The problemof interception of an evasive spacecraft by a pursuing spacecraft is formulated as a differential game.rnEach spacecraft is given amodest capability tomaneuver in the three-dimensional space. Interception concludes therngame and occurs if the pursuing spacecraft reaches the instantaneous position of the evading spacecraft. Thernobjective of the pursuer is to minimize the time for interception, whereas the evader tries to delay it indefinitely.rnSaddle-point equilibrium solutions are found using a recently developed direct numerical method that uses thernanalytical necessary conditions (unlike ordinary direct methods) to find the optimal control for one of the players.rnThemethod requires an initial guess of the solution, and this is provided by generating an approximate solution usingrngenetic algorithms. The evolutionary algorithm is employed as a preprocessing technique and is very useful in thisrncontext because the trial-and-error selection of first-attempt values for the variables involved is very challenging forrnthe problem at hand. The numerical method is tested on a variety of different starting conditions related to therndistinct initial orbits of the two spacecraft. It successfully finds the saddle-point trajectories of the two spacecraft, thusrnproving its effectiveness and robustness in solving a quite complicated problemsuch as the three-dimensional orbitalrngame at hand.
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