Added code base for paper

README.md

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+# Scalable techniques for autonomous construction of a paraboloidal space telescope in an elliptic orbit
+
+Code for the paper 'Scalable techniques for autonomous construction of a paraboloidal space telescope in an elliptic orbit' by Aaron John Sabu and Dwaipayan Mukherjee
+
+***
+### Abstract
+
+It is well acknowledged that human-made technology is not always at par with human curiosity, and an example is the inability to send large telescopes to outer space despite their higher resolution and less atmospheric interference. In this paper, we develop a framework for autonomous in-orbit construction using spacecraft formation such that a large telescope can be built in an elliptic orbit using multiple spacecraft. We split this problem into four steps for converging the position and attitude of each spacecraft at predefined values around a central spacecraft. Each spacecraft performs attitude synchronization with its neighbors to match its three degrees of freedom in orientation as a parabolic mirror. Simulations validate our proposed methods and the paper concludes with an open possibility of using other techniques to improve upon existing results.
+
+***
+### Disclaimers
+
+The work was supported in part by an ISRO funded project bearing code RD/0120-ISROC00-007. Aaron John Sabu (<p><a href="mailto:[email protected]">[email protected]</a></p>) is an undergraduate student and Dwaipayan Mukherjee (<p><a href="mailto:[email protected]">[email protected]</a></p>) is an Asst. Professor with the Dept. of Electrical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra, India}

