21st ISSFD Toulouse

GNC SOLUTIONS FOR NEXT-MOON LUNAR LANDER MISSION

Sara Melloni(1)

, Marco Mammarella(1)

, Jesús Gil-Fernández(1)

,

Pablo Colmenarejo Matellano(1)

, Maren Homeister(2)

(1)

Newton 11, P.T.M Tres Cantos 28760 (Spain), +34918072100, smelloni@gmv.com,

mmammarella@gmv.com, jesusgil@gmv.com, pcolmenarejo@gmv.com (2)

OHB, homeister@ohb-system.de

ABSTRACT

NOMENCLATURE

DL Descent and Landing

DOI Descent Orbit Injection

FOV Field Of View

FPA Flight Path Angle

GT Ground Tracking

HG High Gate

LS Landing Site

KLN Known Landmark Navigation

MECO Main Engine Cut-Off

TG Terminal Gate

2

ULN Unknown Landmark Navigation

1. INTRODUCTION

In 2001 the European Space Agency set a new programme for a European long-term plan of missions

for robotic and human exploration of the Solar System. Within this plan a precursor mission named

NEXT has been established to undergo the Phase-A level for a technology demonstration on a Lunar

high precision landing with Hazard Avoidance, focused on in-situ science.

The space race for the exploration supremacy arisen during the Cold War gave place to a long list of

missions [7] aimed to observe the Moon, bring on Earth Moon’s rock samples or even visit the satellite

through manned explorations. Despite all the Moon successful missions, only a very limited area was

sampled [3], reason why NEXT mission will target to the South Pole of the Moon on the near side

where scientists have great interest because of the close presence of the Aitken basin, second biggest

crater of the Solar System and source of old Moon material and instruments can enjoy a quasi-eternal

illumination [6].

The scientific patrimony that investigations over areas such as Lunar geophysics, geochemistry, Life

sciences would bring to current state of knowledge about the Earth’s natural satellite, that the presence

on-board of a rover was set as baseline of the project for which the overall design of the mission is

strongly constrained by the propellant mass saving.

The GNC design for the Phase-A of NEXT Moon Lunar Lander considers the Descent and Landing

trajectory, which

Table 1

Phase Sub-Phase Events Altitude (m) In Fig.1

Orbital

Phase

Circular Orbit

Last nominal Tracking Orbit

Determination

(120 m, 0.012 m/s)

105 Till point 1

Coasting Phase DOI and start of elliptical orbit 10

5 (Aposelenium) to

15000 (Periselenium) Point 1

Main Braking Start of Main Braking 15000 Point 2

Visual Phase

High Gate

(Start of Landmark navigation &

relative velocity determination)

3000 Point 3

- Navigation results available

(~5s after High Gate)

- Define Guidance Correction

- Start Corrective Manoeuvre to

achieve correct guidance (500 m

maximum divert)

~2670 -

- 1st Hazard Map available

(Slopes, Light, Roughness)

- Start of “ 1st Retargeting

Manoeuvre”

(200m maximum divert)

1144 -

- 2nd

Hazard Map available

(Slopes, Light, Rocks)

- Start of “2nd

Retargeting

Manoeuvre”

(50m maximum divert)

85 -

3

Terminal Descent Phase

- Terminal Gate

(Nominal horizontal speed=0 m/s)

- Vertical descent with -1 m/s

vertical speed

5 Point 4

Touch Down

(Nominal vertical speed=-0.2 m/s) 0 Point 5

Table 1: Definition of the sevaral phases and main events

Fig.1: Scheme of the overall mission

2. GUIDANCE SCHEME

impact the quality and outcome of the results of the mission Phase-A analyses. The main

reason for this choice is the fact that during the part the trajectory which would be affected the most by

the out-of-plane components, the Visual Phase, a transversal retargeting could be accomplished by

imposing a thrust bank angle which falls between 1% and 3% of the typical thrust pitch angles required

for longitudinal manoeuvres and therefore the lateral problem can be considered as a perturbation to the

in-plane motion. Moreover the increase in ΔV expenditure due to pure transversal manoeuvres, which

amplitude is the maximum range established for the longitudinal problem, is less than 2% (<4m/s) of

the total Visual Phase ΔV for nominal trajectory, while the ΔV required for the longitudinal manoeuvre

can reach the 14% (no control included in both situations).

