Optimal interplanetary spacecraft flights design with many-revolution braking maneuver by a low thrust jet engine

The optimal control problem of the spacecraft (SC) interplanetary transfer from the Earth to Mars is considered. The orbits of the Earth and Mars are necessary to be circular and noncoplanar. The SC starts from the artificial Earth satellite circular orbit (AESCO) and finishes at the artificial Mars satellite circular orbit (AMSCO). The SC position on an initial AESCO at the starting point and position on an AMSCO at the finish are optimized. Acceleration of the SC near the Earth and braking near Mars, that are carried out by jet engines of big thrust, are approximated by pulse excitations. On the rest of the trajectory the control of the SC is realized by a low thrust jet engine vector. In connection with the taking into account the loss of accuracy effect, the inertial heliocentric and the noninertial rotating marsand geocentric reference frames are used at the solution creation. Total flight time is minimized. The considered problem is formalized as a variable structure dynamic system optimal control problem. On the basis of the Pontryagins maximum principle its solving is reduced to the 42nd order boundary value problem solving. The boundary value problem is solved numerically by a shooting method with selection of 13 parameters. The vector function root is found with the use of Newton's method with Isaev-Sonin's modification and Fedorenko's normalization in the convergence conditions. The Cauchy problems of shooting method are solved numerically by the explicit 8th order Runge-Kutta's method based on Dormand-Prince's 8(7) calculating formula with the automatic step choice. Main result: The original problem has been solved. Pontryagin's extremals are defined out as a boundary value problem solution result. The analysis depending on problem parameters is carried out. Various AMSCO were considered during calculating. Particularly we succeed constructed Pontryagin's extremals in problems of transition to AMSCO which are close approximates Phobos and Deimos orbits without pulse influences at the finish moment. The SC performs a sixty-six and a nineteen many-revolution brakings near Mars respectively at these constructed trajectories on the final part of flight. The parameters continuation of the planar case of problem solution is used to construct trajectories in the major case. Using of high and low thrust propulsion in combination for space missions allows increase the useful weight and makes the project cheaper, that is actual now. Expeditions to Mars and its natural satellites can help to provide solution of a wide range of scientific physics problems of the Solar system. © 2017 Univelt Inc. All rights reserved