src/algoCompare-cases.txt

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+3.0
+
+--A--
+D > G > S
+[[-1.99784066,  0.61604728,  1.44877280],
+       [ 0.43721149, -1.30390749,  1.55301486],
+       [ 0.55915338,  2.13624886, -0.14987920],
+       [ 0.74984804, -0.75304311, -0.66474228],
+       [ 0.77075604,  0.87307288, -1.74438445],
+       [-2.48796971,  0.33908818,  0.52480498],
+       [-1.44477932,  2.52165383,  2.41264048],
+       [ 1.55365393, -1.82890293, -0.55059913],
+       [ 1.45058134,  1.89266631,  0.43396470],
+       [ 0.22868990,  2.95146754, -2.74768372],
+       [-1.71631586,  2.58945856, -0.11163515],
+       [-0.84144055, -2.40168379, -2.58900144],
+       [-0.44148137,  1.84936233,  0.67115186],
+       [-0.06777739,  2.44530060,  2.95190673],
+       [ 0.14748820,  0.12127658, -0.61558311],
+       [-1.80767048, -1.17608603, -2.55560203],
+       [-1.34076421, -1.64031815,  0.73177507],
+       [ 2.53145494, -1.02498501,  1.35597693]]
+
+--B--
+D > G > S
+[[ 2.46627585, -0.00365783, -0.86766388],
+       [ 1.38883444, -0.56932258,  0.85956188],
+       [-1.25104624, -2.68999598, -0.15664761],
+       [ 2.16808202, -0.95045921,  1.20754068],
+       [-1.08903682,  2.60837156, -2.49131614],
+       [-1.04670232,  1.20957410, -0.72505279],
+       [-0.84559224,  0.68161740,  2.11365239],
+       [ 0.64575732, -2.13576666,  0.09339260],
+       [-2.55221737, -1.67415379,  0.47248629],
+       [ 0.41558132,  1.75146335,  0.00541343],
+       [ 2.86279623,  1.26809123, -2.71293342],
+       [-2.88389105, -2.95786390,  2.92524385],
+       [ 0.84024423,  1.61057085,  0.91733068],
+       [ 0.10149796, -2.83326188, -1.57948462],
+       [-0.15197260, -0.44450887,  0.2405081 ],
+       [ 1.27905471, -0.58512968, -2.53469193],
+       [ 2.49569954,  1.30540283,  0.43167947],
+       [-2.65665346,  1.99028373, -0.42741740]]
+
+1.0
+
+--C--
+D = G > S
+[[-2.29364301,  1.26911104, -1.71273596],
+       [-0.30499439,  1.46048986,  0.84474138],
+       [ 1.20553178,  0.33463571, -0.45545043],
+       [ 0.00737466,  2.69883730,  2.20860278],
+       [-0.13433824, -2.45255776,  0.01869546],
+       [ 0.87274879, -1.20121056, -2.55504595],
+       [ 1.82212589, -2.88499068, -2.82692798],
+       [ 1.32413586,  1.38993451, -1.85659537],
+       [ 2.79356145, -1.84074991,  1.31134734],
+       [-2.45089991,  2.86245750, -0.92419686],
+       [ 0.15760877, -1.63576172, -0.10413470],
+       [ 0.22633934,  2.55351914, -2.75085611],
+       [-2.19934209, -1.28014131,  1.85593947],
+       [ 1.72048638,  1.75400878, -1.49284592],
+       [ 2.66459536,  0.56970289, -1.64283741],
+       [-0.26072675,  1.64575550, -1.69458091],
+       [-1.34255969,  2.06506644, -1.14374557],
+       [ 1.99163571, -0.24707069,  1.72698837]]
+
+--D--
+D = G > S
+[[-0.19737204, -0.29886555,  0.36305570],
+       [ 0.30534063, -2.06205336,  0.85791965],
+       [-0.31816348, -1.50494332,  1.20013356],
+       [ 2.37388446, -0.77882058, -2.38966806],
+       [-1.26343545,  1.35004930, -2.50027709],
+       [-2.79467901,  1.98856370, -2.35316213],
+       [ 2.13003201, -1.86269152,  1.10253472],
+       [-0.67690309,  0.79051274,  2.26351260],
+       [-0.59926310, -1.34331266,  2.17618607],
+       [ 1.53274718,  2.75566058, -2.39949286],
+       [ 2.50468947, -0.79161118,  1.89192649],
+       [-1.34296578, -2.47305670,  0.32794480],
+       [ 0.04971921,  0.31507048,  1.23422994],
+       [-1.49500104,  1.42257160,  0.02548234],
+       [ 1.64378575,  0.50837734, -1.16396825],
+       [-0.15880788, -1.60500876,  0.57350283],
+       [ 1.97794503, -1.58259626,  0.98126498],
+       [-2.37234622, -2.92121553, -0.15240542]]
+
+0.25
+
+--E--
+D = G = S
+[[-1.92787107,  0.63939344, -1.74877778],
+       [-0.30968752, -2.78756743, -1.91208517],
+       [-1.69563097, -0.54375145, -2.04193897],
+       [-1.19935501,  1.31577906, -2.54588322],
+       [-2.98803831, -0.36685609, -2.54239741],
+       [ 1.12833730, -2.12756837, -1.36607097],
+       [ 1.61800051,  0.18784015,  0.28711688],
+       [ 1.92682527,  2.09294888,  0.98220375],
+       [ 1.97998589,  2.24655191,  0.14703710],
+       [ 0.47940243,  1.69466183,  0.05916908],
+       [-2.68327754, -1.14751618,  2.31631216],
+       [ 0.18796644,  2.84885841,  1.20630379],
+       [-1.69364916,  0.59877788,  2.61884078],
+       [ 1.43370002,  2.63335636, -1.51988725],
+       [-1.03356433,  2.15331561, -2.18635319],
+       [ 2.88018742, -2.11038576, -0.34113182],
+       [-2.52695979,  2.31005279,  1.70296583],
+       [-0.95626977, -1.69848325,  1.65944077]]
+
+--F--
+D = G = S
+[[ 0.59172304,  2.18793548,  1.10135151],
+       [ 0.62986765, -0.44234319, -1.62572802],
+       [-0.95098904, -2.35326135,  0.49000436],
+       [-1.32871148, -2.64306835, -2.85634444],
+       [-1.09643693, -2.35856294,  0.17633947],
+       [ 0.3299397 ,  2.37370064,  0.27763727],
+       [-2.69151347, -1.59395844, -2.30497489],
+       [ 1.08577260, -0.95740143,  2.48758025],
+       [ 2.67521330,  2.29325859, -1.98293085],
+       [ 2.43850247,  1.28220791,  2.44042221],
+       [-1.97818562, -0.47634221, -0.88855438],
+       [ 0.93433954, -0.24520145,  1.18601613],
+       [-1.60052782,  0.68527799,  1.53182175],
+       [-0.61836986,  0.16281878,  2.30119389], 
+       [-0.09954839,  0.96592547,  0.57013133],
+       [ 2.62370233,  0.60724350,  2.32005221],
+       [ 1.13604260,  1.25932709,  1.28721869],
+       [ 0.79380202, -1.49476592, -0.22534066]]

