Demonstrate the safe ellipse for safe relative orbit guidance

Show how the target safe ellipse changes during relative motion

Since version 10.
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See also HillsEqnsSLO, SafeEllipseParams, NominalSafeGuidance, AnimateRE
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Contents

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%   Copyright (c) 2012 Princeton Satellite Systems, Inc.
%   All rights reserved.
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Demo parameters

n = 1E-3;     % mean orbit rate
nOrb = 5;     % number of orbits
dMin = 60;    % minimum separation distance for avoidance region

r0 = [300;4;0];   % initial relative position in SLO frame
v0 = [2;-1;-5]*n; % initial relative velocity in SLO frame

Define time vector and initial state vector

T = 2*pi/n;
nPPO = 300;   % number of points per orbit
t = linspace(0,nOrb*T,nOrb*nPPO);
xSLO = HillsEqnsSLO([r0;v0],n,t);

initialize fields used in NominalSafeGuidance

inputs.maneuverImmediately = 0;
state.n = n;
state.tM = 60;
parameters.minTimeBtwnDeltaVs = 300;
parameters.dMin = dMin;
parameters.margin = dMin/2;

Initialize arrays for plotting

nt = length(t);
x0 = zeros(1,nt);     x02=x0;
aE = zeros(1,nt);     aE2=aE;
yA = zeros(1,nt);     yA2=yA;
yR = zeros(1,nt);     yR2=yR;
alpha = zeros(1,nt);
dV    = zeros(1,nt);

Compute safe ellipse across all relative states

for j=1:length(t)

  % Compute the nearest "safe ellipse" that touches this position
  rSLO = xSLO(1:3,j);
  vSLO = xSLO(4:6,j);
  [x0(j),aE(j),yA(j),yR(j),alpha(j)] = SafeEllipseParams( rSLO,vSLO,n );

  % Compute a target "safe ellipse" that is outside the projection of the
  % avoidance region onto the cross-track / radial plane
  state.xSLO = [rSLO;vSLO];
  state.xH = LVLH2Hills(state.xSLO);
  [deltaV,desTraj,tracking] = NominalSafeGuidance( inputs, parameters, state );

  dV(j) = sum(Mag(deltaV.dV));

  % Store results into plotting arrays
  x02(j) = desTraj.x0;
  aE2(j) = desTraj.aE;
  yA2(j) = desTraj.yA;
  yR2(j) = desTraj.yR;

end

Compare and animate the safe ellipse from NominalSafeGuidance

Plot2D(t/T,[x0;x02],'Time (orbits)','Along-Track Offset')
Plot2D(t/T,[aE;aE2],'Time (orbits)','Semi-Major Axis of Safe Ellipse')
Plot2D(t/T,[yA;yA2],'Time (orbits)','Cross-Track at x-crossing')
Plot2D(t/T,[yR;yR2],'Time (orbits)','Cross-Track at z-crossing')

AnimateRE( xSLO, x02, aE2, yA2, yR2, dMin, dV );

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Published with MATLAB® R2014b