The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-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 20123MS3-MN-11

The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-MN-11

h=18 kmVn=1690 m/sVr=0

h=1500 mVn=0 Vr=-5m/s

h=50 mVn=0 Vr=-5m/s h=0

Vn=0 Vr=-2 m/s

1

2

3 4

Pre-landing orbit 18x100 kmPeriluna

Phase 1

Phase 2

Phase 3

1. Phases of Landing Trajectory

The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-MN-11

Range of the initial true anomaly -10oo +10o

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 42020 kgf (tolerance)

Regulation range 400480 kgf (+13-33 km)

2. Main Deceleration Phase 1 with Downrange Maneuver

The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-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: tguid=1 s, tstab=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 20123MS3-MN-11

Terminal conditions for the Phase 1: Vn1=0 (stop of prediction),

Vr1=-5 m/s, h1=1500 m (corrected values).

Adaptation algorithm: m(t)=? P(t)=?

Phantom acceleration: W=P/m=P/(m0-│dm/dt│t)=g0Psp/(-t),

where =m0/│dm/dt│- “total burning time”.

Measurements W1 for t1 and W2 for t2 →

parameters of adaptation , Psp

4. Algorithm of Adaptation

The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-MN-11

Numerical derivative ∂Φ/∂P=-0.021 deg/kgf.

Predicted angular error due to thrust variation

and de-orbit point shift: ΔΦi pred.

Thrust correction: ΔP= -ΔΦi pred/(∂Φ/∂P). Thrust is unknown.

P, kgf Δo, deg h1, m Vr, m/s Δmprop, kg

420 0 1504 -5.0 0

440 0 1499 -5.0 0

400 0 1500 -4.6 0

446.3 +0.5 1504 -5.2 -0.3

396.7 -0.5 1499 -5.0 +0.3

5. Thrust Correction

The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-MN-11

6. Phase 1. Trajectory with Linear Pitch Guidance

The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-MN-11

Engine C1.154.0000.0-0 with thrust of 42020 kgf (tolerance)

Regulation range 400480 kgf

Initial errors: ΔΦ1, Δh1, ΔVr1.

Corrected values: Vr2=-5 m/s, h2=50 m, ΔΦ2=0

Parameters of control: 2(t2)= 02+ 2t2, tign2 – time ignition

(ignition altitude hign2).

Four predicted trajectories.

Linear correction of guidance parameters: 0i =0i-1+0i,

i= i-1+ i, tign2(i) =tign2(i-1)+tign2(i)

7. Phase 2. Precision Deceleration

The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-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→ , Psp.

Thrust correction ΔP=- Δh/(∂P/∂h), Δh=hpred2-h2.

Thrust is unknown.

8. Phase 2. Adaptation Algorithm

The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-MN-11

300 320 3400.0

0.5

1.0

1.5

-60

-40

-20

0

0

150

300

450

P,kgf

P

h,km

Vy,m/s

h

Vr

t, s0

9. Phase 2. Parameters of Nominal Trajectory

The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-MN-11

10. Phase 2. Correction of Initial Downrange Error

The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-MN-11

11. Phase 2. Correction of Initial Velocity Error

The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-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: tign3 – time of engine ignition.

The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-MN-11

13. Phase 3. Single-parameter guidance

The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-MN-11

14. Phase 3. Two-parameter guidance

The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-MN-11

15. Phase 3. Simulation Results

Parameters Thrust, kgf Comments120 130 110

hign1, m 43.3 43.3 43.3 The first ignition

hoff1, m 10.5 17.6 0.3

hign2, m 6.5 10.6 - The second ignitionhoff1, m 0.3 0.3 -

mprop3, kg 0 -0.1 -0.9 Propellant consumption

The Third Moscow International Solar System Symposium. Moscow, 8-12 October 20123MS3-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 ±0.5o 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 ±20o from the local vertical.

4. For the Phase 3 NPC provides adaptation to the real motion

conditions.