src/algoCompare.py

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+from copy            import deepcopy
+from math            import sqrt, sin, cos, radians
+from simulate        import simulatePL
+from glideslope      import multiAgentGlideslope
+from initializations import poseInit
+
+numAgents = 18
+numJumps  = 5
+
+innerRad = 0.4
+R_T      = [[innerRad*1*sin(radians(  0)), innerRad*1*cos(radians(  0)), 0.000],
+            [innerRad*1*sin(radians( 60)), innerRad*1*cos(radians( 60)), 0.000],
+            [innerRad*1*sin(radians(120)), innerRad*1*cos(radians(120)), 0.000],
+            [innerRad*1*sin(radians(180)), innerRad*1*cos(radians(180)), 0.000],
+            [innerRad*1*sin(radians(240)), innerRad*1*cos(radians(240)), 0.000],
+            [innerRad*1*sin(radians(300)), innerRad*1*cos(radians(300)), 0.000],
+
+            [innerRad*2*sin(radians(  0)), innerRad*2*cos(radians(  0)), 0.000],
+            [innerRad*2*sin(radians( 30)), innerRad*2*cos(radians( 30)), 0.000],
+            [innerRad*2*sin(radians( 60)), innerRad*2*cos(radians( 60)), 0.000],
+            [innerRad*2*sin(radians( 90)), innerRad*2*cos(radians( 90)), 0.000],
+            [innerRad*2*sin(radians(120)), innerRad*2*cos(radians(120)), 0.000],
+            [innerRad*2*sin(radians(150)), innerRad*2*cos(radians(150)), 0.000],
+            [innerRad*2*sin(radians(180)), innerRad*2*cos(radians(180)), 0.000],
+            [innerRad*2*sin(radians(210)), innerRad*2*cos(radians(210)), 0.000],
+            [innerRad*2*sin(radians(240)), innerRad*2*cos(radians(240)), 0.000],
+            [innerRad*2*sin(radians(270)), innerRad*2*cos(radians(270)), 0.000],
+            [innerRad*2*sin(radians(300)), innerRad*2*cos(radians(300)), 0.000],
+            [innerRad*2*sin(radians(330)), innerRad*2*cos(radians(330)), 0.000],]
+Rdot0    = [[0.00, 0.00, 0.00] for i in range(numAgents)]
+R        = 6870 + 405
+mu       = 398600.50
+omega    = sqrt(mu/R**3)
+nframes  =   400
+dt       =  4000.0/nframes
+e        =  0.05
+h        = (R**2)*omega
+config   = [[1, 2, 1, 1, 1, 2],
+            [2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2]]
+fConfig  = [i for i in range(numAgents)]
+
+Neighbors = [[0 for i in range(numAgents)] for i in range(numAgents)]
+Nghradius = 3.00
+
+# RRR, _ = poseInit(numAgents)
+# print(RRR)
+
+RRR = [[ 2.29364301,  1.26911104, -1.71273596],
+       [-2.30499439,  1.46048986,  0.84474138],
+       [-2.20553178,  0.33463571, -0.45545043],
+       [-2.00737466,  2.69883730,  2.20860278],
+       [-2.13433824, -2.45255776,  0.01869546],
+       [-2.87274879, -1.20121056, -2.55504595],
+       [-2.82212589, -2.88499068, -2.82692798],
+       [-2.32413586,  1.38993451, -1.85659537],
+       [-2.79356145, -1.84074991,  1.31134734],
+       [-2.45089991,  2.86245750, -0.92419686],
+       [-2.15760877, -1.63576172, -0.10413470],
+       [-2.22633934,  2.55351914, -2.75085611],
+       [-2.19934209, -1.28014131,  1.85593947],
+       [-2.72048638,  1.75400878, -1.49284592],
+       [-2.66459536,  0.56970289, -1.64283741],
+       [-2.26072675,  1.64575550, -1.69458091],
+       [-2.34255969,  2.06506644, -1.14374557],
+       [-2.99163571, -0.24707069,  1.72698837]]
+
+R_0 = deepcopy(RRR)
+Neighbors = [[0 for i in range(numAgents)] for i in range(numAgents)]
+X, Y, Z, Deltav, Energy, NeighborsOutput = multiAgentGlideslope(Neighbors, Nghradius,
