GNC/guidance/guidance_rollout.py — guidance-only rollout

Integrates the guidance tower over orbit windows without controller dynamics. A fake motion state replaces the plant — fast coverage and selection oracle.

Arclength clock

At step $k$ the arclength progress along the active window is:

$$s_k = \min\!\bigl(k \Delta t\cdot v_{\mathrm{ref}}, s_{\mathrm{end}}\bigr)$$

Local fractional progress is then recovered by linear interpolation over the precomputed arclength samples $\{s_i\}$:

$$\text{progress}_k = i_{\mathrm{start}} + \operatorname{interp}(s_k, \{s_i\}, \{i\})$$

Nominal CoM kinematics at step $k$

Desired CoM velocity and centripetal acceleration (from §5.2–5.3):

$$\bm v_{cd} = v_{\mathrm{ref}} \hat{\bm t}(\text{progress}_k),\qquad \bm a_{cd} = v_{\mathrm{ref}}^2 \bm\kappa(\text{progress}_k) \tag{5.3}$$

$\hat{\bm t}$ and $\bm\kappa$ are the unit tangent and curvature vector of the discrete helix $\Lambda$.

Fake motion state

The plant is replaced by a fake motion state:

$$\text{fake}_k = \begin{cases} \bm p_c,\bm v_c,\bm a_c & \leftarrow \text{desired CoM at step } k \\ \bm p_e,\bm z_e,\bm R_e,\bm\nu_e & \leftarrow \text{desired EE command at step } k-1 \end{cases}$$

On step $k=0$ no previous EE command exists; the base desired alone is used.

Per-step recurrence

$$\text{des}_k = \mathcal G\!\left(\text{fake}_k, \text{des}^{\text{base}}_k, \text{des}_{k-1}\right)$$

where $\mathcal G$ is the EE-goal map (add_ee_goal). FOV marking fires every $N_s = 5$ steps when a valid pose exists:

$$k \bmod N_s = 0 \text{ and } \bm p_e \neq \varnothing \Rightarrow \text{mark FOV}(\bm p_e, \bm R_e)$$

Output

Each step appends a StepLog to the logger:

$$\text{StepLog}_k = \bigl(\text{des}_k, \text{actual}=\varnothing, \text{guidance}, \text{inspection}\bigr)$$

$$\text{inspection} = \bigl(n_{\text{tri}}, A_{\text{cov}}\bigr),\qquad A_{\text{cov}} = \frac{\text{unique triangles seen}}{\text{total triangles}}$$

The function returns Package(logger, log_path=None) — no NPZ is written.

Coverage is traversal-driven

$$A_{\text{cov}} \approx 1 \iff \text{progress}_k \to \text{path end}$$

A short run covers only the southern orbital cap ($A_{\text{cov}} \approx 0.47$). The full 30-revolution helix is required for $A_{\text{cov}} \to 1$.

Marking stride $N_s$ (not angular resolution) is the dominant cost lever.