Industrial Applications of Genetic Algorithms:Optimized Non-Coplanar Orbital Transfers Using Genetic Algorithms

Previous | Table of Contents | Next

Case I

Table 8.5 Initial and final orbits parameters for two non-coplanar elliptical orbits.
| Initial Orbit | Final Orbit
--- | --- | ---
Eccentricity | 0.1 | 0.2
Inclination | 0° | 10°
Semi-major axis | 6500 km | 6800 km

Figure 8.16 Total Produced by the GA vs. number of generations.

When the GA is run on this case, the results shown in Table 8.6 were obtained. These results are also shown in Figure 8.17.

Table 8.6 GA results for transfer orbit parameters for non-planar elliptical initial and final orbits. (GA population size=150, number of generations=15, probability of crossover=0.9, probability of mutation=0.001)
| GA Results
--- | ---
Eccentricity | 0.1652
α1 | 0.6222°
Semi-major axis | 7007.6 km
| 2.6019 km/sec

Figure 8.17 Initial and final orbits along with GA-produced transfer orbit.

Case II

Table 8.7 Initial and final orbits parameters for two non-coplanar elliptical orbits.
| Initial Orbit | Final Orbit
--- | --- | ---
Eccentricity | 0.01 | 0.5
Inclination | 5° | 12°
Semi-major axis | 6500 km | 7500 km

Figure 8.18 Total ΔV produced by the GA vs. number of generations.

When the GA is run on this case, the following results (Table 8.8) (Figure 8.19), were obtained:

Table 8.8 GA results for transfer orbit parameters for non-planar elliptical initial and final orbits, (GA population size=150, number of generations=15, probability of crossover=0.9, probability of mutation=0.001.)
| GA Results
--- | ---
Eccentricity | 0.2717
α1 | 4.2387°
Semi-major axis | 8835.6 km
| 5.736 km/sec

Figure 8.19 Initial and final orbits along with GA-produced transfer orbit.

Case III

Table 8.9 Initial and final orbits parameters for two non-coplanar elliptical orbits.
| Initial Orbit | Final Orbit
--- | --- | ---
Eccentricity | 0.2 | 0.2
Inclination | 5° | 5°
Semi-major axis | 8000 km | 8500 km

When the GA is run on this case, it produced the following results (Table 8.10) (Figure 8.20):

Table 8.10 GA results for transfer orbit parameters for non-planar elliptical initial and final orbits. (GA population size=150, number of generations=10, probability of crossover=0.9, probability of mutation=0.01.)
| Analytical Results | GA Results
--- | --- | ---
Eccentricity | 0.2289 | 0.241
α1 | 0° | 0°
Semi-major axis | 8300 km | 8432 km
| 0.5963 km/sec | 0.6643 km/sec

Figure 8.20 (a) Initial and final orbits along with analytical transfer orbit (b) Initial and final orbits along with GA produced transfer orbit.

CONCLUSIONS

A genetic algorithm was used to search for transfer orbits which minimize the velocity change needed to transverse from one orbit to another. The effectiveness of using this approach was tested through comparison to two problems with known solutions. The GA produced near optimum results for the coplanar and non-coplanar Hohmann transfer problems. The GA was then used to search for transfer orbits between non-circular orbits which are inclined. While no analytical solutions exist for such problems, the resulting GA solution appeared quite reasonable. Therefore, it can be concluded that a genetic algorithm can be used successfully to find near optimum transfer orbits for ΔVTOT requirements.

REFERENCES

  1 Chobotov, V. A. (1991). Orbital mechanics, Washington, DC: American Institute of Aeronautics and Astronautics, Inc.
  2 Bender, D.F. (1962). Optimum coplanar two-impulse transfers between elliptic orbits. Aerospace Engineering, 21(Oct.), 44-52.
  3 Lawden, D. S. (1962). Impulsive transfer between elliptical orbits. Optimization Techniques (Chapter 11), edited by G. Leitmann, New York: Academic Press.
  4 Baker, J. M. (1966). Orbit transfer and rendezvous maneuvers between inclined circular orbits. Journal of Spacecraft and Rockets, 3, 1216-1220.
  5 Reichert, A. (1993). Optimum two-impulse transfer between coplanar, nonaligned elliptical orbits. Paper presented at the 1993 Southeast Regional AIAA Conference, Tuscaloosa, AL.
  6 Pinon, E. III, & Fowler, W. T. (1995). Use of a genetic algorithm to generate earth to moon trajectories. AAS Paper Number 95-141.
  7 Bate, R. R., Mueller, D. D., & White, J. E. (1971). Fundamentals of astrodynamics. New York: Dover Publications Inc.
  8 Gerald, C. F., & Wheatley, P. O. (1989). Applied numerical analysis, 4th Edition (pp. 141-145). Reading, MA: Addison-Wesley Publishing Company.
  9 Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning. Reading, MA: Addison-Wesley Publishing Company.

Previous | Table of Contents | Next

Copyright © CRC Press LLC