Low-thrust Pluto trajectory
disp('Low-thrust Mars demo using Simplex')
d.method = 'downhill simplex';
d.repeat = 1;
lbFToKg = Constant('lb force to kg');
aU = Constant('au');
muSun = Constant('mu sun');
secInDay = 86400;
m0 = 10000*lbFToKg;
[name,a] = Planets('rad',4);
aF = aU*a(1);
v0 = VOrbit(aU,aU,muSun);
vF = VOrbit(aF,aF,muSun);
d.d.mu = Constant('mu sun');
d.d.mDot = 6.7727e-5;
d.d.thrust = 0.002;
d.d.rhsFun = @FLowThrust2D;
d.d.plotFun = @Plot2DTrajectory;
d.d.stateTol = 1e-12;
d.d.funTol = 1e-12;
d.d.nIts = 10000;
d.d.costFun = @CostLowThrust2D;
d.d.lambda0 = [0;0.5;2]*1e5;
d.d.x0 = [aU;0;v0;m0];
d.d.xF = [aF;0;vF];
d.d.rF = d.d.xF(1);
d.d.data.absTol = 1e-10;
d.d.data.relTol = 2.5e-8;
d.d.data.maxStep = 0.1;
d.d.tEnd = 300*secInDay;
d.d.errorScale = [1; 3e6; 1e7; 1e-2];
[lambda,xF,tF] = TrajectoryOptimization( d );
disp('Initial costate guess:')
disp(d.d.lambda0)
disp('Costate returned by Simplex:')
disp(lambda{1})
Low-thrust Mars demo using Simplex
Case 1: Method: downhill simplex
Iteration Func-count f(x) Procedure
0 1 5.15502e+07
1 4 5.12213e+07 initial simplex
2 6 5.03997e+07 expand
3 7 5.03997e+07 reflect
4 9 4.94165e+07 expand
5 11 4.81477e+07 expand
6 12 4.81477e+07 reflect
7 14 4.60287e+07 expand
8 16 4.43102e+07 expand
9 17 4.43102e+07 reflect
10 19 4.1764e+07 expand
11 21 4.02932e+07 expand
12 22 4.02932e+07 reflect
13 24 3.86808e+07 expand
14 26 3.78078e+07 expand
15 27 3.78078e+07 reflect
16 29 3.71304e+07 expand
17 31 3.66683e+07 expand
18 32 3.66683e+07 reflect
19 34 3.64195e+07 expand
20 36 3.61857e+07 expand
21 37 3.61857e+07 reflect
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23 40 3.59954e+07 expand
24 41 3.59954e+07 reflect
25 43 3.58524e+07 expand
26 44 3.58524e+07 reflect
27 46 3.57379e+07 expand
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30 51 3.52983e+07 reflect
31 53 3.50756e+07 expand
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33 57 3.45757e+07 reflect
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36 62 3.45159e+07 reflect
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286 619 3.4513e+07 contract outside
Optimization terminated:
the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-12
and F(X) satisfies the convergence criteria using OPTIONS.TolFun of 1.000000e-12
Radial position error = 14162705.8210 (km)
Radial velocity error = 9.7753 (km/s)
Tangential velocity error = 1.0224 (km/s)
Time of minimum error = 5.6089 month
Initial costate guess:
0
50000
200000
Costate returned by Simplex:
0.40819
-8.5576e+06
9.0827e+06