4

The guidance for the nominal LS foresees a constant thrust but different levels for both Main Braking

and Visual Phase. In particular, during the Main Braking the thrust is kept constant.

At the start of the Main Braking the orbital conditions are transformed into Moon centred inertial frame

with the Z-axis pointing outwards, to the nominal LS and this frame of reference is kept till the

touchdown (see Fig.2).

Fig.2: Frames of reference adopted

[1]

Fig.2

(1)

(1)

5

□ Angle formed by the apses line of the transfer elliptical orbit wrt the position of the nominal LS

(see Fig.2)

□ Duration of the Main Braking

□ Thrust Pitch angle coefficients for Main Braking Phase (bilinear tangent law)

□ Duration of the Visual Phase (or Throttle Back)

□ Thrust Pitch angle for Visual Phase

[8

Fig.3

6

Fig.3 Double branches guidance problem Fig.4 Initial guess simplification

Eqs.(2)-(3).

(2)

(3)

(4)

(4)

7

Fig.5: Incidence angle for a re-targeting

manoeuvre [-500:100:500] m

Fig.6: variation in function of

Fig.7: variation in function of

Fig.8: variation in function of

Fig.9: variation in function of

The thrust levels have to be chosen primarily in the region of the existence of the solution, but also in

order to maximize and therefore the permanence of the LS inside the FOV of the instruments,

Other criteria can be taken into account for the choice of the thrust level couple, such as the

8

minimization of the difference between the angles, in order to have a shorter transient due to the real

rotating capabilities of the Lander.

Once chosen the thrust couples, the control solutions have been used to generate look-up tables, for on-

board purposes, to reduce the computational demands.

3. NAVIGATION SCHEME

The designed navigation allows two scenarios: Scenario 1, considers a mature technology, Scenario 2

for innovative technologies. During the Orbital Phase an absolute navigation is used, while the Visual

and Terminal Descent Phases foresee relative navigation wrt the LS.

For what concerns the trajectory and in case of first scenario, the IMU accelerometers are used for the

DOI and one single measurement correction is provided by the Ground Tracking at DOI. During the

Main Braking it is used a calibrated IMU and camera and/or relative LIDAR technology is in use

during the Visual Phase. The Terminal Descent Phase makes use of IMU and a Radar Altimeter detects

the altitude above the target.

The innovative technology scenario differs from the mature by the use of Camera-based surface Known

Landmark Navigation (see 3.1) until the Periselenium is reached.

At the start of the Visual Phase, camera or/and Absolute LIDAR are used to identify the LS by

applying KLN-like technology. During the Visual Phase the ULN ([10], [11]) can be used (less CPU

demanding) and during the Terminal Descent Phase, high frequency propagation IMU and Radar

Altimeter are foreseen.

[9] [12 (see Table 2)

[12 [9

9

Table 2: Detailed sensors baseline for the mission

Fig.10: Schematic model of the KLN

The expected performances results of the KLN have been quantified through the following analysis it

has been chosen a 1024x1024 pixels camera, oriented at -90º wrt the longitudinal axis of the Lander,

FOV of 50º.

Table

3 In Table 4, the manoeuvre simulated is a straight flight with constant altitude of 3 km and velocity

equal to 60 m/s.

Pixels

errors

xerr (99%)

[m]

yerr (99%)

[m]

zerr (99%)

[m]

0 34.173 48.006 86.515

1 35.672 50.555 88.901

2 36.215 51.216 86.161

4 39.480 51.208 92.902

10 56.498 71.592 153.413

Pixels

errors

xerr (99%)

[m]

yerr (99%)

[m]

zerr (99%)

[m]

0 1.118 1.537 3.302

1 1.104 1.475 3.398

2 1.112 1.487 4.231

4 1.532 2.153 4.525

10 5.300 4.398 7.056

10

Table 3: KLN sensitivity analysis @ 100km altitude,

velocity 1.6*103m/s

Table 4: KLN sensitivity analysis @ 3km altitude,

velocity 60m/s

Fig.11: KLN sensitivity analysis between 100 km

and 15 km altitude

4. CONTROL SCHEME

During the Visual Phase, the Lander is controlled though the thrust magnitude and direction, using

pulsing thrusters.

