1. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 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)

2. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 3 -MN-11

3. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 3 -MN-11 1. Phases of Landing Trajectory

4. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 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 C1.154.0000.0-0 with thrust of 420  20 kgf (tolerance) Regulation range 400  480 kgf (+13  -33 km) 2. Main Deceleration Phase 1 with Downrange Maneuver

5. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 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

6. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 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

7. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 3 -MN-11 Numerical derivative ∂Φ/∂P=-0.021 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 42001504-5.00 44001499-5.00 40001500-4.60 446.3+0.51504-5.2-0.3 396.7-0.51499-5.0+0.3 5. Thrust Correction

8. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 3 -MN-11 6. Phase 1. Trajectory with Linear Pitch Guidance

9. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 3 -MN-11 Engine C1.154.0000.0-0 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 )=  02 + 2t2, 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

10. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 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

11. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 3 -MN-11 9. Phase 2. Parameters of Nominal Trajectory

12. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 3 -MN-11 10. Phase 2. Correction of Initial Downrange Error

13. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 3 -MN-11 11. Phase 2. Correction of Initial Velocity Error

14. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 3 -MN-11 12. Phase 3. Landing on the Moon Engine 2554.487.00-0 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.

15. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 3 -MN-11 13. Phase 3. Single-parameter guidance

16. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 3 -MN-11 14. Phase 3. Two-parameter guidance

17. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 3 -MN-11 15. Phase 3. Simulation Results ParametersThrust, kgfComments 120130110 h ign1, m43.3 The first ignition h off1, m10.517.60.3 h ign2, m6.510.6-The second ignition h off1, m0.3 -  m prop3, kg 0-0.1-0.9Propellant consumption

18. The Third Moscow International Solar System Symposium. Moscow, 8-12 October 2012 3MS 3 -MN-11 16. 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.