3rd Global Trajectory Optimisation Competition Workshop

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3rd Global Trajectory Optimisation Competition Workshop

  1. 1. 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
  2. 2. Contents <ul><li>Problem statement </li></ul><ul><li>DEIMOS Space team </li></ul><ul><li>Asteroid family analysis </li></ul><ul><li>Solution steps: </li></ul><ul><ul><li>Step 0: Asteroid Database Pruning </li></ul></ul><ul><ul><li>Step 1: Ballistic Global Search </li></ul></ul><ul><ul><li>Step 2a: Gradient Restoration Optimisation </li></ul></ul><ul><ul><li>Step 2b: Local Direct Optimisation </li></ul></ul><ul><li>DEIMOS solution presentation </li></ul><ul><li>Conclusions </li></ul>
  3. 3. Problem Statement <ul><li>Escape from Earth, rendezvous with 3 asteroids and rendezvous with Earth </li></ul><ul><li>Depature velocity below 0.5 km/s </li></ul><ul><li>Launch between 2016 and 2025 </li></ul><ul><li>Total trip time less than 10 years </li></ul><ul><li>Minimum stay time of 60 days at each asteroid </li></ul><ul><li>Initial spacecraft mass of 2,000 kg </li></ul><ul><li>Thrust of 0.15 N and Isp of 3,000 s </li></ul><ul><li>Only Earth GAMs allowed (R min = 6,871 km) </li></ul><ul><li>Minimise following cost function: </li></ul>
  4. 4. DEIMOS Space Team <ul><li>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 </li></ul><ul><li>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) </li></ul><ul><li>Francesco Cacciatore , Junior Engineer, has been in charge of the analysis of preliminary low-thrust solutions by means of a shape function optimiser </li></ul><ul><li>Mariano Sánchez , Head of Mission Analysis Section, has provided support in a number of issues </li></ul>
  5. 5. <ul><li>Semi-major axis range: [0.9 AU-1.1 AU] </li></ul><ul><li>Eccentricity range: [0.0-0.9] </li></ul><ul><li>Inclination range: [0º-10º] </li></ul><ul><li>Solution makes use of low eccentricity, low inclination asteroids </li></ul>Asteroid Family Analysis
  6. 6. <ul><li>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 </li></ul><ul><li>This distance is defined as the minimum Delta-V to transfer between Earth and the asteroid orbits </li></ul><ul><li>By selecting all asteroids with “distance” to the Earth bellow 2.5 km/s, we get the following list of candidates: </li></ul><ul><ul><li>5, 11, 16, 19, 27, 30, 37, 49, 61, 64, 66, 76, 85, 88, 96, 111, 114, 122 & 129 </li></ul></ul><ul><li>In this way, the initial list of 140 asteroids is reduced down to 19 </li></ul><ul><li>Among them numbers 37, 49, 76, 85, 88 and 96 shall be the most promising candidates </li></ul>Step 0 : Asteroid Database Pruning
  7. 7. <ul><li>The first step was based on a Ballistic Scanning Process between two bodies (including Earth swingbys) and saving them into databases of solutions </li></ul><ul><li>Assumptions: </li></ul><ul><ul><li>Ballistic transfers </li></ul></ul><ul><ul><li>Use of powered swingbys </li></ul></ul><ul><ul><li>Compliance with the problem constrains </li></ul></ul><ul><li>This process was repeated for all the possible phases </li></ul><ul><li>As solution space quickly grew to immense numbers, some filtering techniques were used to reduce the space </li></ul><ul><li>The scanning procedure used the following search values: </li></ul><ul><ul><li>Sequence of asteroids to visit </li></ul></ul><ul><ul><li>Event dates for the visits </li></ul></ul><ul><li>An effective Lambert solver was used to provide the ballistic solutions between two bodies </li></ul>Step 1: Ballistic Global Search
  8. 8. <ul><li>Due to the limited time to solve the problem, only transfer options with the scheme were tested: </li></ul><ul><li>E-E–A1–E–E–A2–E–E–A3–E–E </li></ul><ul><li>All possible options with that profile were investigated, including Earth singular transfers of 180º and 360º </li></ul><ul><li>The optimum sequence found is: </li></ul><ul><li>E–49–E–E–37–85–E–E </li></ul><ul><li>Cost function in this case is: J = 0.8708 </li></ul><ul><li>This step provided the clues to the best families of solutions </li></ul>Step 1: Ballistic Global Search
  9. 9. <ul><li>A tool to translate the best ballistic solutions into low-thrust solutions was used </li></ul><ul><li>A further assumption was to use prescribed thrust-coast sequences and fixed event times </li></ul><ul><li>The solutions were transcribed to this formulation and solved for a number of promising cases </li></ul><ul><li>Optimum thrust directions and event times were obtained in this step </li></ul><ul><li>A Local Direct Optimisation Tool was used to validate the solution obtained </li></ul>Step 2 a : Gradient Restoration Optimisation
  10. 10. <ul><li>Final spacecraft mass: 1716.739 kg </li></ul><ul><li>Stay time at asteroids: 135.2 / 60.0 / 300.3 days </li></ul><ul><li>Minimum stay time at asteroid: 60 days </li></ul><ul><li>Cost function </li></ul><ul><li>Solution structure: </li></ul><ul><li>Mission covers the 10 years of allowed duration </li></ul><ul><li>Losses from ballistic case account to a 0.05% </li></ul>Best Solution Found E – TCT – 49 – TC – E – C – E – TCT – 37 – TCT – 85 – TC – E – CTCT – E
  11. 11. Best Solution Found
  12. 12. Best solution: Full trajectory
  13. 13. Best solution: Distances
  14. 14. Best solution: Mass
  15. 15. Best solution: Thrust components
  16. 16. Best solution: From Earth to asteroid 37 <ul><li>Segment Earth to asteroid 49: </li></ul><ul><ul><li>E–TCT–49 </li></ul></ul><ul><ul><li>2½ revolutions about Sun </li></ul></ul><ul><ul><li>Duration of 1,047 days </li></ul></ul><ul><li>Segment asteroid 49 to 37: </li></ul><ul><ul><li>49-TC-E-C-E-TCT-37 </li></ul></ul><ul><ul><li>2½ revolutions about Sun </li></ul></ul><ul><ul><li>Duration of 852 days </li></ul></ul>
  17. 17. Best solution: From asteroid 37 to Earth <ul><li>Segment asteroid 37 to 85: </li></ul><ul><ul><li>37–TCT–85 </li></ul></ul><ul><ul><li>1¼ revolutions about Sun </li></ul></ul><ul><ul><li>Duration of 450 days </li></ul></ul><ul><li>Segment asteroid 85 to Earth: </li></ul><ul><ul><li>85–TC–E–CTCT–E </li></ul></ul><ul><ul><li>2½ revolutions about Sun </li></ul></ul><ul><ul><li>Duration of 836 days </li></ul></ul>
  18. 18. <ul><li>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 </li></ul><ul><li>Such approach saves a lot of computational time by avoiding the use of other implementations with larger complexity (e.g. shape-based functions) </li></ul><ul><li>Transcription of ballistic into low-thrust trajectories by using a GR algorithm has shown to be very efficient </li></ul><ul><li>Failure to find a better solution is due to: </li></ul><ul><ul><li>The a priori imposed limit in the number of Earth swingbys (best solution shows up to 3 Earth-GAMs) </li></ul></ul><ul><ul><li>Non-optimality of the assumed thrust-coast structures between phases </li></ul></ul>Conclusions

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