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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, [email protected],
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
[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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