The attitude control is a hybrid of

(5)

(5)

11

Where , since the LS is typically observable during the second branch

of the manoeuvre.

Inside Eq.(5), are the reference values for the thrust magnitude and direction for the current

control point and for the present guidance they are constant along the same trajectory branch.

Linearizing the problem for small variations on the controls and expressing recursively the following

point in function on the previous one, we get to the expression of the final point in function of the

initial point (see Eq.(6)).

(6)

The system described in the Eq.(6), can be optimized and solved wrt , obtaining a low consumption

correction profile for thrust magnitude and direction, which leads to the nominal final point in presence

of errors on the initial state vector of the reference profile.

The same procedure can be done in correspondence of each control point so as to correct also the

actuation errors occurring during the trajectory.

Limitation on the present controller scheme is the number of control point, which should not be less

than 2 in order to be able to solve the determined problem with 4 constraints at the target point.

5. RESULTS

A High Fidelity Functional Engineering Simulator has been developed, in which all GNC algorithms

have been modelled and tested both in open and closed loop. The simulations start with the circular

orbit and the results are given between the DOI manoeuvre and the Terminal Gate.

The simulator has been split into 3 sub-simulators to simplify the analysis of the results: circular orbit,

DOI and elliptical trajectory are modelled in the first simulator; Main Braking in the second; Visual

Phase in the third.

In order to characterize the end to end performances and robustness of the present Next Moon LL GNC

system, the simulators have been run using the output conditions of a sub-simulator as inputs to the

following one. In particular in the present section will be given the results relative to a Monte Carlo

batch made of 225 runs which guarantee 2 performance with an estimation uncertainty of 10 % (as

outlined in literature, the number of runs increases rapidly with the confidence level and the estimation

uncertainty, and is around 1000 to be able to estimate the 3 value with 5% of uncertainty).

The parameters of the simulations are:

□ Initial state errors: attitude, angular rate, position, velocity, etc.

□ Lander MCI: mass, inertia and COM.

□ Navigation sensor (IMU, TRN, etc.) measurement errors and noise, inc. alignment error.

□ Engines’ errors: thrust noise, alignment (direction and position).

□ Lunar gravity field disturbances.

□ Landing terrain topography (distribution of safe and hazardous areas).

Hereafter will follow a description of the results for the Elliptical trajectory and the Main Braking

Phase. A snap of the simulated Elliptical trajectories is reported in Fig.12.

12

In both scenarios the true dispersion at Periselenium

doesn’t allow following the reference Main Braking

profile without losing the LS. In case of Scenario 1, the

accuracy provided by the Ground Tracking at DOI

computation introduces navigation errors at Periselenium

having the same order of magnitude as the true dispersion

and therefore no solution can be addressed not to lose the

landing site during the following phase.

On the other hand, in case of Scenario 2 (see Table 5),

the non-spherical gravitational field of the Moon,

associated to a Keplerian DOI manoeuvre computation

still bring to a high true dispersion at the Periselenium

but one order of magnitude smaller than for Scenario 1,

hence the true dispersion can be recovered by re-

computing the Main Braking profile.

Fig.12: Last 20 km of the Elliptical Orbit

Results

@ Peri-

selenium

True Dispersion Navigation Errors

Scenario 1 Scenario 2

Down

[m]

Alt

[m]

V_hor

[m/s]

V_ver

[m/s]

Down

[m]

Alt

[m]

V_hor

[m/s]

V_ver

[m/s]

Down

[m]

Alt

[m]

V_hor

[m/s]

