Optimal Stabilization of an Asymmetrical Descent Spacecraft Relatively to the Center of Mass in the Atmosphere of Mars

The article discusses the solution of the scientific problem of ensuring stable orientation of a weakly asymmetric spacecraft in the atmosphere of Mars. The solution of the problem is required to perform the failure-free deployment of braking parachute. The known quasi-static equations of spacecraft rotational motion has a small mass-aerodynamic asymmetry are applied. Let us noted that before solving the control synthesis problem, these equations are linearized by two orientation angles are three angular velocities. The aim of the work is to ensure a law of optimal controlled stabilization of a spacecraft with small mass-aerodynamic asymmetry. Simultaneous stabilization is achieved in terms of orientation angles and angular velocity vector during descent into the Martian atmosphere. When synthesizing expressions for optimal stabilization of a spacecraft, the classical method of dynamic programming is used. The main simplifying assumptions used in the work are: assumptions about the smallness of angular velocities, angles of attack and slip, displacement of the center of mass, aerodynamic moments from the violation of the axisymmetric shape, as well as the assumption about the implementation of a coplanar combination of the asymmetry of the spacecraft. Based on the results of numerical modeling: the use of the obtained expressions for control allows minimizing the orientation angles and angular velocities to the required small values over a time interval equal to a half of the movement interval from the beginning of the atmospheric descent to the moment of opening of the braking parachute.

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