Demonstrate the different solutions found by the optimal assignment method and the privileged assignment method, in an eccentric orbit.

Since version 7.
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Form:
FFEccAssignmentDemo
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See also TeamGoals_Structure, FFEccGoals, FFEccProp, FFEccEstimateCost,
InitializeCostMatrix, OptimalAssignment, PopulateCostMatrix,
PrivilegedAssignment, SetupAssignmentProblem, DataSize, NuDot, OrbRate,
El2RV, M2Nu
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Contents

%-------------------------------------------------------------------------------
%   Copyright 2004 Princeton Satellite Systems, Inc.
%   All rights reserved.
%-------------------------------------------------------------------------------

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reference orbit

%----------------
a   = 6928.14;       % semi-major axis
inc = 35.4*pi/180;   % inclination
e   = 0.5;           % eccentricity
per = pi/2;          % argument of perigee
lan = pi/4;          % longitude of ascending node
M   = pi/3;          % mean anomaly

element differences for relative satellites

%--------------------------------------------
nSC  = 4;

initial team motion

%---------------------
clear q0;
for i=1:nSC
   g0(i) = struct('y0',1,'xMax',0.5,'nu_xMax',2*pi*i/nSC,'zMax',0,'nu_zMax',0);
end

ID's of relative spacecraft

%----------------------------
relIDs = [31 44 28 19];

remaining fuel percentage

%--------------------------
rfp = [.2 .3 .4 .5];

fuel weighting factor

%----------------------
x = 0;

weight

%-------
weight = rfp.^-x;

desired team motion

%--------------------
clear gD;
for i=1:nSC
   gD(i) = struct('y0',1,'xMax',1,'nu_xMax',2*pi*i/nSC,'zMax',0,'nu_zMax',0);
end

the time window

%----------------
window           = struct;
window.startTime = 0;
window.nOrbMin   = 1;
window.nOrbMax   = 2;
window.minWait   = 60;

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reference orbit

%----------------
el0     = [a, i, lan, per, e, M];
[r0,v0] = El2RV(el0);
x0      = [r0;v0];
n       = OrbRate(a);
nu      = M2Nu(e,M);

compute initial relative states

%--------------------------------
xH = [];
for i=1:nSC
   [D,xH0]   = FFEccGoals( e, g0(i).y0, g0(i).xMax, g0(i).nu_xMax, g0(i).zMax, g0(i).nu_zMax );
   xH(:,i)   = FFEccProp( D, nu, e );
   xH(4:6,i) = xH(4:6,i)*NuDot(n,e,nu);
end

set up team goals data structure

%---------------------------------
teamGoals = TeamGoals_Structure(nSC);
teamGoals.geometry = gD;
teamGoals.teamID   = 99;
for i=1:nSC
   teamGoals.constraints(i).variable = 0; % this is an absolute constraint for eccentric orbits!
end
teamGoals.dPhi = 15*pi/180;

ds0 = DataSize(teamGoals);

compute the cost estimates for each spacecraft

%-----------------------------------------------
clear costEstimate;
for i=1:nSC
   fprintf('Estimating costs for %d of %d spacecraft.\n',i,nSC);
   costEstimate(i) = FFEccEstimateCost( el0, xH(:,i), teamGoals, relIDs(i), window, weight(i) );
end
disp('done');

Estimating costs for 1 of 4 spacecraft.
Estimating costs for 2 of 4 spacecraft.
Estimating costs for 3 of 4 spacecraft.
Estimating costs for 4 of 4 spacecraft.
done

define the assignment problem parameters

%-----------------------------------------
[N,M,P,Pu,Q,phi,u] = SetupAssignmentProblem( teamGoals );

create the cost matrix

%-----------------------
f = InitializeCostMatrix( teamGoals, length(relIDs) );
for i=1:N
   f = PopulateCostMatrix( f, costEstimate(i), teamGoals, relIDs );
end

use the privileged assignment method (minimum metric)

%-------------------------------------
disp('Calling "PrivilegedAssignment" algorithm (minimum metric).');
tic
[order1,phi1,cost1,cv1] = PrivilegedAssignment( N, P, Pu, Q, f, phi, u, 1 );
t1 = toc;

Calling "PrivilegedAssignment" algorithm (minimum metric).

use the privileged assignment method (mean metric)

%-------------------------------------
disp('Calling "PrivilegedAssignment" algorithm (mean metric).');
tic
[order2,phi2,cost2,cv2] = PrivilegedAssignment( N, P, Pu, Q, f, phi, u, 2 );
t2 = toc;

Calling "PrivilegedAssignment" algorithm (mean metric).

use the optimal assignment method

%----------------------------------
disp('Calling "EqualAssignment" algorithm.');
tic
[order3,phi3,cost3,cv3] = OptimalAssignment( N, P, Pu, Q, f, phi, u );
t3 = toc;


NewFig('Costs');
bar([cost1,cost2,cost3]), title('costs')
NewFig('Run Times');
bar([t1,t2,t3]), title('run times')

cost1uw = sum( cv1 ./ weight(order1) );
cost2uw = sum( cv2 ./ weight(order2) );
cost3uw = sum( cv3 ./ weight(order3) );

costSavings32UW = abs(cost3uw-cost2uw)/cost2uw*100;
costSavings31UW = abs(cost3uw-cost1uw)/cost1uw*100;

costSavings32 = abs(cost3-cost2)/cost2*100;
costSavings31 = abs(cost3-cost1)/cost1*100;

costVec1 = [];
costVec2 = [];
costVec3 = [];
for i=1:nSC
   costVec1(order1(i)) = cv1(i);
   costVec2(order2(i)) = cv2(i);
   costVec3(order3(i)) = cv3(i);
end

costVec1UW = costVec1 ./ weight;
costVec2UW = costVec2 ./ weight;
costVec3UW = costVec3 ./ weight;

%--------------------------------------

Calling "EqualAssignment" algorithm.

Published with MATLAB® R2019a