Module: oneAxisSolarArrayPoint

Executive Summary

This module computes a reference attitude frame that simultaneously satisfies multiple pointing constraints. The first constraint consists of aligning a body-frame direction \({}^\mathcal{B}\hat{h}_1\) with a certain inertial reference direction \({}^\mathcal{N}\hat{h}_\text{ref}\). This locks two out of three degrees of freedom that characterize a rigid body rotation. The second constraints consists in achieving maximum power generation on the solar arrays, assuming that the solar arrays can rotate about their drive axis. This condition is obtained ensuring that the body-fixed solar array drive direction \({}^\mathcal{B}\hat{a}_1\) is as close to perpendicular as possible to the Sun direction. When maximum power generation is possible, two solutions can be found that satisfy the previous two constraints simultaneously. When this happens, it is possible to consider a third body-fixed direction \({}^\mathcal{B}\hat{a}_2\) which should remain as close as possible to the Sun direction, while maintaining the other two constraints satisfied. This allows to discriminate between the two frames, and to pick the one that drives \({}^\mathcal{B}\hat{a}_2\) closer to the Sun. It is possible to provide a second body frame direction \({}^\mathcal{B}\hat{h}_2\) as an optional parameter: in this case the module chooses whether to align \({}^\mathcal{B}\hat{h}_1\) or \({}^\mathcal{B}\hat{h}_2\) with \({}^\mathcal{N}\hat{h}_\text{ref}\) depending on which provides a better alignment of \({}^\mathcal{B}\hat{a}_2\) with the Sun direction.

Message Connection Descriptions

The following table lists all the module input and output messages. The msg type contains a link to the message structure definition, while the description provides information on what this message is used for.

Module I/O Messages

Msg Variable Name	Msg Type	Description
attNavInMsg	NavAttMsgPayload	Input message containing current attitude and Sun direction in body-frame coordinates. Note that, for the Sun direction to appear in the message, the SpicePlanetStateMsgPayload must be provided as input msg to Module: simpleNav, otherwise the Sun direction is zeroed by default.
bodyHeadingInMsg	BodyHeadingMsgPayload	(optional) Input message containing the body-frame direction \({}^\mathcal{B}\hat{h}\). Alternatively, the direction can be specified as input parameter h1Hat_B. When this input msg is connected, the input parameter is neglected in favor of the input msg.
inertialHeadingInMsg	InertialHeadingMsgPayload	(optional) Input message containing the inertial-frame direction \({}^\mathcal{N}\hat{h}_\text{ref}\). Alternatively, the direction can be specified as input parameter hHat_N. When this input msg is connected, the input parameter is neglected in favor of the input msg.
ephemerisInMsg	EphemerisMsgPayload	(optional) Input message containing the inertial position of a celestial object, whose direction with respect to the spacecraft serves as the inertial reference direction \({}^\mathcal{N}\hat{h}_\text{ref}\). This input msg must be provided together with transNavInMsg to compute the relative position of the celestial object to the spacecraft. If both inertialHeadingInMsg and ephemerisInMsg are connected, the inertial reference direction \({}^\mathcal{N}\hat{h}_\text{ref}\) is computed according to inertialHeadingInMsg.
transNavInMsg	NavTransMsgPayload	(optional) Input message containing the inertial position and velocity of the spacecraft. This message must be connected together with ephemerisInMsg to allow to compute \({}^\mathcal{N}\hat{h}_\text{ref}\).
attRefOutMsg	AttRefMsgPayload	Output attitude reference message containing reference attitude, reference angular rates and accelerations.

