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where s 5 is the final heading angle of each player, which is the same for both of them.
Only two parameters are needed to obtain these trajectories: the final time t f and the final heading angle s 5.
where k 1, k 2, and k 3 are constants; d f is the final distance between players, computed using the trajectories values; l is capture distance; s 5 is the final heading angle supposed a priori; and (hat {s_{5}}) is the final heading angle, computed with the trajectories using Eq. (33).
The longitudinal sub-planner determines the magnitude of the bank angle, whereas the lateral sub-planner determines the appropriate sign of the bank angle for passing waypoints, avoiding no-fly zones, and minimizing the final heading error.
Hence, in this case, we first obtain the final time analytically, by numerically solving Eq. (31), and afterwards, we perform a minimization of the cost function defined in Eq. (34) over the final heading angle s 5.
The duple (s 5, t f ) that is considered the solution is chosen as the duple where capture happens, that is, final distance between players is equal or smaller than capture distance l, and which has the smaller absolute error between the final heading angle obtained in the trajectories and the introduced a priori in the duple.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com