+                                                                R_0, Rdot0, R_T, R, e, h, omega,
+                                                                numJumps, dt, nframes,
+                                                                auctionParams = (True, 'Standard', False),
+                                                                Config        = (config, fConfig))
+NeighborsDistanceOT = NeighborsOutput[0]
+NeighborsConfigOT   = NeighborsOutput[1]
+simulatePL ('08A-Standard.html', X, Y, Z, ['Spacecraft '+str(agent) for agent in range(numAgents)])
+
+R_0 = deepcopy(RRR)
+Neighbors = [[0 for i in range(numAgents)] for i in range(numAgents)]
+X, Y, Z, Deltav, Energy, NeighborsOutput = multiAgentGlideslope(Neighbors, Nghradius,
+                                                                R_0, Rdot0, R_T, R, e, h, omega,
+                                                                numJumps, dt, nframes,
+                                                                auctionParams = (True, 'Distributed', False),
+                                                                Config        = (config, fConfig))
+NeighborsDistanceOT = NeighborsOutput[0]
+NeighborsConfigOT   = NeighborsOutput[1]
+simulatePL ('08B-Distributed.html', X, Y, Z, ['Spacecraft '+str(agent) for agent in range(numAgents)])
+
+# R_0 = deepcopy(RRR)
+# Neighbors = [[0 for i in range(numAgents)] for i in range(numAgents)]
+# X, Y, Z, Deltav, Energy, NeighborsOutput = multiAgentGlideslope(Neighbors, Nghradius,
+                                                                # R_0, Rdot0, R_T, R, e, h, omega,
+                                                                # numJumps, dt, nframes,
+                                                                # auctionParams = (True, 'Consensus', False),
+                                                                # Config        = (config, fConfig))
+# NeighborsDistanceOT = NeighborsOutput[0]
+# NeighborsConfigOT   = NeighborsOutput[1]
+# simulatePL ('08C-Consensus.html', X, Y, Z, ['Spacecraft '+str(agent) for agent in range(numAgents)])
+
+R_0 = deepcopy(RRR)
+Neighbors = [[0 for i in range(numAgents)] for i in range(numAgents)]
+X, Y, Z, Deltav, Energy, NeighborsOutput = multiAgentGlideslope(Neighbors, Nghradius,
+                                                                R_0, Rdot0, R_T, R, e, h, omega,
+                                                                numJumps, dt, nframes,
+                                                                auctionParams = (True, 'Greedy', False),
+                                                                Config        = (config, fConfig))
+NeighborsDistanceOT = NeighborsOutput[0]
+NeighborsConfigOT   = NeighborsOutput[1]
+simulatePL ('08D-Greedy.html', X, Y, Z, ['Spacecraft '+str(agent) for agent in range(numAgents)])

src/anomaly.py

@@ -0,0 +1,18 @@
+from numpy import cos, sin, multiply
+
+# True Anomaly from Time
+def getTrueAnomalyFromTime(omega, e, T, calcDerivs = False):
+  M    = multiply(omega, T)
+  c1   =  (2.0*e   -(e**3.0)/4.0)
+  c2   =  (5.0/4)  *(e**2.0)
+  c3   =  (13.0/12)*(e**3.0)
+  F    = M + c1*sin(M) + c2*sin(2.0*M) + c3*sin(3.0*M)
+  if not calcDerivs:
+    return F
+  cd1  =  (1.0+(e*cos(F)))**2
+  cd2  =  (1.0-(e**2.0))  **(3.0/2)
+  Fd   = cd1*omega/cd2
+  cdd1 = -2.0*e*(Fd**2.0)
+  cdd2 =  (1+(e*cos(F)))
+  Fdd  = cdd1*sin(F)/cdd2
+  return F, Fd, Fdd