GNC/guidance/detour_planner.py — Build-Time Coverage Predictor

Offline oracle: replay an aim-point schedule through the finder's coverage marker and return the area-weighted coverage fraction.

Camera Pose per Schedule Step

At orbit CoM point $\bm p_c^{(i)}$ and aim point $\bm x_{\text{aim}}^{(i)}$:

$$\hat{\bm u}^{(i)} = \frac{\bm x_{\text{aim}}^{(i)} - \bm p_c^{(i)}}{\|\bm x_{\text{aim}}^{(i)} - \bm p_c^{(i)}\|}$$

$$\bm p_e^{(i)} = \bm p_c^{(i)} + r_{\text{cam}} \hat{\bm u}^{(i)}$$

EE placed on the camera sphere of radius $r_{\text{cam}}$; look-axis $\bm z_e = \bm x_{\text{aim}}^{(i)} - \bm p_e^{(i)}$.

Camera Orientation

Roll reference fixed to world-$x$: $\bm e_x = [1,0,0]^\top$.

$$\bm z_e^{(i)} = \frac{\bm x_{\text{aim}}^{(i)} - \bm p_e^{(i)}}{\|\bm x_{\text{aim}}^{(i)} - \bm p_e^{(i)}\|}$$

$$R_e^{(i)} = \text{frame}_{xz}\!\left(\bm e_x, \bm z_e^{(i)}\right)$$

Roll continuity ($R_{\text{prev}}$ chaining) is irrelevant — visibility uses only $\bm z_e$.

Strided Coverage Replay

Strided sweep over $N$ orbit samples with stride $\Delta_s$:

$$\mathcal{S} = \bigcup_{k=0}^{\lfloor N/\Delta_s \rfloor} \mathcal V\!\left(\text{pose}_{k\Delta_s}\right)$$

where $\mathcal V$ is the visible-triangle set at a given pose. Finder state (seen_triangles, triangle_stats) is deep-snapshotted before the sweep and restored in-place in a finally block — side-effect-free by construction.

Area-Weighted Coverage Fraction

Let $\mathcal{S} \subseteq \{0,\ldots,N_\triangle-1\}$ be the seen triangle set.

$$\hat f_{\text{cov}} = \min\!\left(\frac{\displaystyle\sum_{j \in \mathcal{S}} A_j}{A_{\text{total}}}, 1\right)$$

$A_j$ = area of triangle $j$; $A_{\text{total}} = \sum_{j=0}^{N_\triangle - 1} A_j$.

This is identical to the sim's inspection.area_coverage_frac by construction.