1. ---- TITLE "GTOC9: Methods and Results from the Jet Propulsion Laboratory Team" 2. ---- AUTHORS Anastassios Petropoulos Anastassios.E.Petropoulos@jpl.nasa.gov Daniel Grebow Daniel.Grebow@jpl.nasa.gov Drew Jones Drew.R.Jones@jpl.nasa.gov Gregory Lantoine Gregory.Lantoine@jpl.nasa.gov Austin Nicholas Austin.K.Nicholas@jpl.nasa.gov Javier Roa javier.roa@jpl.nasa.gov Juan Senent Juan.Senent@jpl.nasa.gov Jeffrey Stuart Jeffrey.R.Stuart@jpl.nasa.gov Nitin Arora Nitin.Arora@jpl.nasa.gov Thomas Pavlak Thomas.A.Pavlak@jpl.nasa.gov Try Lam try.lam@jpl.nasa.gov Timothy McElrath timothy.p.mcelrath@jpl.nasa.gov Ralph Roncoli ralph.b.roncoli@jpl.nasa.gov David Garza David.M.Garza@jpl.nasa.gov Nicholas Bradley Nicholas.E.Bradley@jpl.nasa.gov Damon Landau Damon.Landau@jpl.nasa.gov Zahi Tarzi Zahi.B.Tarzi@jpl.nasa.gov Frank Laipert Frank.E.Laipert@jpl.nasa.gov Eugene Bonfiglio eugene.bonfiglio@jpl.nasa.gov Mark Wallace mark.s.wallace@jpl.nasa.gov Jon Sims jon.a.sims@jpl.nasa.gov Physical Mailing Address for all authors: Jet Propulsion Laboratory California Institute of Technology 4800 Oak Grove Dr. Pasadena, CA 91109 USA 3. ---- CORRESPONDING AUTHOR Anastassios Petropoulos Anastassios.E.Petropoulos@jpl.nasa.gov 4. ---- PAPER ABSTRACT The removal of 123 pieces of debris from the Sun-synchronous LEO environment is accomplished by a 10-spacecraft campaign wherein the spacecraft, flying in succession over an 8-yr period, rendezvous with a series of the debris objects, delivering a de-orbit package at each one before moving on to the next object by means of impulsive manoeuvres. This was the GTOC9 problem, as posed by the European Space Agency. The methods used by the Jet Propulsion Laboratory team are described, along with the winning solution found by the team. Methods include branch-and-bound searches that exploit the natural nodal drift to compute long chains of rendezvous with debris objects, beam searches for synthesising campaigns, ant colony optimisation, and a genetic algorithm. Databases of transfers between all bodies on a fine time grid are made, containing an easy-to-compute yet accurate estimate of the transfer Delta-V. Lastly, a final non-linear programming optimisation is performed to ensure the trajectories meet all the constraints and are locally optimal in initial mass. 5. ---- CRITERIA MET BY WORK (D) The result is publishable in its own right as a new scientific result independent of the fact that the result was mechanically created. (G) The result solves a problem of indisputable difficulty in its field. (H) The result holds its own or wins a regulated competition involving human contestants (in the form of either live human players or human-written computer programs). 6. ---- JUSTIFICATION OF WHY CRITERIA ARE MET (D) The removal of orbital debris around the Earth is a very active area of research in Aerospace Engineering, with many contributions appearing regularly on one of the main sub-problems, namely that of designing trajectories to actually reach each of pieces of debris. The methods developed here, most notably the encoding for the Genetic Algorithm and several of the delta-V computation methods, have not been been found in the literature before. (G) There are no analytic solutions to the problem, and an exhaustive search of all possibilities within the design space is not feasible with even the world's largest supercomputer (estimated wall-clock time that would be needed: years). The difficulty of the problem is also evidenced by the large spread in objective function values seen in the solutions submitted by 36 different research teams to the competition set up by the European Space Agency to solve this problem. (H) By a large margin, our result was the winning entry out of entries from 36 different research teams around the world to the 9th Global Trajectory Optimisation Competition (GTOC9) hosted by the Advanced Concepts Team of the European Space Agency. GTOC9 Problem Home Page: https://sophia.estec.esa.int/gtoc_portal/?page_id=814 GTOC9 Ranking of Entries: https://sophia.estec.esa.int/gtoc_portal/wp-content/uploads/2017/05/gtoc9_rankings.pdf 7. ---- PAPER CITATION Anastassios Petropoulos, Daniel Grebow, Drew Jones, Gregory Lantoine, Austin Nicholas, Javier Roa, Juan Senent, Jeffrey Stuart, Nitin Arora, Thomas Pavlak, Try Lam, Timothy McElrath, Ralph Roncoli, David Garza, Nicholas Bradley, Damon Landau, Zahi Tarzi, Frank Laipert, Eugene Bonfiglio, Mark Wallace, Jon Sims, "GTOC9: Methods and Results from the Jet Propulsion Laboratory Team" June 3-9, 2017 Joint Conference of the 31st ISTS, 26th ISSFD, 8th NSAT ( ISTS, ISFD, NSAT are: International Symposium on Space Technology and Science International Symposium on Space Flight Dynamics Nano-Satellite Symposium ) Special Session: 9th Global Trajectory Optimisation Competition (GTOC9), the Kessler Run Proceedings: https://sophia.estec.esa.int/gtoc_portal/?page_id=847 8. ---- PRIZE MONEY STATEMENT Should any prize monies be awarded, they should be divided as follows: 8% should go to each of these 5 authors (40% altogether) Anastassios Petropoulos, Daniel Grebow, Drew Jones, Gregory Lantoine, Austin Nicholas, 6% should go to each of these 6 authors (36% altogether) Javier Roa, Juan Senent, Jeffrey Stuart, Nitin Arora, Thomas Pavlak, Try Lam, 3% should go to each of these 7 authors (21% altogether) Timothy McElrath, Ralph Roncoli, David Garza, Nicholas Bradley, Damon Landau, Zahi Tarzi, Frank Laipert, 1% should go to each of these 3 authors (3% altogether) Eugene Bonfiglio, Mark Wallace, Jon Sims 9. ---- REASON FOR CATEGORIZING AS "BEST" By a large margin, our result was the winning entry out of entries from 36 different research teams around the world to the 9th Global Trajectory Optimisation Competition (GTOC9) hosted by the Advanced Concepts Team of the European Space Agency. This demonstrates that our work, in which evolutionary algorithms formed a critical part in generating our result, is significantly better than "human-guided" efforts to solve this problem. Many entries to the competition where largely "human-guided" and so it is clear that our method is significantly better than human searches. Other entries did use evolutionary algorithms, and here we demonstrated that amongst them, ours had the greatest advantage over human searches. GTOC9 Problem Home Page: https://sophia.estec.esa.int/gtoc_portal/?page_id=814 GTOC9 Ranking of Entries: https://sophia.estec.esa.int/gtoc_portal/wp-content/uploads/2017/05/gtoc9_rankings.pdf 10. ---- TYPE OF COMPUTATION Genetic Algorithm Ant Colony Optimisation