### Quasi-optimal quaternion genetic algorithm for reorientation of the spacecraft orbit

#### Abstract

The problem of optimal reorientation of the spacecraft orbit is considered in quaternion formulation. Control (acceleration from jet thrust vector orthogonal to the plane of the orbit) is limited in magnitude. It is necessary to minimize the energy costs for the process of reorientation of the spacecraft orbit. The actual special case of the problem, when the spacecraft's orbit is circular and control is constant on adjacent parts of active spacecraft motion was considered. We have to determine the lengths of the sections of the spacecraft motion and the magnitude of control on each section. Original genetic algorithm for finding the trajectories of spacecraft optimal flights is built. Examples of numerical solution of the problem for the case when the difference between the initial and final orientations of the spacecraft's orbit is equal to a few degrees in angular measure are given. Specific features and regularities of the process of optimal reorientation of the spacecraft orbit are established.

#### Full Text:

PDF#### References

S. N. Kirpichnikov, A. N. Bobkova, Yu. V. Os'kina, “Minimal'nye po vremeni impul'snye perelety mezhdu krugovymi komplanarnymi orbitami (Minimum-time impulse transfers between coplanar circular orbits)”, Kosmicheskie issledovaniia (Cosmic Research), vol. 29, no 3, pp. 367-374, 1991 (in Russian).

K. G. Grigoriev, I. S. Grigoriev, Yu. D. Petrikova, “The fastest maneuvers of a spacecraft with a jet engine of a large limited thrust in a gravitational field in a vacuum”, Cosmic Research, vol. 38, no. 2, pp. 160-181, 2000.

B. M. Kiforenko, Z. V. Pasechnik, S. B. Kyrychenko, I. Yu. Vasiliev, “Minimum time transfers of a low-thrust rocket in strong gravity fields”, Acta Astronautica, vol. 52, no. 8, pp. 601-611, 2003.

S. A. Fazelzadeh, G. A. Varzandian, “Minimum-time earth-moon and moon-earth orbital maneuevers using time-domain finite element method”, Acta Astronautica, vol. 66, no. 3-4, pp. 528-538, 2010.

K. G. Grigoriev, A. V. Fedyna, “Optimalnye perelety kosmicheskogo apparata s reaktivnym dvigatelem bolshoi ogranichennoi tiagi mezhdu komplanarnymi krugovymi orbitami (Optimal flights of a spacecraft with jet engine large limited thrust between coplanar circular orbits)”, Kosmicheskie issledovaniia (Cosmic Research), vol. 33, no 4, pp. 403-416, 1995 (in Russian).

S. Y. Ryzhov, I. S. Grigoriev, “On solving the problems of optimization of trajectories of many-revolution orbit transfers of spacecraft”, Cosmic Research, vol. 44, no. 3, pp. 258-267, 2006.

I. S. Grigoriev, K. G. Grigoriev, “The use of solutions to problems of spacecraft trajectory optimization in impulse formulation when solving the problems of optimal control of trajectories of a spacecraft with limited thrust engine: I”, Cosmic Research, vol. 45, no. 4, pp. 339-347, 2007.

I. S. Grigoriev, K. G. Grigoriev, “The use of solutions to problems of spacecraft trajectory optimization in impulse formulation when solving the problems of optimal control of trajectories of a spacecraft with limited thrust engine: II”, Cosmic Research, vol. 45, no. 6, pp. 523-534, 2007.

S. N. Kirpichnikov, A. N. Bobkova, “Optimalnye impulsnye mezhorbitalnye perelety s aerodinamicheskimi manevrami (Optimal impulse interorbital flights with aerodynamic maneuvers)”, Kosmicheskie issledovaniia (Cosmic Research), vol. 30, no 6, pp. 800-809, 1992 (in Russian).

S. N. Kirpichnikov, L. A. Kuleshova, Yu. L. Kostina, “A qualitative analysis of impulsive minimum-fuel flight paths between coplanar circular orbits with a given launch time”, Cosmic Research, vol. 34, no. 2, pp. 156-164, 1996.

Yu. N. Chelnokov, “The use of quaternions in the optimal control problems of motion of the center of mass of a spacecraft in a newtonian gravitational field: I”, Cosmic Research, vol. 39, no. 5, pp. 470-484, 2001.

S. A. Ishkov, V. A. Romanenko, “Forming and correction of a high-elliptical orbit of an Earth satellite with low-thrust engine”, Cosmic Research, vol. 35, no. 3, pp. 268-277, 1997.

O. M. Kamel, A. S. Soliman, “On the optimization of the generalized coplanar Hohmann impulsive transfer adopting energy change concept”, Acta Astronautica, vol. 56, no. 4, pp. 431-438, 2005.

B. E. Mabsout, O. M. Kamel, A. S. Soliman, “The optimization of the orbital Hohmann transfer”, Acta Astronautica, vol. 65, no. 7-8, pp. 1094-1097, 2009.

A. Miele, T. Wang, “Optimal transfers from an Earth orbit to a Mars orbit”, Acta Astronautica, vol. 45, no. 3, pp. 119-133, 1999.

S. Yu. Ryzhov, I. S. Grigoriev, “On solving the problems of optimization of trajectories of many-revolution orbit transfers of spacecraft”, Cosmic Research, vol. 44, no. 3, pp. 258-267, 2006.

Yu. N. Chelnokov, I. A. Pankratov, Ya. G. Sapunkov, “Optimal reorientation of spacecraft orbit”, Archives of Control Sciences, vol. 24, no. 2, pp. 119-128, 2014.

E. A. Kozlov, Yu. N. Chelnokov, I. A. Pankratov, “Investigation of the problem of optimal correction of angular elements of the spacecraft orbit using quaternion differential equation of orbit orientation”, Izv. Saratov. Univ. (N. S.), Ser. Math. Mech. Inform., vol. 16, no. 3, pp. 336-344, 2016 (in Russian).

L. S. Pontryagin, V. G. Boltianskii, R. V. Gamkrelidze, Mishchenko E. F. Matematicheskaia teoriia optimal'nykh protsessov (The mathematical theory of optimal processes). Moscow: Nauka, 1983, 393 p. (in Russian).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes 3rd Edition: The Art of Scientific Computing: Cambridge University Press, 2007, 1235 p.

V. Coverstone-Carrol, J. W. Hartmann, W. J. Mason, “Optimal multi-objective low-thrust spacecraft trajectories”, Computer methods in applied mechanics and engineering, vol. 186, no. 2-4, pp. 387-402, 2000.

B. Dachwald, “Optimization of very-low-thrust trajectories using evolutionary neurocontrol”, Acta Astronautica, vol. 57, no. 2-8, pp. 175-185, 2005.

A. E. Eiben, J. E. Smith, “Introduction to Evolutionary Computing”, Berlin: Springer-Verlag, 2015, 287 p.

I. A. Pankratov, Yu. N. Chelnokov, “Analytical Solution of Differential Equations of Circular Spacecraft Orbit Orientation”, Izv. Saratov. Univ. (N. S.), Ser. Math. Mech. Inform., vol. 11, no. 1, pp. 84-89, 2011 (in Russian).

T. V. Bordovitsyna, “Sovremennye chislennye metody v zadachakh nebesnoi mekhaniki (Modern numerical methods in problems of celestial mechanics)”, Moscow: Nauka, 1984, 136 p (in Russian).

### Refbacks

- There are currently no refbacks.

Abava Absolutech IT-EDU 2019

ISSN: 2307-8162