A Technique for the Earth–Venus Optimal Transfer Trajectory by the Aerodynamic Maneuver in Its Atmosphere for the Purpose of the Spacecraft Excess Energy Dissipation

Aeronautical and Space-Rocket Engineering


Аuthors

Nikolichev I. A.*, Vereshchagin Y. O.1**, Y. 2***

1. Air force academy named after professor N.E. Zhukovskogo and Y. A. Gagarin, 54a Starye Bolshevikov str., Voronezh, 394064, Voronezh Region
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: ianikolichev@gmail.com
**e-mail: vereshagin762@gmail.com
***e-mail: ralfhp@yandex.ru

Abstract

The presented article deals with the development of an end-to-end trajectory optimization method for solving the ballistic problem for the Earth to Venus interplanetary flight. The spacecraft aerodynamic maneuvering is supposed to be employed in the atmosphere of the planet of destination to dissipate the excess planetocentric energy. The last-mentioned allows significant savings of the spacecraft characteristic velocity expenditures connected with the transfer. The aerodynamic maneuver is being considered active, i.e. controlled; it is assumed that  while moving in the atmosphere of Venus the spacecraft is controlled by the angle of attack and roll velocity angle. It is assumed as well that during the spacecraft dive into the atmosphere, the controlled motion of its center of mass satisfies pointwise constraints for the total linear overload, the minimum flight altitude above the Venus surface, and a constraint on the total heat flux density at the critical point.
This article considers a model problem, which solution allows evaluating the active aerodynamic maneuvering effectiveness of a spacecraft in the atmosphere of Venus during a single dive in terms of its planetocentric energy dissipation. Analysis of the planetocentric segment of the spacecraft motion in the vicinity of Venus is proposed herewith to be performed a comprehensive manner, i.e. within the framework of considering the complete transfer trajectory of the spacecraft. To implement this scheme, the authors of the article proposed a special approach to formalizing the optimization problem corresponding to the considered ballistic design problem in an “end-to-end” formulation. The optimization problem is considered as an optimal control problem. This approach is based on dividing the spacecraft transfer trajectory into separate segments:
- planetocentric (near Earth and Venus);
- heliocentric and planetocentric atmospheric (the spacecraft controlled motion during a single dive in the atmosphere of Venus).
It is assumed herewith that the spacecraft motion in separate segments of the trajectory is described within the framework of the same motion model, namely the restricted perturbed four-body problem. Formalization of the corresponding optimal control problem within the framework of the proposed approach of dividing the trajectory into separate segments requires determining the appropriate transformation of the functional Lagrange multipliers (conjugate variables) at the corresponding transfer points; it is necessary in order to preserve the “end-to-end” formulation of the problem. The authors proposed a relatively simple and effective (from a practical point of view) approach to obtaining corresponding transformations for the conjugate variables (canonical transformations). The approach is based on the transversality conditions application of the maximum principle, as well as the spacecraft phase vector replacement by a linear non-autonomous transformation such as the translation of the center of the coordinate system and with rescaling the state and independent variables. As the result, a complete set of docking conditions and optimality conditions for the optimal control problem under consideration was obtained, its complete and detailed formalization was performed, and reduction to a five-point boundary value problem was ensured. Relationships determining the spacecraft optimal control in the atmospheric segment were obtained; an analysis of the compatibility of pointwise mixed (overload) and pure state (altitude and heat flux) constraints was performed. As the result of the numerical solution of the maximum principle boundary value problem, a solution to the model problem, confirming the effectiveness of the proposed method, was obtained. The resulting optimal Earth-to-Venus transfer trajectory ensures the spacecraft excess planetocentric energy dissipation. A single atmospheric entry allows orbital closure by dint of a significant reduction in the spacecraft planetocentric velocity (~2 km/s). The dive duration and depth of are comparatively short, amounting to ~83 s and 15 km respectively; and the limits for total overload and heat flux are not exceeded during the dive.

Keywords:

spacecraft, maximum principle, atmospheric dive, canonical transformations, end-to-end optimization, restricted four-body problem, trajectory partitioning, atmospheric braking

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