V_ver

[m/s]

percentile

68.27%

-619610

± 1564

14387

± 101

1692,3

± 0,1

-0,0286

± 0,0297

-106 ±

891

67 ±

231

-0,079 ±

0,237

0,06 ±

0,35

9,56 ±

0,13

49,6

± 0,2

0,083 ±

0,002

-0,01 ±

0,012

percentile

95%

-624000

± 6757

14324

± 532

1692,3

± 0,4

-0,1584

± 0,1601

-235 ±

1496

478 ±

950

-0,213 ±

0,869

-0,11 ±

1,50

9,37 ±

0,43

49,5

± 0,3

0,083 ±

0,003

-0,134

± 0,022

percentile

99%

-628000

± 10915

14305

± 699

1692,4

± 0,6

-0,2386

± 0,2405

-497

±1880

594 ±

1606

-0,148 ±

1,100

-0,31 ±

1,95

9,19 ±

0,70

49,5

± 0,5

0,083 ±

0,003

-0,018

± 0,028

Optimal -621440 15000 1692,1 0 - - - - - - - -

Table 5: Monte Carlo results at Periselenium

The simulations revealed a high sensitivity of the system wrt the mass knowledge: knowing the state

vector with enough precision at Periselenium (Scenario 2), uncertainties on the initial mass bigger than

5% in that point brings to an ineffective Main Braking profile re-computation.

When assuming the Lander mass known, the true dispersion at HG is dramatically improved, but still in

a few cases in which velocity dispersion at PDI is especially large, the MB new re-optimized profile

does not fit properly (see Fig.14). The reason for this is the fact that the Aposelenium and Periselenium

altitude, and therefore the Periselenium velocity are not optimization parameters, but inputs to the MB

profile computation.

13

Fig.13: Main Braking trajectory, without re-

computation of Main Braking profile (Scenario 1)

Fig.14: Main Braking trajectory, with re-

computation of Main Braking profile (Scenario 2)

When the Main Braking profile can be re-computed (for Scenario 2) the reduction of the dispersion is

dramatic, as it can be observed by comparing the results obtained at the High Gate for the two

scenarios (see Table 6 and Table 7). In case of Scenario 1, in fact, since the navigation errors at the

Periselenium have the same order of magnitude as the true dispersion, it is impossible to assess with

enough precision the real error wrt to the nominal position and this makes it impossible nor to re-

compute of an effective new Main Braking profile neither to achieve the Safe and Soft Landing

requirement (see velocity true dispersion in Table 6).

Results @

High Gate

Scenario 1

True Dispersion Navigation Errors

Down

[m] Alt [m]

V_hor

[m/s]

V_ver

[m/s]

Down

[m] Alt [m]

V_hor

[m/s]

V_ver

[m/s]

percentile

68.27%

-13400 ± 17111

3000,4 ± 2,6

92,8± 120,1

-53,74 ± 120,10

-219 ± 893

212 ± 424

-0,208 ± 0,241

0,348 ± 0,241

percentile

95%

-3,31e5 ± 3,41e5

8712,6 ± 5715,8

610,6 ± 1060,3

-39,7 ± 1060,3

-267 ± 1626

1020 ± 1650

-0,41 ± 0,665

0,762 ± 0,665

percentile

99%

-3,40e5 ± 3,55e5

8836,0 ± 5839,5

587,6 ± 1084,9

-40,5 ± 1084,9

-464 ± 1974

1140 ± 2572

-0,393 ± 0,848

0,854 ± 0,848

Optimal -2500 3000 50,17 -60,15 - - - -

Table 6: Monte Carlo results at High Gate, Scenario 1

Results @

High Gate

Scenario 2

True Dispersion Navigation Errors

Down

[m] Alt [m]

V_hor

[m/s]

V_ver

[m/s]

Down

[m] Alt [m]

V_hor

[m/s]

