Minimum time trajectory generation for relative guidance of aircraft

Abstract : In this communication is considered the problem of on line generation of minimum time trajectories to be followed by an aircraft to achieve relative convergence maneuvers. Here the trajectory generation problem is first considered as a minimum time control problem. The analysis of the resulting set of complex optimality conditions shows that the minimum time trajectories are produced by bang-bang control laws and can be characterized by some few geometric parameters. Then regular minimum time convergence trajectories can be defined. For practical considerations it appears necessary to solve on line this problem. Taking into consideration the structure of the regular minimum time convergence trajectories, an equivalent mathematical programming problem is formulated. . An off line exhaustive solution approach, based on reverse dynamic programming, is proposed to cover a large set of initial relative positions. Then a feed forward neural network can be trained to associate to an initial relative position the parameters of an optimal regular minimum time convergence trajectory.