Mars Soft Landing Database

Using the technical specifications from SpaceX's Dragon 2 lander, the problem a soft (i.e. zero velocity). Martian landing is computed for various initial starting states.

Model

Maximum Thrust: $T = 68.17~kN$
Specific Impulse: $I_{sp} = 243~s$
Coefficient of Drag: $C_D = 1.4~m^2$
Atmospheric Density: $\rho = 0.02~m/s^2$
Planaform Area: $A = 10.52~m^2$
Gravity: $g = 3.711~m/s^2$

Optimisation

Hermite Simpson Seperated (HSS)
20 Segments
Sequential Least Squares Quadratic Programming (SLSQP)
Monotonic Basin Hopping (MBH)



In [2]:

    
# Resources
import sys
sys.path.append('../')
from Trajectory import Point_Lander_Drag
from Optimisation import HSS
from PyGMO import *
from numpy import *



In [4]:

    
# Load initial states
si_list = load('../Data/Point_Lander_Mars_Initial_States.npy')



In [6]:

    
# Define the algorithms to use
algo_local = algorithm.scipy_slsqp(max_iter=5000, acc=1e-10, screen_output=True)
algo_meta  = algorithm.mbh(algo_local, stop=1, screen_output=True)



In [7]:

    
# Load initial guess
z = load('../Data/HSS_20_Mars.npy')



In [8]:

    
# Optimise
n_traj = len(si_list)

# For each initial state
for i in range(n_traj):
    # Initialise the model at that state
    model = Point_Lander_Drag(si_list[i])
    # Initialise the HSS problem
    prob  = HSS(model, nsegs=20)
    # Create empty population
    pop   = population(prob)
    # Guess the previous solution
    pop.push_back(z)
    # Optimise from that solution
    pop = algo_meta.evolve(pop)









    Out[8]:





array([   75.57121355,     0.        ,  5000.        ,   150.        ,
         -10.        ,  8165.        ,     1.        ,     3.11847497,
         255.74527016,  4976.47975218,   134.27893053,   -16.07157138,
        8113.54529188,     1.        ,     3.09212745,   483.25346698,
        4942.4234465 ,   118.61352293,   -21.71119026,  8062.09058377,
           1.        ,     3.06435849,   682.62212949,  4898.62256727,
         103.00041959,   -26.89398136,  8010.63587565,     1.        ,
           3.03437844,   853.94554451,  4845.93350567,    87.4402669 ,
         -31.5907103 ,  7959.18116754,     1.        ,     3.00265528,
         997.32007194,  4785.24878632,    71.93631659,   -35.77021849,
        7907.72645942,     1.        ,     2.96842782,  1112.85679518,
        4717.54162334,    56.49759122,   -39.39639764,  7856.27175131,
           1.        ,     2.93208123,  1200.67927608,  4643.82934407,
          41.13663998,   -42.4317185 ,  7804.81704319,     1.        ,
           2.89299442,  1260.95178306,  4565.22566903,    25.87484878,
         -44.83335209,  7753.36233508,     1.        ,     2.85139579,
        1293.86639628,  4482.89573712,    10.73851394,   -46.55893414,
        7701.90762696,     1.        ,     2.80709909,  1299.69517703,
        4398.11010464,    -4.23198449,   -47.56294762,  7650.45291885,
           1.        ,     2.76000512,  1277.24730243,  4313.02995785,
         -19.47564489,   -47.50223289,  7597.21341056,     0.92703023,
           2.71053587,  1234.08608295,  4225.38343263,   -27.2555789 ,
         -50.4155654 ,  7569.70125632,     0.        ,     3.14159265,
        1185.09553904,  4128.76073703,   -27.19818285,   -56.97951048,
        7569.70125632,     0.        ,     2.85433838,  1136.21318515,
        4020.35102611,   -27.13532198,   -63.51723785,  7569.70125632,
           0.        ,     2.62290481,  1087.4488914 ,  3900.2031849 ,
         -27.06694516,   -70.02590813,  7569.70125632,     0.        ,
           3.10654749,  1038.8125984 ,  3768.37284521,   -26.99304473,
         -76.50273626,  7569.70125632,     0.        ,     0.        ,
         990.31424365,  3624.9189628 ,   -26.91362935,   -82.94497043,
        7569.70125632,     0.        ,     2.16563457,   941.96371218,
        3469.90700511,   -26.82873408,   -89.349934  ,  7569.70125632,
           0.        ,     3.13647986,   893.77083934,  3303.40562754,
         -26.73840457,   -95.7149919 ,  7569.70125632,     0.        ,
           2.02204034,   845.7453295 ,  3125.48969984,   -26.64270435,
        -102.0375986 ,  7569.70125632,     0.        ,     2.98903695,
         797.89680562,  2936.23711822,   -26.54170445,  -108.31525638,
        7569.70125632,     0.        ,     0.00606273,   750.23470457,
        2735.73165039,   -26.43548897,  -114.5455682 ,  7569.70125632,
           0.        ,     2.57092272,   702.76835849,  2524.05990909,
         -26.32414767,  -120.72618979,  7569.70125632,     0.        ,
           3.14159265,   655.5068721 ,  2301.31399969,   -26.20778038,
        -126.85488648,  7569.70125632,     0.        ,     0.11245263,
         608.45922744,  2067.58867516,   -26.08649133,  -132.92948036,
        7569.70125632,     0.        ,     0.66729569,   561.63414689,
        1822.98377351,   -25.96039271,  -138.9479102 ,  7569.70125632,
           0.        ,     2.3262085 ,   513.8763236 ,  1574.79669853,
         -27.24967243,  -135.57116856,  7539.68600992,     1.        ,
           1.71382909,   463.12067766,  1339.96932802,   -29.29257557,
        -124.09813972,  7483.94340946,     1.        ,     1.66312203,
         409.41216777,  1125.88686157,   -30.28152134,  -113.85027348,
        7432.48870135,     1.        ,     1.61529276,   354.59766407,
         930.30616157,   -30.52192569,  -103.53279072,  7381.03399323,
           1.        ,     1.57079518,   299.99803223,   753.33434847,
         -30.05648272,   -93.17384465,  7329.57928512,     1.        ,
           1.52901136,   246.83482417,   595.02104924,   -28.92529131,
         -82.79321157,  7278.124577  ,     1.        ,     1.49016422,
         196.2815751 ,   455.39456065,   -27.16792521,   -72.4071906 ,
        7226.66986889,     1.        ,     1.45376912,   149.42184324,
         334.45167033,   -24.81982004,   -62.02575025,  7175.21516077,
           1.        ,     1.41988444,   107.29728531,   232.17908735,
         -21.91527349,   -51.65616927,  7123.76045266,     1.        ,
           1.38816615,    70.8728585 ,   148.55152529,   -18.48392847,
         -41.30116898,  7072.30574454,     1.        ,     1.35855038,
          41.07880316,    83.5418534 ,   -14.5540436 ,   -30.96143718,
        7020.85103642,     1.        ,     1.33082708,    18.78306179,
          37.12515461,   -10.1492949 ,   -20.63444064,  6969.39632831,
           1.        ,     1.30484229,     4.82608725,     9.28061469,
          -5.29193319,   -10.31609661,  6917.94162019,     1.        ,
           1.2805062 ,     0.        ,     0.        ,     0.        ,
           0.        ,  6866.48691208,     1.        ,     1.25760056])



In [ ]: