Use of the Method of Guidance by a Required Velocity in Control of Spacecraft Attitude

Source:
By:Mikhail Valer’evich Levskii

DOI: https://doi.org/10.30564/jmer.v4i2.3725

Abstract: We apply the method of guidance by a required velocity for solving the optimal control problem over spacecraft’s reorientation from known initial attitude into a required final attitude. We suppose that attitude control is carried out by impulse jet engines. For optimization of fuel consumption, the controlling moments are calculated and formed according to the method of free trajectories together with principle of iterative control using the quaternions for generating commands to actuators. Optimal solution corresponds to the principle “acceleration - free rotation - separate corrections - free rotation - braking”. Rotation along a hitting trajectory is supported by insignificant correction of the uncontrolled motion at discrete instants between segments of acceleration and braking. Various strategies of forming the correction impulses during stage of free motion are suggested. Improving accuracy of achievement of spacecraft's final position is reached by terminal control using information about current attitude and angular velocity measurements for determining an instant of beginning of braking (condition for start of braking based on actual motion parameters is formulated in analytical form). The described method is universal and invariant relative to moments of inertia. Developed laws of attitude control concern the algorithms with prognostic model, the synthesized control modes are invariant with respect to both external perturbations and parametric errors. Results of mathematical modeling are presented that demonstrate practical feasibility and high efficiency of designed algorithms. References:

[1]Branets, V.N., Shmyglevskii, I.P., Use of Quaternions in Problems of Orientation of Solid Bodies, Nauka, Moscow, 1973. [in Russian] [2]Razorenov, G.N., Bakhramov, E.A., Titov, Yu.F., Control systems of flight vehicle (ballistic rockets and their head parts), Mashinosrtoenie, Moscow, 2003. [in Russian] [3]Steven Parsons, Planet Discovered Transiting a Dead Star, Nature, 585(7825), 2020, 354-355. [4]Eliza Kempton., First Exoplanet Found around a Sun-like Star, Nature, 575(7784), 2019, 43-44. [5]Kelley C. Wells, Dylan B. Millet & Jose D. Fuentes., Satellite Isoprene Retrievals Constrain Emissions and Atmospheric Oxidation, Nature, 585(7824), 2020, 225-233. [6]Raushenbakh, B.V., Tokar, E.N., Spacecraft Orientation Control, Nauka, Moscow, 1974. [in Russian] [7]Alekseev, K.B., Malyavin, A.A., Shadyan, A.V., Extensive Control of Spacecraft Orientation Based on Fuzzy Logic, Flight, No. 1, 2009, 47-53. [in Russian] [8]Velishchanskii, M. A., Krishchenko, A. P., Tkachev, S. B., Synthesis of Spacecraft Reorientation Algorithms Using the Concept of the Inverse Dynamic Problem, Journal of Computer and System Sciences International, 42(5), 2003, 811-818. [9]Ermoshina, O.V., Krishchenko, A.P., Synthesis of Programmed Controls of Spacecraft Orientation by the Method of Inverse Problem of Dynamics, Journal of Computer and Systems Sciences International, 39(2), 2000, 313-320. [10]Junkins, J. L., Turner, J. D., Optimal Spacecraft Rotational Maneuvers, Elsevier, Amsterdam, 1986. [11]Levskii, M.V., On Optimal Spacecraft Damping, Journal of Computer and System Sciences International, 50(1), 2011, 144-157. [12]Levskii, M. V., Pontryagin’s Maximum Principle in Optimal Control Problems of Orientation of a Spacecraft, Journal of Computer and System Sciences International, 47(6), 2008, 974-986. [13]Reshmin, S.A., Threshold Absolute Value of a Relay Control when Time-optimally Bringing a Satellite to a Gravitationally Stable Position, Journal of Computer and Systems Sciences International, 57(5), 2018, 713-722. [14]Reshmin, S.A., The threshold Absolute Value of a Relay Control Bringing a Satellite to a Gravitationally Stable Position in Optimal Time, Doklady Physics, 63(6), 2018, 257-261. [15]Li, F., Bainum, P.M., Numerical Approach for Solving Rigid Spacecraft Minimum Time Attitude Maneuvers, Journal of Guidance, Control, and Dynamics, 13(1), 1990, 38-45. [16]Byers, R., Vadali, S., Quasi-closed-form Solution to the Time-optimal Rigid Spacecraft Reorientation Problem, Journal of Guidance, Control, and Dynamics, 16(3),1993, 453-461. [17]Scrivener, S., Thompson, R., Survey of Time-optimal Attitude Maneuvers, Journal of Guidance, Control, and Dynamics, 17(2), 1994, 225-233. [18]Liu, S., Singh, T., Fuel/time Optimal Control of Spacecraft Maneuvers, Journal of Guidance, 20(2), 1996, 394-397. [19]Shen, H., Tsiotras, P., Time-optimal Control of Axi-symmetric Rigid Spacecraft with Two Controls, Journal of Guidance, Control, and Dynamics, 22(5), 1999, 682-694. [20]Molodenkov, A. V., Sapunkov, Ya. G., Analytical Solution of the Minimum Time Slew maneuver Problem for an Axially Symmetric Spacecraft in the Class of Conical Motions, Journal of Computer and Systems Sciences International, 57(2), 2018, 302-318. [21]Molodenkov, A. V., Sapunkov, Ya. G., A solution of the Optimal Turn Problem of an Axially Symmetric Spacecraft with Bounded and Pulse Control under Arbitrary Boundary Conditions, Journal of Computer and System Sciences International, 46(2), 2007, 310- 323. [22]Molodenkov A. V., Sapunkov Ya. G. Analytical Quasi-Optimal Solution of the Slew Problem for an Axially Symmetric Rigid Body with a Combined Performance Index, Journal of Computer and System Sciences International, 59(3), 2020, 347-357. [23]Levskii, M.V., Optimal Control of a Programmed Turn of a Spacecraft, Cosmic Research, 41(2), 2003, 178-192. [24]Levskii, M.V., Optimal Spacecraft Terminal Attitude Control Synthesis by the Quaternion Method, Mechanics of Solids, 44(2), 2009, 169-183. [25]Zubov, N.E., Li, M.V., Mikrin, E.A., Ryabchenko, V.N.,Terminal Synthesis of Orbital Orientation for a Spacecraft, Journal of Computer and Systems Sciences International, 56(4), 2017, 721-737. [26]Levskii, M.V., On Improving the Maneuverability of a Space Vehicle Managed by Inertial Executive Bodies, Journal of Computer and Systems Sciences International, 59(5), 2020, 796-815. [27]Kovtun, V.S., Mitrikas, V.V., Platonov, V.N., Revnivykh, S.G., Sukhanov, N.A., Mathematical Support for Conducting Experiments with Attitude Control of Space Astrophysical Module Gamma, News from Academy of Sciences USSR. Technical Cybernetics, 1990, No. 3, 144-157. [in Russian] [28]Levskii, M.V., Special Aspects in Attitude Control of a Spacecraft, Equipped with Inertial Actuators, Journal of Computer Science Applications and Information Technology, 2(4), 2017, 1-9. [29]Levskii, M.V. RF Patent No. 2076833, 1997. [in Russian] [30]Levskii, M.V. RF Patent No. 2146638, 2000. [in Russian]