The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN-11 LANDING DYNAMICS ON THE «LUNA-GLOB» PROJECT Sikharulidze Yu.G., Zhukov B.I., Tuchin A.G. (Keldysh Institute of Applied Mathemathics RAS) Zaiko Yu.K., Fedotov V.P., Likhachov V.N., Rozin P.E. (Lavochkin Design Center)

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN-11

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN Phases of Landing Trajectory

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN-11 Range of the initial true anomaly -10 o  o  +10 o Variation of the initial time  3 min De-orbit point shift  306 km Propellant consumption 389 kg (initial Lander mass 911 kg) The optimal pitch angle guidance and linear pitch law Engine C with thrust of 420  20 kgf (tolerance) Regulation range 400  480 kgf (+13  -33 km) 2. Main Deceleration Phase 1 with Downrange Maneuver

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN-11 Terminal guidance algorithm with numerical prediction of remaining trajectory (Numerical Predictor-Corrector NPC). Two-parametric guidance:  (t)=  0 + t. Three predicted trajectories. Multistep process:  t guid =1 s,  t stab =0.05 s. Linear correction of guidance parameters:  0i =  0i-1 +   0i i = i-1 +  i 3. Numerical Predictor-Corrector

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN-11 Terminal conditions for the Phase 1: V n1 =0 (stop of prediction), V r1 =-5 m/s, h 1 =1500 m (corrected values). Adaptation algorithm: m(t)=? P(t)=? Phantom acceleration: W=P/m=P/(m 0 -│dm/dt│t)=g 0 P sp /(  -t), where  =m 0 /│dm/dt│- “total burning time”. Measurements W 1 for t 1 and W 2 for t 2 → parameters of adaptation , P sp 4. Algorithm of Adaptation

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN-11 Numerical derivative ∂Φ/∂P= deg/kgf. Predicted angular error due to thrust variation and de-orbit point shift: ΔΦ i pred. Thrust correction: ΔP= -ΔΦ i pred /(∂Φ/∂P). Thrust is unknown. P, kgf Δ  o, deg h 1, mV r, m/sΔm prop, kg Thrust Correction

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN Phase 1. Trajectory with Linear Pitch Guidance

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN-11 Engine C with thrust of 420  20 kgf (tolerance) Regulation range 400  480 kgf Initial errors: ΔΦ 1, Δh 1, ΔV r1. Corrected values: V r2 =-5 m/s, h 2 =50 m, ΔΦ 2 =0 Parameters of control:  2 (t 2 )=  t2, t ign2 – time ignition (ignition altitude h ign2 ). Four predicted trajectories. Linear correction of guidance parameters:  0i =  0i-1 +  0i, i = i-1 +  i, t ign2(i) = t ign2(i-1) +  t ign2(i) 7. Phase 2. Precision Deceleration

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN-11 After engine ignition: two-parametric control & thrust regulation  0i =  0i-1 +   0i, i = i-1 +  i Numerical derivative ∂P/∂h=1.14 kgf/m. Measurements of phantom acceleration W→ , P sp. Thrust correction ΔP=- Δh/(∂P/∂h), Δh=h pred2 -h 2. Thrust is unknown. 8. Phase 2. Adaptation Algorithm

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN Phase 2. Parameters of Nominal Trajectory

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN Phase 2. Correction of Initial Downrange Error

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN Phase 2. Correction of Initial Velocity Error

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN Phase 3. Landing on the Moon Engine Thrust 2x(65±5) kgf (tolerance), without thrust regulation. Specific thrust 287.7±5 s (tolerance) Terminal conditions: altitude 0.3 m, vertical velocity -2.5±1 m/s, side velocity ≤1 m/s Single control parameter: t ign3 – time of engine ignition.

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN Phase 3. Single-parameter guidance

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN Phase 3. Two-parameter guidance

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN Phase 3. Simulation Results ParametersThrust, kgfComments h ign1, m43.3 The first ignition h off1, m h ign2, m The second ignition h off1, m0.3 -  m prop3, kg Propellant consumption

The Third Moscow International Solar System Symposium. Moscow, 8-12 October MS 3 -MN Results 1. The terminal guidance algorithm (NPC) with adaptation to real motion conditions was developed for landing on the Moon. 2. For the Phase 1 NPC provides compensation of initial de- orbit point error within ±0.5 o or ±15 km in downrange (±9 s). 3. For the Phase 2 NPC provides compensation of initial errors within ±40 m in downrange or ±2 m/s in side velocity by the pith angle of ±20 o from the local vertical. 4. For the Phase 3 NPC provides adaptation to the real motion conditions.