Demonstrate the different solutions found by the optimal assignment method and the privileged assignment method.

Since version 7.
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Form:
AssignmentDemo
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See also RotateState, TeamGoals_Structure, EstimateCost,
GenerateTeamGoals, InitializeCostMatrix, OptimalAssignment,
PopulateCostMatrix, PrivilegedAssignment, SetupAssignmentProblem,
Goals2DeltaElem, DataSize
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Contents

------------------------------------------------------------------------- Copyright 2003 Princeton Satellite Systems, Inc. All rights reserved. -------------------------------------------------------------------------

clear power; clear costEstimate;
fprintf('\nSetting up problem...\n');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%    BEGIN USER - DEFINED INFO    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Setting up problem...

reference orbit

%----------------
el0 = [6928.14, 0, 35.4*pi/180, 0, 0, 0];

element differences for relative satellites

%--------------------------------------------
nSC  = 8;

initial team motion

%--------------------
fType_init = 2;
fSize_init = 0.2;

ID's of relative spacecraft

%----------------------------
relIDs = [31 44 28 19 93 67 52 17];

remaining fuel percentage

%--------------------------
rfp = [.9 .8 .7 .6 .5 .4 .3 .2];
rfp = [.2 .3 .4 .5 .6 .7 .8 .9];

fuel weighting factor

%----------------------
x = 1;

weight

%-------
weight = power(rfp,-x);

desired team motion

%--------------------
fType_des = 5;
fSize_des1 = 0.5; nSC1 = floor(nSC/2);
fSize_des2 = 1.0; nSC2 = nSC - nSC1;

the time window

%----------------
window.startTime = 0;
window.nOrbMin   = 1;
window.nOrbMax   = 3;

%%%%%%%    END OF USER - DEFINED INFO    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

fprintf('\nGenerating team goals...\n');

Generating team goals...

compute initial state and desired team goals

%---------------------------------------------
tG0 = GenerateTeamGoals( el0, fType_init, fSize_init, nSC, [], [] );
dEl = [];
k   = 0;
for i=1:tG0.nU,
   k        = k + 1;
   geom     = tG0.geometry(i);
   dEl(k,:) = Goals2DeltaElem( el0, geom );
   for j=1:tG0.constraints(i).nDuplicates
      k        = k+1;
      phase    = tG0.constraints(i).phase(j);
      dEl(k,:) = Goals2DeltaElem( el0, RotateState(geom,phase) );
   end
end
teamGoals1 = GenerateTeamGoals( el0, fType_des, fSize_des1, nSC1, 99, 5*pi/180 );
teamGoals2 = GenerateTeamGoals( el0, fType_des, fSize_des2, nSC2, 99, 5*pi/180 );
teamGoals  = TeamGoals_Structure;
teamGoals.nU          = teamGoals1.nU + teamGoals2.nU;
teamGoals.geometry    = [teamGoals1.geometry,    teamGoals2.geometry   ];
teamGoals.constraints = [teamGoals1.constraints, teamGoals2.constraints];

ds0 = DataSize(teamGoals);

fprintf('\nEstimating cost for each spacecraft...\n');

Estimating cost for each spacecraft...

compute the cost estimates for each spacecraft

%-----------------------------------------------
for i=1:nSC
   costEstimate(i) = EstimateCost( el0, dEl(i,:), teamGoals, relIDs(i), window, weight(i) );
end

define the assignment problem parameters

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

fprintf('\nPopulating cost matrix...\n');

Populating cost matrix...

create the cost matrix

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

fprintf('\nPrivileged assignment method (min metric)...\n');

Privileged assignment method (min metric)...

use the privileged assignment method (minimum metric)

%-------------------------------------
tic
[order1,phi1,cost1,cv1] = PrivilegedAssignment( N, P, Pu, Q, f, phi, u, 1 );
t1 = toc;

fprintf('\nPrivileged assignment method (mean metric)...\n');

Privileged assignment method (mean metric)...

use the privileged assignment method (mean metric)

%-------------------------------------
tic
[order2,phi2,cost2,cv2] = PrivilegedAssignment( N, P, Pu, Q, f, phi, u, 2 );
t2 = toc;

fprintf('\nOptimal assignment method...\n');

Optimal assignment method...

use the optimal assignment method

%----------------------------------
tic
[order3,phi3,cost3,cv3] = OptimalAssignment( N, P, Pu, Q, f, phi, u );
t3 = toc;

fprintf('\nPlotting...\n');

figure, bar([cost1,cost2,cost3]), title('costs')
figure, 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;

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;

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

Plotting...

Published with MATLAB® R2019a