ADCS.CONOPS.goals.vector_goal module

class ADCS.CONOPS.goals.vector_goal.Vector_Goal(boresight_name=None)

Bases: Goal

Abstract base class for vector-alignment pointing goals.

This class specializes Goal for goals that align a specified spacecraft body-frame vector with a desired inertial-frame direction. Typical examples include aligning a sensor boresight with a target vector expressed in the ECI frame.

Subclasses define a desired inertial direction \(\mathbf{v}_{\mathrm{ref}} \in \mathbb{R}^3\) as a function of the orbital state. The reference mapping takes the form

\[G_{\mathrm{vec}}(\mathcal{O}(t)) = \left( \mathbf{v}_{\mathrm{ref}}, \boldsymbol{\omega}_{\mathrm{ref}} \right)\]

where \(\boldsymbol{\omega}_{\mathrm{ref}}\) is typically zero or defined by the subclass.

This class provides a common geometric error computation based on quaternion representations of vector alignment.

Subclasses must implement to_ref().

See also

Goal, Attitude_Goal

Parameters:

boresight_name (str | None)

error(q, body_boresight, os0)

Compute the vector-alignment attitude error.

Let \(\mathbf{v}_{b}\) be the normalized boresight vector expressed in the spacecraft body frame, and let \(\mathbf{v}_{\mathrm{ref}}\) be the desired inertial direction returned by to_ref().

The reference direction is transformed into the body frame using the direction cosine matrix derived from the current attitude quaternion \(\mathbf{q}\):

\[\mathbf{v}_{\mathrm{ref}}^{b} = \mathbf{R}(\mathbf{q})^{\mathsf{T}} \mathbf{v}_{\mathrm{ref}}\]

A quaternion representing the shortest rotation that aligns \(\mathbf{v}_{b}\) with \(\mathbf{v}_{\mathrm{ref}}^{b}\) is then constructed.

For the nominal case, the error quaternion is

\[\begin{split}\mathbf{q}_{\mathrm{err}} = \frac{1}{\sqrt{2(1 + d)}} \begin{bmatrix} 1 + d \\ \mathbf{v}_{\mathrm{ref}}^{b} \times \mathbf{v}_{b} \end{bmatrix}\end{split}\]

where

\[d = \mathbf{v}_{b}^{\mathsf{T}} \mathbf{v}_{\mathrm{ref}}^{b}\]

In the singular case \(d \approx -1\), corresponding to a 180-degree misalignment, an arbitrary orthogonal rotation axis is selected.

The returned error vector is the vector part of the error quaternion, with sign chosen to enforce the shortest rotation.

Parameters:

• q (numpy.ndarray) – Current spacecraft attitude quaternion.

• body_boresight (numpy.ndarray) – Boresight direction expressed in the spacecraft body frame.

• os0 (Orbital_State) – Current orbital state.

Returns:

Vector-alignment attitude error.

Return type:

numpy.ndarray

to_ref(os0)

Generate a reference inertial direction and angular velocity.

Subclasses must implement this method to compute a desired inertial reference vector

\[\mathbf{v}_{\mathrm{ref}} \in \mathbb{R}^3\]

based on the current orbital state. The returned vector is expected to be nonzero and will typically be normalized by the downstream error computation.

Parameters:

os0 (Orbital_State) – Current orbital state.

Returns:

Reference inertial direction and reference angular velocity.

Return type:

Tuple[numpy.ndarray, numpy.ndarray]