Calculation method of suboptimal spacecraft paths in the powered flight phases of satellite orbit ascent

Space technologies


Sokolov N. L.

Central Research Institute of Machine Building, 4, Pionerskaya st., Korolev, Moscow region, 141070, Russia


The calculation method of suboptimal spacecraft paths of space vehicle is elaborated in the powered flight phases to the earth satellite orbits during the engine thrust vector control. The problem of one-stage-space vehicle ascent is considered for the vertical and horizontal launches. The maximum of spacecraft finite mass is used as an optimality criterion which is equivalent to the providing minimum fuel consumption. The restrictions of maximum admissible overload values and velocity head are considered.
The method consists in the conditional partition of spacecraft path into specific areas: vertical take-off, gravity turn, generation of terminal conditions. In each area the rational control programs are determined and the obtained results are conjugated. As a result the task of control functions search comes to iteration task of parameterization of a number of varying parameters. After the determination of first approximation parameters, with which the spacecraft injection to the specified orbit is provided, the successive variations of each parameter are specified in order to provide the local maximums of spacecraft finite mass. The iteration process is over when the variation of any one of the parameters doesn’t result in the improvement of optimality criteria. Application of this method allows to avoid the complex calculation procedures used for calculation of optimal paths by classic methods. There are presented the results of elaborated method approbation for calculation of the ascent trajectories in the wide range of change of boundary conditions, mass, power and design, and ballistic parameters of spacecraft.
The new injection scenario of spacecraft to satellite orbit is proposed. It consists in the preliminary shaping of an interim orbit with the apogee altitude less than the specified one and the further two-impulse orbit correction. The high efficiency of the proposed scenario is shown. The fuel mass gain as compared with the traditional spacecraft injection scenario for the considered variation ranges of initial data is ~ 3,0 — 3,5 tons for the vertical takeoff and 2,5 — 3,0 tons for the horizontal takeoff.
The developed method can be the basis for the developed adaptive board algorithms which allow to correct the control program depending on the values of current parameters of spacecraft motion.


spacecraft, suboptimal control, powered phase, satellite orbits, maximization of finite mass, velocity head, overload, specific flight phases


  1. Pontryagin L.S., Boltyanskiy V.P., Gamkrelidze R.V., Mishchenko E.F. Matematicheskaja teorija optimal’nyh processov (Mathematical theory of optimal processes), Moscow, Science, 1969, 393 p.
  2. Bellman R. Dinamicheskoe programmirovanie (Dynamic Programming), Moscow, Foreign literature, 1960, 400 p.
  3. Letov A.M. Dinamika poleta i upravlenija (Flight dynamics and control), Moscow, Science, 1969, 359 p.
  4. Krylov I.A., Chernousko F.L. Zhurnal vychislitel’noi matematiki i matematicheskoi fiziki, 1972, vol. 12, no.1, pp. 14-34.
  5. Avduevsky V.S., Antonov B.M., Anfimov. N.A. Osnovy teorii poleta kosmicheskih apparatov (The theory of space flight), Moscow, Mashinostroeniye, 1972, 345 p.
  6. Sikharulidze Y.G. Ballistika letatel’nyh apparatov (Ballistics of space vehicles), Moscow, Nauka, 1982, 352 p.
  7. Elyasberg P.E. Vvedenie v teoriju poleta iskusstvennyh sputnikov Zemli (Introduction to the theory of flight of artificial earth satellites), Moscow, Nauka, 1965, 537 p.
  8. Ivanov N.M., Dmitrievsky A.A., Lysenko L.N. Ballistika i navigacija kosmicheskih apparatov (Ballistics and navigation of spacecrafts), Moscow, Mashinostroenie, 1986, 295 p.

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