V_ver

[m/s]

percentile

68.27%

-5047 ± 2504

3000 ± 2 136,3 ±

97,9 -72,7 ±

97,9 -10,5 ±

52,4 137 ± 68

-0,001 ± 0,160

0,242 ± 0,160

percentile

95%

-16947 ± 22282

3000 ± 6 312,8 ± 460,6

-126,5 ± 460,6

-29,7 ± 127,0

144 ± 141

0,165 ± 0,535

0,183 ± 0,535

percentile

99%

38437 ± 291760

3000 ± 998

1005,5 ± 1206,5

-126,1 ± 1206,5

-33,0 ± 163,9

160 ± 192

0,122 ± 0,626

0,083 ± 0,626

Optimal -2500 3000 50,17 -60,15 - - - -

Table 7: Monte Carlo results at High Gate, Scenario 2

In The visual Phase has been simulated considering a first corrective manoeuvre performed at High

Gate, followed by a single re-targeting manoeuvre. The amplitude of the manoeuvres respectively

depend on the state vector at the High Gate and the output of the Hazard Avoidance computation,

which assesses the magnitude of the retargetings inside a maximum range defined in Table 1.

Because of the high navigation errors at the High Gate, for the Visual Phase the navigation has been

reset to ±500m for downrange, ±50m for the altitude and ±3m/s for both velocity components and the

initial conditions have been taken from the results of the Main Braking simulations performed with

perfect knowledge of the initial mass, which trajectories are shown in Fig.15.

14

Fig.15: Main Braking trajectory with perfect knowledge of the initial mass (Scenario 2)

The results at Terminal Gate are reported in Table 8 , Table 9 and Table 10, respectively in case of

navigation with LIDAR, NPAL (scenario 1) or KLN plus radar altimeter (scenario 2).

Results @

Terminal

Gate

Scenario 1 (LIDAR)

True Dispersion Navigation Errors

Down

[m] Alt [m]

V_hor

[m/s]

V_ver

[m/s]

Down

[m]

Alt

[m]

V_hor

[m/s]

V_ver

[m/s]

percentile

68.27%

-0,25 ± 1,456

5,62 ± 0,67

-0,137 ± 0,764

-0,904 ± 0,668

0,619 ± 0,647

-0,053 ± 0,083

0,0350 ± 0,068

-0,0070 ± 0,0370

percentile

95%

1,89 ± 10,79

9,83 ± 4,90

-0,458 ± 1,506

-1,995 ± 2,010

0,882 ± 1,589

-0,049 ± 0,159

0,030 ± 0,134

-0,0040 ± 0,0720

percentile

99%

17,84 ± 74,75

24,96 ± 20,06

-1,974 ± 7,454

-4,292 ± 4,327

0,927 ± 2,270

-0,141 ± 0,357

0,026 ± 0,164

-0,0060 ± 0,0880

Optimal 0,00 5,00 0,000 -1,000 - - - -

Table 8: Monte Carlo results at Terminal Gate, Scenario 1 (LIDAR technology)

Results @

Terminal

Gate

Scenario 1 (NPAL)

True Dispersion Navigation Errors

Down

[m] Alt [m]

V_hor

[m/s]

V_ver

[m/s]

Down

[m]

Alt

[m]

V_hor

[m/s]

V_ver

[m/s]

percentile

68.27%

-0,85 ± 1,05

6,24 ± 1,26

-0,101 ± 0,665

-1,192 ± 1,187

0,002± 0,075

0,002 ± 0,120

0,003 ± 0,022

-0,0001 ± 0,0398

percentile

95%

-16,03 ± 22,38

12,34 ± 7,41

-0,157 ± 2,581

-3,320 ± 3,348

0,006 ± 0,201

-0,002 ± 0,253

0,003 ± 0,059

0,0147 ± 0,0852

percentile

99%

34,40 ± 89,23

19,51 ± 14,61

-0,543 ± 6,602

-4,859 ± 4,900

0,022 ± 0,517

0,039 ± 0,468

-0,001 ± 0,112

0,0150 ± 0,1170

Optimal 0,00 5,00 0,000 -1,000 - - - -

Table 9: Monte Carlo results at Terminal Gate, Scenario 1 (NPAL technology)

Results @

Terminal

Gate

Scenario 2 (KLN)

True Dispersion Navigation Errors

Down

[m] Alt [m]

V_hor

[m/s]

V_ver

[m/s]

Down

[m]

Alt

[m]

V_hor

[m/s]

