attTrackingError#

Attitude Tracking Error#

Executive Summary#

The Attitude Tracking Error module reads in current spacecraft attitude, where it should be and a reference correction motion. It then computes the attitude and rate errors and express it all reference motion in the spacecraft body frame. This module is intended to be the last module in the guidance module chain. It’s output is at the guidance attitude tracking errors relative to a moving reference frame.

Module Input/Output Messages#

The following table lists all the module input and output messages:

Module I/O Messages#

Msg Variable Name

Msg Type

Description

attGuidOutMsg

AttGuidMsgPayload

attitude guidance tracking errors output message

attNavInMsg

NavAttMsgPayload

attitude navigation input message

attRefInMsg

AttRefMsgPayload

attitude reference input message

Module Functions#

Below is a list of functions that this simulation module performs

  • Reads the incoming attitude navigation and reference attitude message

  • Adjust the reference attitude

  • Computes the attitude tracking error

  • Computes the angular velocity of reference frame relative to inertial frame in body frame components

  • Computes the angular velocity error in body frame

  • Computes the angular acceleration in body frame

  • Writes the guidance module output message

Module Description#

The following text describes existing function in details and the mathematics behind the attTrackingError module.

The attTrackingError module computes attitude and rate tracking errors between a commanded reference frame and the spacecraft’s current navigation estimate. It outputs a guidance payload containing: (1) the attitude error expressed with Modified Rodrigues Parameters (MRPs), (2) the angular velocity tracking error expressed in body-frame components, and (3) the reference angular velocity and angular acceleration expressed in the body frame. These outputs are commonly consumed by downstream attitude controllers.

Parameter

  • \(\mathbf\sigma_{R_0R}\) : a configurable MRP correction mapping between an original reference frame (R0) and a corrected reference frame (R). This allows the module to apply a fixed reference offset to the incoming reference attitude.

Outputs

  • AttGuidMsgPayload:

    • \(\mathbf\sigma_{BR}\): MRPs describing the attitude error of (B) relative to (R)

    • \(^{B}\mathbf\omega_{BR}\): angular velocity error of (B) relative to (R), expressed in (B)

    • \(^{B}\mathbf\omega_{RN}\): reference angular velocity expressed in (B)

    • \(^{B}\mathbf\dot\omega_{RN}\): reference angular acceleration expressed in (B)

1. Reference attitude correction

The module begins by applying the configured correction \(\mathbf\sigma_{R_0R}\) to the incoming reference attitude to form an updated reference frame.

2. Attitude tracking error

The attitude tracking error \(\mathbf\sigma_{BR}\) is computed by finding the relative rotation from the corrected reference frame (R) \(\mathbf\sigma_{RN}\) to the body frame (B) \(\mathbf\sigma_{BN}\).

3. Reference angular velocity expressed in body components

Reference angular velocity is provided in inertial components \(^{N}\mathbf\omega_{RN}\). For control applications, it is often preferred in body components. Using the DCM \(\mathbf\left[BN]\) , the transformation is:

\(^{B}\mathbf\omega_{RN}\) = \(\mathbf\left[BN]\) \(^{N}\mathbf\omega_{RN}\)

4. Angular velocity tracking error

The angular velocity error is computed as the difference between the measured body rate and the reference rate, both expressed in body components:

\(^{B}\mathbf\omega_{BR}\) = \(^{B}\mathbf\omega_{BN}\) - \(^{B}\mathbf\omega_{RN}\)

5. Reference angular acceleration expressed in body components

Similarly, the reference angular acceleration is transformed into body components: \(^{B}\mathbf\dot\omega_{RN}\) = \(\mathbf\left[BN]\) \(^{N}\mathbf\dot\omega_{RN}\)

Overall, attTrackingError acts as a kinematic “bridge” between navigation and control: it aligns reference signals into the body frame and provides consistent tracking error quantities for downstream attitude control laws.

Test Description#

This unit test confirms correct implementation of the attitude tracking transformations by comparing its outputs to independently computed truth values. Known navigation and reference attitude states, angular rates, angular accelerations,and a reference correction are provided to the module. The test passes if the computed attitude error, angular rate error, and reference angular rate and acceleration expressed in the body frame match the expected values within a specified numerical tolerance.

User Guide#

The module is configured by:

attitudeTrackingError = attTrackingError.AttTrackingError()
attitudeTrackingError.modelTag = "attTrackingError"
attitudeTrackingError.setSigma_R0R(sigma_R0R)

Class AttTrackingError#

class AttTrackingError : public SysModel#

Data structure for module to compute the attitude tracking error between the spacecraft attitude and the reference.

Public Functions

AttTrackingError() = default#

Constructor.

~AttTrackingError() = default#

Destructor.

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

Returns:

void

void updateState(uint64_t callTime) override#

The Update method performs reads the Navigation message (containing the spacecraft attitude information), and the Reference message (containing the desired attitude). It computes the attitude error and writes it in the Guidance message.

Parameters:

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

Returns:

void

void setSigma_R0R(const Eigen::Vector3d &sigma_R0R)#

Setter method for sigma_R0R.

Parameters:

sigma_R0R –

Returns:

void

const Eigen::Vector3d &getSigma_R0R() const#

Getter method for sigma_R0R.

Returns:

const Eigen::Vector3d

Public Members

Message<AttGuidMsgPayload> attGuidOutMsg#

Output attitude guidance message.

ReadFunctor<NavAttMsgPayload> attNavInMsg#

Input msg measured attitude.

ReadFunctor<AttRefMsgPayload> attRefInMsg#

Input msg of reference attitude.

BSKLogger bskLogger = {}#

BSK Logging.