Transcript Document

DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
DEIMOS SPACE SOLUTION
TO THE 3rd GLOBAL
TRAJECTORY OPTIMISATION
COMPETITION (GTOC3)
Miguel Belló, Juan L. Cano
Mariano Sánchez, Francesco Cacciatore
DEIMOS Space S.L., Spain
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
3rd Global Trajectory Optimisation Competition Workshop
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Aula Magna del Lingotto, Turin (Italy), June 27, 2008
Contents
• Problem statement
DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
• DEIMOS Space team
• Asteroid family analysis
• Solution steps:
– Step 0: Asteroid Database Pruning
– Step 1: Ballistic Global Search
– Step 2a: Gradient Restoration Optimisation
– Step 2b: Local Direct Optimisation
• DEIMOS solution presentation
• Conclusions
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Problem Statement
• Escape from Earth, rendezvous with 3 asteroids and
DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
rendezvous with Earth
• Depature velocity below 0.5 km/s
• Launch between 2016 and 2025
• Total trip time less than 10 years
• Minimum stay time of 60 days at each asteroid
• Initial spacecraft mass of 2,000 kg
• Thrust of 0.15 N and Isp of 3,000 s
• Only Earth GAMs allowed (Rmin = 6,871 km)
• Minimise following cost function:
min( 1, 2 , 3 )
mf
J
K
mi
 max
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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DEIMOS Space Team
• Miguel Belló Mora, Managing Director of DEIMOS Space,
DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
in charge of the systematic analysis of ballistic solutions
and the reduction to low-thrust solutions by means of the
gradient-restoration algorithm
• Juan L. Cano, Senior Engineer, has been in charge of the
low-thrust analysis of solution trajectories making use of a
local optimiser (direct method implementation)
• Francesco Cacciatore, Junior Engineer, has been in
charge of the analysis of preliminary low-thrust solutions
by means of a shape function optimiser
• Mariano Sánchez, Head of Mission Analysis Section, has
provided support in a number of issues
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Aula Magna del Lingotto, Turin (Italy), June 27, 2008
DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
Asteroid Family Analysis
• Semi-major axis range: [0.9 AU-1.1 AU]
• Eccentricity range: [0.0-0.9]
• Inclination range: [0º-10º]
• Solution makes use of low eccentricity, low inclination
asteroids
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Step 0: Asteroid Database Pruning
• To reduce the size of the problem, a preliminary analysis
DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
of earth-asteroid transfer propellant need is done by
defining a “distance” between two orbits
• This distance is defined as the minimum Delta-V to
transfer between Earth and the asteroid orbits
• By selecting all asteroids with “distance” to the Earth
bellow 2.5 km/s, we get the following list of candidates:
– 5, 11, 16, 19, 27, 30, 37, 49, 61, 64, 66, 76, 85, 88, 96, 111,
114, 122 & 129
• In this way, the initial list of 140 asteroids is reduced
down to 19
• Among them numbers 37, 49, 76, 85, 88 and 96 shall be
the most promising candidates
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Step 1: Ballistic Global Search
• The first step was based on a Ballistic Scanning Process
DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
between two bodies (including Earth swingbys) and saving
them into databases of solutions
• Assumptions:
– Ballistic transfers
– Use of powered swingbys
– Compliance with the problem constrains
• This process was repeated for all the possible phases
• As solution space quickly grew to immense numbers, some
filtering techniques were used to reduce the space
• The scanning procedure used the following search values:
– Sequence of asteroids to visit
– Event dates for the visits
• An effective Lambert solver was used to provide the
ballistic solutions between two bodies
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Step 1: Ballistic Global Search
• Due to the limited time to solve the problem, only
DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
transfer options with the scheme were tested:
E-E–A1–E–E–A2–E–E–A3–E–E
• All possible options with that profile were
investigated, including Earth singular transfers of
180º and 360º
• The optimum sequence found is:
