DEIMOS SPACE SOLUTION TO THE 3 rd GLOBAL TRAJECTORY OPTIMISATION COMPETITION (GTOC3)

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DEIMOS SPACE SOLUTION TO THE 3 rd GLOBAL TRAJECTORY OPTIMISATION COMPETITION (GTOC3). Miguel Belló, Juan L. Cano Mariano Sánchez, Francesco Cacciatore DEIMOS Space S.L., Spain. Contents. Problem statement DEIMOS Space team Asteroid family analysis Solution steps:

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Presentation Transcript
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

Contents
• 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
Problem 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:
DEIMOS 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
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
Step 0: Asteroid Database Pruning
• 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 1: Ballistic Global Search
• 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 Search
• 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
• 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
Best Solution Found
• 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%

E – TCT – 49 – TC – E – C – E – TCT – 37 – TCT – 85 – TC – E – CTCT – E

Best solution: From Earth to asteroid 37

Segment Earth to asteroid 49:

• E–TCT–49
• Duration of 1,047 days
• Segment asteroid 49 to 37:
• 49-TC-E-C-E-TCT-37
• Duration of 852 days
Best solution: From asteroid 37 to Earth

Segment asteroid 37 to 85:

• 37–TCT–85