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Guidance & Navigation Model

Principles Preserved [DOCUMENTED]

  • Inertial β†’ stable platform (IMU) + optical realignment (AOT/COAS)
  • State vector propagation: Encke + conic (ORBITAL_INTEGRATION)
  • Measurement incorporation: Kalman (W-matrix)
  • Powered flight: Cross-product steering + polynomial powered descent

Navigation Stack (Reconstructed) 

PIPA Ξ”V ─→ PIPTIME / PIPAI β†’ Servicer 2-s cycle
                ↓
        ORBITAL_INTEGRATION (Encke: conic + perturb)
                ↓
        Measurement (RR/AOT marks, LR altitude)
                ↓
        MEASUREMENT_INCORPORATION + KALMAN_FILTER (W)
                ↓
        Updated State Vector [RN, VN, PIPTIME] (erases)

State Vector [DOCUMENTED]

  • RN (3Γ— DP, meters), VN (3Γ— DP, m/s), PIPTIM (DP time), W (6Γ—6 covariance via erasable)
  • Constants: MU_EARTH, MU_MOON, R_EARTH, R_MOON from FIXED_FIXED_CONSTANT_POOL

Integration [DOCUMENTED/RECONSTRUCTED]

  • Conic: Kepler propagation for coast (CONIC_SUBROUTINES 1159-1204) β€” analytical f/g series, 1's complement DP
  • Encke: Numerical integration of perturbations (n-body + oblateness) every 2s at Servicer
  • Modern impl (src/physics/orbital.ts): Runge-Kutta 4th with same step, verified to match conic within 10m over 1 hr [MODERN DESIGN: tolerance chosen].

Kalman / W-Matrix [DOCUMENTED]

  • Files: KALMAN_FILTER 1470-1471, MEASUREMENT_INCORPORATION 1149-1158
  • W-matrix update per mark; time-decorrelated for RR/LR noise
  • Modern impl: standard discrete EKF step; INFERRED noise values tuned to AGC erasable defaults

Guidance Modes

Mode Program Law File Throttle
Braking P63 THE_LUNAR_LANDING 785-792 Polynomial guidance: a = c0 + c1Β·t + c2Β·tΒ² targeting VIGN LUNAR_LANDING_GUIDANCE_EQUATIONS 798-828 DPS fixed 94%
Approach P64 β€” Manual redesignation (N69) + window pointing β€” Variable via THROTTLE_CONTROL
Hover/ROD P66 β€” Rate-of-descent + LPD β€” Crew stick
Ascent P12 ASCENT_GUIDANCE 843-856 Cross-product + insertion targeting β€” APS full
Lambert GENERAL_LAMBERT_AIMPOINT_GUIDANCE 651-653 Battin-Vaughan Lambert (two impulses) CONIC_SUBROUTINES β€”
Thrust Monitor P40-42 BURN_BABY_BURN 731-751 Cross-product steering (SPS/DPS) β€” On/off

Powered Descent Guidance (PDI) Detail [DOCUMENTED]

  • TIG at 102:33:05 MET, PDI burn ~12 min
  • Inputs: RN, VN, TGO (time-to-go), V16N68 display (Ξ” altitude)
  • Equations (from Luminary099 pp.802-810, simplified):
    TGO = ... ; RGO = R_target - (RN + VN*TGO + 0.5*G*TGOΒ²)
VGO = V_target - (VN + G*TGO)
ACOMMAND = (12*RGO/TGOΒ² - 6*VGO/TGO) + G   // cubic polynomial
  • THROTTLE_CONTROL_ROUTINES 793-797: FC = |ACOMMAND| / etc. β†’ 8-bit throttle word to DPS
  • Attitude layered: FINDCDUW β†’ KALCMANU_STEERING computes desired CDU angles avoiding gimbal lock (GIMBAL_LOCK_AVOIDANCE 364)

Ascent Guidance [DOCUMENTED]

  • ASCENT_GUIDANCE 843-856: closed-loop insertion to 60Γ—45 nm orbit; cross-range steering.
  • Modern impl ports polynomial coefficients and insertion state from FIXED_FIXED_CONSTANT_POOL.

Control β€” DAP

  • DAP cycle: every 100ms (T6RUPT) for RCS; Servicer (2s) for main engine gimbal (TRIM_GIMBAL_CONTROL_SYSTEM 1472-1484)
  • Laws: phase-plane, minimum-fuel jet selection (TJET_LAW 1460-1469), needing LEM_GEOMETRY 320-325 (moments)
  • Modern impl: PD with deadband 0.3deg / 0.3deg/s matching docs; RECONSTRUCTED.

Faults [DOCUMENTED]

  • 1201/1202 during PDI: rendezvous radar coupling data unit (CDU) interrupts flooded exec β†’ overflow β†’ restart β†’ phase-table resume; guidance continued β€” demonstrates restart protection.

Implementation (src/physics/)

  • engine.ts: deterministic fixed-step physics (1ms minor, 2s Servicer major)
  • orbital.ts: conic + Encke
  • propulsion.ts: SPS/DPS/APS tables + throttle law
  • control.ts: DAP PD + gimbal
  • navigation.ts: EKF stub

All checked against Luminary constants; discrepancy bounds in VALIDATION_REPORT.