triad

Executive Summary

This module computes a reference attitude frame using the TRIAD method that simultaneously satisfies multiple pointing constraints. The TRIAD Method determines spacecraft attitude by aligning two sets of vector observations. the input arguments are two non-parallel vectors in the body frame ( \({}^\mathcal{B}\hat{h}_1\) and \({}^\mathcal{B}\hat{a}_1\) ) and two targeted non-parallel vector in the inertial frame. The mathematical details of the triad algorithm can be found in R. Calaon phd “Guidance, Control and Momentum Management of Spacecraft with Multiple Pointing Constraints “. it creates a rotational matrix that prioritise the alignment of the body-frame direction \({}^\mathcal{B}\hat{h}_1\) with a the targeted reference direction \({}^\mathcal{N}\hat{h}_\text{ref}\), while taking is account all other constrains of the state.

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.

Figure 1: TRIAD Illustration

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 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

The details of the equations applied by this module can be found in R. Calaon PhD thesis, “Guidance, Control and Momentum Management of Spacecraft with Multiple Pointing Constraints”.

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. This applies on singularities when the Sun Prop Earth angle (SPE) is (0,90,180).

User Guide

The required module configuration is:

attReference = triad.Triad()
attReference.modelTag = "triad"
attReference.a1Hat_B = a1_B
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
h1Hat_B (optional)	[0, 0, 0]	body-frame heading
hHat_N (optional)	[0, 0, 0]	inertial-frame heading
celestialBodyInput (optional)	0	should be set to 1 when the celestial body pointed at is the Sun.

Class Triad

class Triad : public SysModel

Top level structure for the sub-module routines.

Public Functions

void reset(uint64_t callTime) override

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:

callTime – [ns] time the method is called

Returns:

void

void updateState(uint64_t callTime) override

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

Parameters:

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

Returns:

void

void setA1Hat_B(const Eigen::Vector3d &a1Hat_B)

Setter for a1Hat_B variable.

Setter method for sigma_R0R.

Parameters:

a1Hat_B –

Returns:

void

const Eigen::Vector3d getA1Hat_B() const

Getter for a1Hat_B variable.

Getter method for a1Hat_B.

Returns:

const Eigen::Vector3d

void setH1Hat_B(const Eigen::Vector3d &h1Hat_B)

Setter for h1Hat_B variable.

Setter method for sigma_R0R.

Parameters:

h1Hat_B –

Returns:

void

const Eigen::Vector3d getH1Hat_B() const

Getter for h1Hat_B variable.

Getter method for h1Hat_B.

Returns:

const Eigen::Vector3d

void setHHat_N(const Eigen::Vector3d &hHat_N)

Setter for hHat_N variable.

Setter method for sigma_R0R.

Parameters:

hHat_N –

Returns:

void

const Eigen::Vector3d getHHat_N() const

Getter for hHat_N variable.

Getter method for hHat_N.

Returns:

const Eigen::Vector3d

void setCelestialBodyInput(const CelestialBody &celestialBodyInput)

Setter for celestialBodyInput variable.

Setter method for sigma_R0R.

Parameters:

celestialBodyInput –

Returns:

void

const CelestialBody getCelestialBodyInput() const

Getter for celestialBodyInput variable.

Getter method for celestialBodyInput.

Returns:

const CelestialBody

void setBodyAxisInput(const BodyAxisInput &bodyAxisInput)

Setter for bodyAxisInput variable.

Setter method for sigma_R0R.

Parameters:

bodyAxisInput –

Returns:

void

const BodyAxisInput getBodyAxisInput() const

Getter for bodyAxisInput variable.

Getter method for bodyAxisInput.

Returns:

const BodyAxisInput

void setInertialAxisInput(const InertialAxisInput &inertialAxisInput)

Setter for inertialAxisInput variable.

Setter method for sigma_R0R.

Parameters:

inertialAxisInput –

Returns:

void

const InertialAxisInput getInertialAxisInput() const

Getter for inertialAxisInput variable.

Getter method for inertialAxisInput.

Returns:

const InertialAxisInput

Public Members

ReadFunctor<NavAttMsgPayload> attNavInMsg

input msg measured attitude

ReadFunctor<BodyHeadingMsgPayload> bodyHeadingInMsg

input body heading msg

ReadFunctor<InertialHeadingMsgPayload> inertialHeadingInMsg

input inertial heading msg

ReadFunctor<NavTransMsgPayload> transNavInMsg

input msg measured position

ReadFunctor<EphemerisMsgPayload> ephemerisInMsg

input ephemeris msg

Message<AttRefMsgPayload> attRefOutMsg

output attitude reference message

BSKLogger bskLogger = {}

BSK Logging.