Attitude Reference Correction Software

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Description

This module is defined to work as part of a pointing program in an ADCS software chain as shown below.

This module is used to modify an existing pointing reference by a known, constant rotation. Given an input reference frame $\mathcal{R}$ this module computes a corrected frame ${\mathcal{R}}_c$.

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Example Use Cases

• Re-orient an existing pointing reference. For example, modify the Nadir Pointing Software frame to point the z-axis towards the parent body (rather than in the direction of the angular momentum). This may be used for ground-pointing for planetary observation applications.
• Re-orient the spacecraft coordinate system. Allows for aligning specific features or components on the Spacecraft with the pointing reference.

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Module Implementation

The module performs the following computation:

$$[R_{c}N]=[R_{c}R][RN]$$

Where the inputs are the DCM $[RN]$ which represents the input frame $\mathcal{R}$, and the DCM $[R_{c}R]$ which represents the reference frame correction. The DCM $[R_{c}N]$ is the resulting corrected reference frame ${\mathcal{R}}_c$. All inputs and outputs are provided as equivalent MRP Vectors.

The correction $[R_{c}R]$ can be specified directly, in which case the resulting ADCS software chain will align the spacecraft body frame $\mathcal{B}$ with the corrected reference frame ${\mathcal{R}}_c$. Alternatively, a body-frame correction $[B_{c}B]$ can be specified, in which case the resulting ADCS software chain will align a corrected spacecraft body frame ${\mathcal{B}}_c$ with $\mathcal{R}$ instead. This is implemented by finding the equivalent corrected reference frame ${\mathcal{R}}_c$ to achieve this pointing, which is given by

$$[R_{c}R]=[B_{c}B{]}^{-1}=[B{B}_c]$$

This gives the corrected reference frame ${\mathcal{R}}_c$ such that when $\mathcal{B}$ aligns with ${\mathcal{R}}_c$, ${\mathcal{B}}_c$ aligns with $\mathcal{R}$ as desired. The angular velocity and angular acceleration of the corrected frame ${\mathcal{R}}_c$ are the same as for the input frame $\mathcal{R}$.

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Assumptions/Limitations

• Either $[R_{c}R]$ or $[B_{c}B]$ may be specified, but not both. To achieve both a reference frame correction and a body-frame correction two Attitude Reference Correction modules may be used. Alternatively, one Attitude Reference Correction may be used for the reference frame correction, and the body-frame correction specified in the Attitude Tracking Error module.
• The correction $[R_{c}R]$ or $[B_{c}B]$ is assumed to be a constant rotation.

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References

[1] Hanspeter Schaub and John L. Junkins. Analytical Mechanics of Space Systems. AIAA Education Series, Reston, VA, 3rd edition, 2014.