Detailed Module Description

A detailed mathematical derivation of the equations applied by this module can be found in R. Calaon, C. Allard and H. Schaub, “Attitude Reference Generation for Spacecraft with Rotating Solar Arrays and Pointing Constraints”, in preparation for Journal of Spacecraft and Rockets. The input parameter alignmentPriority allows to choose whether the first or the second constraint is strictly enforced. When alignmentPriority = 0, the body heading \({}^\mathcal{B}\hat{h}\) and the inertial heading \({}^\mathcal{N}\hat{h}_\text{ref}\) match exactly, while the incidence angle on the solar arrays is as close to optimal as possible. On the contrary, when alignmentPriority = 1, the solar array drive \({}^\mathcal{B}\hat{a}_1\) is perpendicular to the Sun direction, to ensure maximum power generation, while the body heading and the inertial heading are as close to parallel as possible.

Attention must be paid to how these pieces of input information is provided:

• Input body-frame heading: this can be specified either via the input parameter h1Hat_B, or connecting the input message bodyHeadingInMsg. Specifying the body-frame heading via the input parameter is desirable when such direction does not change over time; vice versa, when the body-frame heading is time varying, this needs to be passed via the bodyHeadingInMsg. When both h1Hat_B and bodyHeadingInMsg are provided, the module ignores h1Hat_B and reads the body-frame direction from the input message.

• Input inertial-frame heading: this can be specified via the input parameter hHat_N, connecting the message inertialHeadingInMsg, or connecting both the messages ephemerisInMsg and transNavInMsg. The input parameter hHat_N is desirable when the inertial heading is fixed in time. The message inertialHeadingInMsg is needed when the heading direction is time-varying. Finally, providing ephemerisInMsg and transNavInMsg allows to compute the inertial heading as the vector difference between the inertial position of a celestial object and the position of the spacecraft: this is useful when the spacecraft needs to point a body-frame heading towards a celestial object. When all of these input messages are connected, the inertial heading is computed from the inertialHeadingInMsg.

Module Assumptions and Limitations

The limitations of this module are inherent to the geometry of the problem, which determines whether or not all the constraints can be satisfied. For example, as shown in in R. Calaon, C. Allard and H. Schaub, “Attitude Reference Generation for Spacecraft with Rotating Solar Arrays and Pointing Constraints,” In preparation for Journal of Spacecraft and Rockets, depending on the relative orientation of \({}^\mathcal{B}h\) and \({}^\mathcal{B}a_1\), it may not be possible to achieve perfect incidence angle on the solar arrays. Only when perfect incidence is obtained, it is possible to solve for the solution that also drives the body-fixed direction \({}^\mathcal{B}a_2\) close to the Sun. When perfect incidence is achievable, two solutions exist. If \({}^\mathcal{B}a_2\) is provided as input, this is used to determine which solution to pick. If this input is not provided, one of the two solution is chosen arbitrarily.

Due to the difficulty in developing an analytical formulation for the reference angular rate and angular acceleration vectors, these are computed via second-order finite differences. At every time step, the current reference attitude and time stamp are stored in a module variable and used in the following time updates to compute angular rates and accelerations via finite differences.

User Guide

The required module configuration is:

attReference = oneAxisSolarArrayPoint.oneAxisSolarArrayPoint()
attReference.ModelTag = "threeAxesPoint"
attReference.a1Hat_B = a1_B
attReference.alignmentPriority = 0
scSim.AddModelToTaskAddModelToTask(simTaskName, attReference)

The module is configurable with the following parameters:

Module Parameters

Parameter	Default	Description
a1Hat_B	[0, 0, 0]	solar array drive direction, it must be specified by the user
alignmentPriority	0	0 to prioritize first constraint, 1 to prioritize second constraint
h1Hat_B (optional)	[0, 0, 0]	body-frame heading
hHat_N (optional)	[0, 0, 0]	inertial-frame heading
a2Hat_B (optional)	[0, 0, 0]	third body frame direction that should be as close as possible to Sun direction.
h2Hat_B (optional)	[0, 0, 0]	second body-frame heading

---

Typedefs

typedef enum alignmentPriority AlignmentPriority

typedef enum bodyAxisInput BodyAxisInput

typedef enum inertialAxisInput InertialAxisInput

Enums

enum alignmentPriority

Values:

enumerator prioritizeAxisAlignment

enumerator prioritizeSolarArrayAlignment

enum bodyAxisInput

Values:

enumerator inputBodyHeadingParameter

enumerator inputBodyHeadingMsg

enum inertialAxisInput

Values:

enumerator inputInertialHeadingParameter

enumerator inputInertialHeadingMsg

enumerator inputEphemerisMsg

Functions

void SelfInit_oneAxisSolarArrayPoint(OneAxisSolarArrayPointConfig *configData, int64_t moduleID)

This method initializes the output messages for this module.