V_ver

[m/s]

percentile

68.27%

-0,29 ± 2,67

6,83 ± 1,85

-0,231 ± 0,867

-1,361 ± 1,356

0,304 ± 2,188

-0,013 ± 0,393

0,0209 ± 0,0763

-0,0075 ± 0,0908

percentile

95%

4,18 ± 10,86

12,17 ± 7,23

-0,917 ± 2,339

-3,551 ± 3,584

-0,050 ± 5,709

-0,047 ± 0,8705

-0,0055 ± 0,1810

-0,0139 ± 0,2030

percentile

99%

32,45 ± 44,22

15,39 ± 10,47

-0,999 ± 4,119

-4,198 ± 4,238

0,287 ± 7,773

-0,031 ± 1,072

0,0145 ± 0,3150

-0,0177 ± 0,2770

Optimal 0,00 5,00 0,000 -1,000 - - - -

Table 10: Monte Carlo results at Terminal Gate, Scenario 2 (KLN technology)

It’s important to notice that the dispersion at Terminal Gate is mainly due to a saturation of the

translational controller, for which is currently being carried out a process of analysis of different

strategies of control, such as feedback LQR, showing good results. This is why the present results can

be considered satisfactory Phase A results, demonstrating the adequacy of the present GNC system to

the mission requirements.

6. CONCLUSIONS

Nowadays the design of a soft, safe and precise landing scheme on the Moon surface is still a

challenging issue.

A preliminary design of the GNC for soft, safe and precise landing in the context of Next Moon Lunar

Lander mission has been presented. In particular, a double branches manoeuvre guidance scheme

guaranteeing the maximum Landing Site visibility has been described. The Known Landmark

Navigation technology has furthermore been presented tested and demonstrated to be feasible,

performing absolute navigation with easy recognition of the LS.

An iterative, fixed horizon and fixed time translational controller accomplishing the Terminal Gate

conditions and the propellant mass expenditure minimization criterion is being part of the presented

GNC scheme. However, this type of translational controller leads to some controls saturation cases, for

which further development is foreseen. The attitude is controlled via a hybrid Bang-Bang, PID classical

controller.

A Monte Carlo batch for the whole Descent and Landing trajectory has been performed, demonstrating

the feasibility of soft and safe landing. The last meters of trajectory, which GNC is still under

assessment, are the key driver to accomplish the precise landing requirement.

REFERENCES

[1] Bryson A.E. and Ho Y.C., Applied Optimal Control, Ed. Hemisphere Publishing Corp., Washington DC, 1975, Chap. 2

[2] Gil-Fernández J., Melloni S., Colmenarejo P., Graziano M., Optimal Precise Landing for Lunar Missions, Space

Technology, American Institute of Aeronautic and Astronautic 092407 [3] http://www.rssd.esa.int/SYS/docs/ll_transfers/1515_2D_Lunar_Science_NEXT_2D_D2E_Koschny.pdf

[4] http://www.lpi.usra.edu/meetings/lpsc2008/pdf/1103.pdf

[5] http://nssdc.gsfc.nasa.gov/planetary/lunar/apollo.html

[6] http://en.wikipedia.org/wiki/South_Pole-Aitken_basin

[7] http://en.wikipedia.org/wiki/Moon_landing

[8] Konopliv A.S., Asmar S.W., Carranza E., Sjogren W.L., and Yuan D.N., Recent Gravity Models as a Result of the

Lunar Prospector Mission, JPL California Institute of Technology, September 27, 2000 [9] Mammarella M., Campa G., Napolitano M.R., Fravolini M.L., Comparison of Point Matching Algorithms for the UAV

Aerial Refueling Problem, Machine Vision and Applications, June 2008 [10] Toda N.F., Schlee F.H., Autonomous Orbital navigation by Optical Tracking of Unknown Landmarks, Journal of

Spacecraft and Rockets December 1967 [11] Levine G.M., A Method of Orbital Navigation Using Optical Sightings to Unknown Landmarks, AIAA Journal

November 1966 [12] Navigation for Planetary Approach & Landing, Final Report. ESA Contract 15618/01/NL/FM. May 2006

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