clockwerkerrors.h

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

/Users/mickey/Documents/Projects/warptwin/warpos/clockwerk/src/dynamics/Quaternion.h
/Users/mickey/Documents/Projects/warptwin/warpos/clockwerk/src/dynamics/Quaternion.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Naming conventions

Constructor & Destructor Documentation

◆ Quaternion() [1/4]

◆ Quaternion() [2/4]

◆ Quaternion() [3/4]

◆ Quaternion() [4/4]

◆ ~Quaternion()

Member Function Documentation

◆ dInvRotatedVec_dQuat() [1/2]

◆ dInvRotatedVec_dQuat() [2/2]

◆ dRate_dOmega() [1/2]

◆ dRate_dOmega() [2/2]

◆ dRate_dQuat() [1/2]

◆ dRate_dQuat() [2/2]

◆ dRotatedVec_dQuat() [1/2]

◆ dRotatedVec_dQuat() [2/2]

◆ inverse() [1/2]

◆ inverse() [2/2]

Quaternion Conversions

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator=()

◆ rate() [1/2]

Dynamics and kinematics functions

◆ rate() [2/2]

◆ rotationAngle() [1/2]

◆ rotationAngle() [2/2]

◆ toDCM() [1/2]

◆ toDCM() [2/2]

Conversions to other attitude representations

◆ toMRP() [1/2]

◆ toMRP() [2/2]