Parameters

• configData – The configuration data associated with this module

• moduleID – The module identifier

Returns

void

void Reset_oneAxisSolarArrayPoint(OneAxisSolarArrayPointConfig *configData, uint64_t callTime, int64_t moduleID)

This method performs a complete reset of the module. Local module variables that retain time varying states between function calls are reset to their default values.

Parameters

• configData – The configuration data associated with the module

• callTime – [ns] time the method is called

• moduleID – The module identifier

Returns

void

void Update_oneAxisSolarArrayPoint(OneAxisSolarArrayPointConfig *configData, uint64_t callTime, int64_t moduleID)

The Update() function computes the reference MRP attitude, reference angular rate and acceleration

Parameters

• configData – The configuration data associated with the module

• callTime – The clock time at which the function was called (nanoseconds)

• moduleID – The module identifier

Returns

void

void oasapComputeFirstRotation(double hRefHat_B[3], double hReqHat_B[3], double R1B[3][3])

This helper function computes the first rotation that aligns the body heading with the inertial heading

void oasapComputeSecondRotation(double hRefHat_B[3], double rHat_SB_R1[3], double a1Hat_B[3], double a2Hat_B[3], double R2R1[3][3])

This helper function computes the second rotation that achieves the best incidence on the solar arrays maintaining the heading alignment

void oasapComputeThirdRotation(int alignmentPriority, double hRefHat_B[3], double rHat_SB_R2[3], double a1Hat_B[3], double R3R2[3][3])

This helper function computes the third rotation that breaks the heading alignment if needed, to achieve maximum incidence on solar arrays

void oasapComputeFinalRotation(int alignmentPriority, double BN[3][3], double rHat_SB_B[3], double hRefHat_B[3], double hReqHat_B[3], double a1Hat_B[3], double a2Hat_B[3], double RN[3][3])

This helper function computes the final rotation as a product of the first three DCMs

struct OneAxisSolarArrayPointConfig

#include <oneAxisSolarArrayPoint.h>

Top level structure for the sub-module routines.

Public Members

double a1Hat_B[3]

arrays axis direction in B frame

AlignmentPriority alignmentPriority

flag to indicate which constraint must be prioritized

double h1Hat_B[3]

main heading in B frame coordinates

double h2Hat_B[3]

secondary heading in B frame coordinates

double hHat_N[3]

main heading in N frame coordinates

double a2Hat_B[3]

body frame heading that should remain as close as possible to Sun heading

BodyAxisInput bodyAxisInput

flag variable to determine how the body axis input is specified

InertialAxisInput inertialAxisInput

flag variable to determine how the inertial axis input is specified

int updateCallCount

count variable used in the finite difference logic

uint64_t T1NanoSeconds

callTime one update step prior

uint64_t T2NanoSeconds

callTime two update steps prior

double sigma_RN_1[3]

reference attitude one update step prior

double sigma_RN_2[3]

reference attitude two update steps prior

NavAttMsg_C attNavInMsg

input msg measured attitude

BodyHeadingMsg_C bodyHeadingInMsg

input body heading msg

InertialHeadingMsg_C inertialHeadingInMsg

input inertial heading msg

NavTransMsg_C transNavInMsg

input msg measured position

EphemerisMsg_C ephemerisInMsg

input ephemeris msg

AttRefMsg_C attRefOutMsg

output attitude reference message

BSKLogger *bskLogger

BSK Logging.