Team 6: University of Colorado Boulder (USA)

Transcription

1 Global Trajectory Optimization Competition 7 Team 6: University of Colorado Boulder (USA) Team Lead: Jeff Parker parkerjs@colorado.edu Team: University of Colorado (USA) We are pleased to provide a solution to the GTOC 7 competition. This submission includes a brief description of our methods, a summary of the solution, and illustrations. The team has explored many methods to complete this solution. First, thousands of representative low- thrust asteroid- asteroid transfers were constructed that required from days of transfer duration. We built ballistic transfers between the asteroids using solutions to Lambert s Problem and compared them to the low- thrust transfers. We were able to identify a polynomial conversion factor that was able to reliably predict the low- thrust cost from the Lambert solution. We were then able to use that in order to build many trillions of Lambert arcs between each of the asteroids while searching for pathways through the asteroids. The team identified all opportunities that the mother ship had to rendezvous with any asteroid during the launch period using all of its fuel. This included numerous opportunities where the mother ship would supplement the free V- infinity with a burn executed immediately at the Earth departure. Ultimately this strategy was indeed employed in order to get the mother ship higher V- infinity values. In all scenarios evaluated (though others were considered hypothetically), the mother ship was sent to rendezvous with an asteroid prior to releasing any probes. After rendezvousing with the first asteroid, the mother ship would coast until the ideal time to release Probe 1; Probe 1 would immediately rendezvous with the first asteroid. The team employed a populated greedy search strategy such that the probe s tour was built one asteroid after another, using the database of Lambert arcs to identify the probe s possible destinations. The best 1000 tours were maintained in a population while searching through the tree of combinations. Numerous tours were identified in this way that obtained a score of 12 or even 13 or 14. The tours were weighted according to how easy it would be to return to the mother ship.

2 The strategy used to build the submitted solution involved keeping the mother ship in the same heliocentric orbit while coasting to the Probe 2 and Probe 3 deployment epochs. Each of these probes tours were also generated using the same populated greedy search strategy. Given a set of three tours one for each probe the sets were evaluated according to how challenging they would be to return to the mother ship. The primary cost function was the difference in heliocentric longitude of each probe with the mother ship at the end of the probe s 6- year life. This was identified as a significant factor in returning the probe to the mother ship. After many surveys it was identified that the best tours placed the probes in a large field of asteroids roughly between 2.7 and 3.0 AU with low heliocentric inclinations. It required most of the mother ship s fuel to reach these asteroids, and little benefit was ever observed to release the probes at lower semi- major axes. After the mother ship rendezvoused with the first asteroid in this field, the mother ship had very little fuel remaining. Hence, the mother ship was treated as ballistic from then on. The team has worked to take advantage of its remaining fuel to improve its rendezvous with Probe 3. The goal was to increase Probe 3 s tour by 1 or more, or at least to increase the amount of fuel remaining in its reserves. The solution presented here does take advantage of a very small amount of fuel to raise the secondary score by a bit over 1 kg. I m sure there are many ways to improve it further, but the time is up! Summary of Submission: Mother Ship launch date: MJD Launch V-infinity: Vinf_x: km/s Vinf_y: km/s Vinf_z: km/s Vinf Mag: km/s Number of Mother Ship burns: 3 Probe 1 Tour: Release of Probe 1: MJD Asteroid 1: GTOC7 ID: 2649 Arrival Date: MJD Asteroid 2: GTOC7 ID: 5026 Arrival Date: MJD Asteroid 3: GTOC7 ID: 7398 Arrival Date: MJD Asteroid 4: GTOC7 ID: 958 Arrival Date: MJD Asteroid 5: GTOC7 ID: Arrival Date: MJD Asteroid 6: GTOC7 ID: 5711 Arrival Date: MJD Asteroid 7: GTOC7 ID: 9725 Arrival Date: MJD Asteroid 8: GTOC7 ID: 2328 Arrival Date: MJD Asteroid 9: GTOC7 ID: 962 Arrival Date: MJD Asteroid 10: GTOC7 ID: Arrival Date: MJD Return of Probe 1: MJD Probe 2 Tour: Release of Probe 2: MJD Asteroid 1: GTOC7 ID: 2649 Arrival Date: MJD Asteroid 2: GTOC7 ID: 3899 Arrival Date: MJD Asteroid 3: GTOC7 ID: 6511 Arrival Date: MJD Asteroid 4: GTOC7 ID: Arrival Date: MJD Asteroid 5: GTOC7 ID: 7384 Arrival Date: MJD

3 Asteroid 6: GTOC7 ID: Arrival Date: MJD Asteroid 7: GTOC7 ID: 3400 Arrival Date: MJD Asteroid 8: GTOC7 ID: Arrival Date: MJD Asteroid 9: GTOC7 ID: 8438 Arrival Date: MJD Asteroid 10: GTOC7 ID: Arrival Date: MJD Return of Probe 2: MJD Probe 3 Tour: Release of Probe 3: MJD Asteroid 1: GTOC7 ID: 2649 Arrival Date: MJD Asteroid 2: GTOC7 ID: Arrival Date: MJD Asteroid 3: GTOC7 ID: 6409 Arrival Date: MJD Asteroid 4: GTOC7 ID: 6376 Arrival Date: MJD Asteroid 5: GTOC7 ID: 656 Arrival Date: MJD Asteroid 6: GTOC7 ID: Arrival Date: MJD Asteroid 7: GTOC7 ID: Arrival Date: MJD Asteroid 8: GTOC7 ID: 873 Arrival Date: MJD Asteroid 9: GTOC7 ID: 3412 Arrival Date: MJD Asteroid 10: GTOC7 ID: 4393 Arrival Date: MJD Return of Probe 3: MJD Final Mass of Probe 1: kg Final Mass of Probe 2: kg Final Mass of Probe 3: kg Final Mass of Mother Ship: kg Primary Performance Index: 28 Secondary Performance Index: Please note: Asteroid 1 is the SAME in all three probe tours. Probe 1 visits it for 30 days; Probes 2 and 3 only visit it for a single day. Hence it is counted as a part of Probe 1 s tour and the total score per probe tour is: Probe 1: 10 Probe 2: 9 Probe 3: 9 Total: 28 Illustrations

4 Figure 1. An illustration of the trajectory: X vs Y in heliocentric J2000 coordinates. Probe 1 is illustrated in red, Probe 2 in blue, Probe 3 in magenta, the mother ship in black.

5 Figure 2. An illustration of the mission's radius over time. Probe 1 (red), Probe 2 (blue), Probe 3 (magenta), mothership (black). Also illustrated are the nearby trajectories of the asteroids each Probe visits. Figure 3. The mass of all vehicles over time. Probe 1 (red), Probe 2 (blue), Probe 3 (magenta), mothership (black).

6 Figure 4. The mass of each probe over time. Figure 5. The probes' thrust over time.