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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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LEM DEIMOS SPACE SOLUTION
TO THE 3rd GLOBAL
TRAJECTORY OPTIMISATION
COMPETITION (GTOC3)
Miguel Belló, Juan L. CanoMariano Sánchez, Francesco Cacciatore
DEIMOS Space S.L., Spain
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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ContentsContents
• Problem statement
• 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
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Problem StatementProblem Statement
• Escape from Earth, rendezvous with 3 asteroids and
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:
max
321
i
f ),,min(K
mm
J
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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DEIMOS Space TeamDEIMOS Space Team
• Miguel Belló Mora, Managing Director of DEIMOS Space,
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
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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• 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
Asteroid Family AnalysisAsteroid Family Analysis
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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• To reduce the size of the problem, a preliminary analysis
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
Step Step 00: : Asteroid Database PruningAsteroid Database Pruning
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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• The first step was based on a Ballistic Scanning Process
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
Step 1: Ballistic Global SearchStep 1: Ballistic Global Search
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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• Due to the limited time to solve the problem, only
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
Step 1: Ballistic Global SearchStep 1: Ballistic Global Search
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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• A tool to translate the best ballistic solutions into
low-thrust solutions was used
• A further assumption was to use prescribed thrust-
coast 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
Step 2Step 2aa: Gradient Restoration Optimisation: Gradient Restoration Optimisation
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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• Final spacecraft mass: 1716.739 kg
• Stay time at asteroids: 135.2 / 60.0 / 300.3 days
• Minimum stay time at asteroid: 60 days
• Cost function
• Solution structure:
• Mission covers the 10 years of allowed duration
• Losses from ballistic case account to a 0.05%
Best Solution FoundBest Solution Found
0.861655365.25*10
60.00*0.2
2000.0001716.739
J
E – TCT – 49 – TC – E – C – E – TCT – 37 – TCT – 85 – TC – E – CTCT – E
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Best Solution FoundBest Solution Found
Celestial Body Arrival /
Start (MJD) Departure / Stop (MJD)
Duration / Stay (days)
Mass (Kg) Excess velocity (km/s)
Perigee radius (km)
Earth - 60963.53 - 2000.00 0.500 -
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 1960.14 0.000 -
Thrust 62135.48 62162.49 27.01
Coast 62162.49 62407.63 245.14
Earth 62407.63 - - 1948.24 1.818 64967.0
Coast 62407.63 62772.88 365.25
Earth 62772.88 - - 1948.24 1.818 62484.0
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 1906.41 0.000 -
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 1818.38 0.000 -
Thrust 63779.95 63916.63 136.68
Coast 63916.63 64144.40 227.77
Earth 64144.40 - - 1758.17 1.349 160054
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 - - 1716.74 - -
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Best solution: Full trajectoryBest solution: Full trajectory
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Best solution: DistancesBest solution: Distances
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Best solution: MassBest solution: Mass
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Best solution: Thrust componentsBest solution: Thrust components
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Best solution: From Earth to asteroid 37Best solution: From Earth to asteroid 37
Segment Earth to asteroid 49:– E–TCT–49– 2½ revolutions about Sun– Duration of 1,047 days
Segment asteroid 49 to 37:– 49-TC-E-C-E-TCT-37– 2½ revolutions about Sun– Duration of 852 days
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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Best solution: From asteroid 37 to EarthBest solution: From asteroid 37 to Earth
Segment asteroid 37 to 85:– 37–TCT–85 – 1¼ revolutions about Sun– Duration of 450 days
Segment asteroid 85 to Earth:– 85–TC–E–CTCT–E– 2½ revolutions about Sun– Duration of 836 days
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3rd Global Trajectory Optimisation Competition Workshop
Aula Magna del Lingotto, Turin (Italy), June 27, 2008© 2008 DEIMOS Space, S.L. – www.deimos-space.com
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• 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
ConclusionsConclusions