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) PowerPoint PPT Presentation


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

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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


Step 2a: Gradient Restoration Optimisation

  • 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 Found


Best solution: Full trajectory


Best solution: Distances


Best solution: Mass


Best solution: Thrust components


Best 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


Best 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


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


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