Team 4 GTOC 7 REPORT

Transcription

1 Team 4 GTOC 7 REPORT Hongwei Yang, Gao Tang, Fanghua Jiang, & Zhiguo Zhang School of Aerospace Engineering, Tsinghua University 6 th, March 2015, Rome

2 Outline Optimization Methods and Tools Preliminary Analysis Impulse Approximation and Searching Phase Free Time Optimal Trajectories Patching Time Optimal Transfer Recursive Approach Final Result 2

3 Optimization Methods and Tools Mother Ship s trajectories Index: min J vi, i 1,2,3 x Tool: fmincon in MATLAB y (km) x (km) x

4 Probes trajectories Optimization Methods and Tools Index: min J t f or J m f Indirect method and tools (Jiang et al., 2012, JGCD) The dynamical equations established by the equinoctial elements (For detail derivation, see the PhD thesis of Dr. Gao from CAS) are used for solving the boundary problems much faster 4

5 Optimization Methods and Tools Three types of optimal control problems (1) Phase free transfer Time Optimal (2) Initial time fixed; terminal time free Fuel Optimal (3) initial time and terminal time fixed Bang-Bang control problem the smoothing technique (Bertrand & Epenoy, 2002, Optim. Control Appl. Meth.) 5

6 Optimization Methods and Tools Computer configuration A workstation with 20 cores (3.00 GHz) and 128GB memory Parallel computing The first time to use parallel technique Feature of <thread> provided by C++11 is utilized 6

7 A very complex problem Preliminary Analysis Three probes should visit different asteroids at almost the same period probes should be returned to the mother ship in time The number of the asteroids is quite large and their distribution in space is wide The maneuvering ability of the mother ship after braking at the main belt becomes low. The semimajor axis of all visited asteroids should be close The duration of separation (6 years) is short. The phase difference of every two visited asteroids should be small 7

8 Preliminary Analysis Decrease asteroids number around 2000 eccentricity inclination Used in Searching; About 1000 Number Semimajor axis (AU) 8

9 Preliminary Analysis Overall process for this mission Ast f Earth Probes Mother Ship Mother Ship Ast 0 9

10 Preliminary Analysis The principle for solving this problem Sequence 1 Ast 0 Sequence 2 Ast f Sequence 3 Different As long as possible! 10

11 Impulse Approximation and Searching Problem: the condition to prune (i.e. judge whether the impulse transfer can be achieved by the low thrust transfer or not) By tentative conditions, a result with 27 asteroids visited is founded By relaxing the condition, the searching data becomes too large. Searching procedure of the branch, bound and prune algorithm (Jiang et al., 2014, Acta Futura) 11

12 Phase Free Time Optimal Trajectories Patching The idea is from The engine can provide years maximal thrust. If each probe can visit about 20 asteroids, the magnitude of the thrust is always full except staying at an asteroid. The time optimal transfers are preferred to visit asteroids as many as possible. Besides, the thrust is max for the time optimal problem as well. Problem: The patching condition is quite strict although the patching phase is varied around the optimal phase 12

13 Time Optimal Transfer Recursive Approach Select the first asteroid based on two former methods Search all asteroids close to the current one Calculate time optimal transfer Increase the length of the sequence one by one Recursion until Fuel exhausted (a little more than 1200 kg) Time exhausted (a little more than 6 years) No new asteroid found Prune 13

14 Time Optimal Transfer Recursive Approach 14

15 Key issue Time Optimal Transfer Recursive Approach The maximal magnitude of the low thrust is set to be less than 0.3 N in solving the time optimal transfer By tentative calculations, the proper value is founded to be around 0.23N 15

16 Time Optimal Transfer Recursive Approach Best three sequences Fuel optimal control Optimize the mother ship s trajectories 16

17 Final Result Mother ship 2 1 Stage 1: Earth Asteroid_0 y (AU) x (AU) Stage 2: Asteroid_0 Asteroid_f y (AU) x (AU) 17

18 Final Result Projection of probes trajectories 2 Red line: flight Blue line : stay y (AU) x (AU) y (AU) 0 y (AU) x (AU) x (AU) 18

19 Final Result Asteroids visited by Probes J=32 J = kg Item Probe1 Probe2 Probe3 Sequence 9613 (Mother Ship) (Mother Ship) 9613(Mother Ship) (Mother Ship) 9613(Mother Ship) (Mother Ship) 19

20 Our Team in GTOC The ability of our software (C/C++, FORTRAN & MATLAB) for the local optimization has been improved greatly since the 1 st GTOC The following aspects should be studied and improved: 1) Looking insight into the approximation for the local optimization; 2) Parallel computing We are looking forward to participant in GTOC8! 20

21 Thanks for your Attention! 21