Methodical aspects of optimization of complex interplanetary trajectories (global trajectory optimization)
- Paper number
IAC-06-C1.4.03
- Author
Prof. Mikhail S. Konstantinov, Moscow Aviation Institute (MAI), Russia
- Coauthor
Dr. Vyacheslav Petukhov, Khrunichev State Research & Production Space Center, Russia
- Year
2006
- Abstract
Results of competition on global trajectory optimization, which was organized by the European Space Agency in the last year, have shown, that there is no full methodical base for optimization of interplanetary trajectories at which a plenty of swingbies can be carried out. The problem solution of global trajectory optimization can be divided into two stages. At the first stage the choice of rational plan of flight (mission) of a spacecraft is being carried out. Thus on the basis of any reasons (sometimes intuitive, sometimes supported by some numerical analysis) the plan of flight of a spacecraft is being determined. The choice of the flight plan consists in fixing a set of discrete and integer parameters. At the second stage for the chosen flight plan an optimum of some continuous characteristics of a spacecraft trajectory is being determined. The local optimization of a trajectory of a spacecraft is being carried out for space of some set of continuous characteristics. Unexpected there was that, all teams, which have considered complex schemes of interplanetary flight, could not or has not wanted to fulfill strictly local optimization of the chosen flight plan, to use conditions of local optimization. For the formulated first investigation phase it is offered to spend the analysis of each arch of flight between intermediate planets in the form of the solution of the equation, which is analogue of Lambert equation. The unknown of this equation is true anomaly of an initial point of a transfer trajectory. For this variable the algorithm of determination of boundaries of 1-connected range is developed. This range is nonclosed. It is proved; that at trajectories with angular distance smaller than one turn the flight time is monotonous function of true anomaly of an initial point of a spacecraft trajectory. The range of values of this function is (0, infinity). Thus, the solution of the equation always exists and it is unique. The problem for multirevolutional trajectories is more complicated. In this case there is minimal time of flight. If time of flight less minimal one then a solution of equation does not exist. If time of flight more minimal one then two solution of equation exist. One solution corresponds to flight on the first semi-coil, another solution - to flight on the second semi-coil. In these conditions at the first investigation phase it is being determined the following characteristics: sequence of swingbies, date of swingbies, quantity of full turns of spacecraft concerning the Sun on each arc of trajectory and an attribute of use of a trajectory of flight on the first or second semi-coil. For the second investigation phase the full formulation of necessary conditions of local optimization in the form of conditions of a principle of a maximum is given. Chosen parameters are: the adjoint variables in an initial point; the adjoint variables to radius vector after each swingby; two parameters of each swingby (two corners). The first corner is an angle of turn of hyperboles asymptote. A range of its change from zero up to the maximal value defined by hyperbolic excess of velocity and a planet characteristics. The second corner defines a plane of a flyby hyperbole. A range of its change is 0...360 degrees. The boundary conditions: radius a vector of a swingby planet; the collinearity conditions of a vector of hyperbolic excess of velocity and Lowden vector in this point of a trajectory; conditions in a terminal point of a trajectory. Total number of chosen parameters and the boundary conditions is 5N+6 (N - number of swingbies). Thus Lowden vector after swingby is being determined from a condition of constancy of the module of Lowden vector before and after swingby (one condition) and a collinearity condition Lowden vector after swingby to hyperbolic excess of velocity after swingby (two conditions). The problem of trajectory optimization to an asteroid 2001 TW229 with use of 5 swingby is analyzed. For this problem the order of a boundary value problem is equal to 31.
- Abstract document
- Manuscript document
IAC-06-C1.4.03.pdf (🔒 authorized access only).
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