E–49–E–E–37–85–E–E
• Cost function in this case is: J = 0.8708
• This step provided the clues to the best families of
solutions
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Step 2a: Gradient Restoration Optimisation
• A tool to translate the best ballistic solutions into
DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
low-thrust solutions was used
• A further assumption was to use prescribed thrustcoast sequences and fixed event times
• The solutions were transcribed to this formulation
and solved for a number of promising cases
• Optimum thrust directions and event times were
obtained in this step
• A Local Direct Optimisation Tool was used to validate
the solution obtained
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Best Solution Found
• Final spacecraft mass: 1716.739 kg
DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
• Stay time at asteroids: 135.2 / 60.0 / 300.3 days
• Minimum stay time at asteroid: 60 days
• Cost function
1716.739
60.00
J
 0.2 *
 0.861655
2000.000
10 * 365.25
• Solution structure:
E – TCT – 49 – TC – E – C – E – TCT – 37 – TCT – 85 – TC – E – CTCT – E
• Mission covers the 10 years of allowed duration
• Losses from ballistic case account to a 0.05%
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Best Solution Found
Celestial Body
Arrival /
Start (MJD)
DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
Earth
-
Departure /
Stop (MJD)
Duration /
Stay (days)
60963.53
-
Thrust
60963.53
60987.23
23.70
Coast
60987.23
61933.52
946.29
Thrust
61933.52
62000.31
66.79
49 (2000 SG344)
62000.31
62135.48
135.17
Thrust
62135.48
62162.49
27.01
Coast
62162.49
62407.63
Earth
62407.63
Coast
62407.63
Earth
62772.88
Thrust
62772.88
62796.30
23.42
Coast
62796.30
62916.02
119.72
Thrust
62916.02
62987.56
71.54
37 (2004 QA22)
62987.56
63047.56
60.00
Thrust
63047.56
63096.34
48.78
Coast
63096.34
63328.57
232.23
Thrust
63328.57
63479.62
151.05
85 (2006 BZ147)
63479.62
63779.95
300.33
Thrust
63779.95
63916.63
136.68
Coast
63916.63
64144.40
Earth
64144.40
Coast
64144.40
64402.20
257.80
Thrust
64402.20
64449.44
47.24
Coast
64449.44
64569.22
119.78
Thrust
64569.22
64616.03
46.81
Earth
64616.03
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
-
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2000.00
0.500
-
1960.14
0.000
-
1948.24
1.818
64967.0
1948.24
1.818
62484.0
1906.41
0.000
-
1818.38
0.000
-
1758.17
1.349
160054
227.77
-
-
Perigee
radius (km)
365.25
-
-
Excess
velocity
(km/s)
245.14
-
62772.88
Mass (Kg)
-
1716.74
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DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
Best solution: Full trajectory
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
Best solution: Distances
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
Best solution: Mass
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
Best solution: Thrust components
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
Best solution: From Earth to asteroid 37
Segment Earth to asteroid 49:
– E–TCT–49
– 2½ revolutions about Sun
– Duration of 1,047 days
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
Segment asteroid 49 to 37:
– 49-TC-E-C-E-TCT-37
– 2½ revolutions about Sun
– Duration of 852 days
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DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
Best solution: From asteroid 37 to Earth
Segment asteroid 37 to 85:
– 37–TCT–85
– 1¼ revolutions about Sun
– Duration of 450 days
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
Segment asteroid 85 to Earth:
– 85–TC–E–CTCT–E
– 2½ revolutions about Sun
– Duration of 836 days
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DEIMOS SPACE SOLUTION TO GTOC3 PROBLEM
Conclusions
• Use of ballistic search algorithms seem to be still applicable
to provide good initial guesses to low-thrust trajectories
even in these type of problems
• Such approach saves a lot of computational time by
avoiding the use of other implementations with larger
complexity (e.g. shape-based functions)
• Transcription of ballistic into low-thrust trajectories by
using a GR algorithm has shown to be very efficient
• Failure to find a better solution is due to:
– The a priori imposed limit in the number of Earth
swingbys (best solution shows up to 3 Earth-GAMs)
– Non-optimality of the assumed thrust-coast structures
between phases
© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Aula Magna del Lingotto, Turin (Italy), June 27, 2008