Direct Multiphase Optimisation of Multiobjective Trajectory Design Problems

In this paper a novel approach to the design of optimal trajectory involving multiple objective functions and multiple players has been presented. The approach is fully direct and can solve efficiently formation flying problems and zero-sum differential games without resorting to differential algebraic equations coming from the optimal control theory. Here instead direct transcription is applied using multiple objective optimization theory and a multiphase approach to handle multiple players. The multiphase philosophy leads naturally to parallelization of the code in particular for mini-max problems with non-collaborative player for which a trade-off method is required. In this respect it has been shown, as the weighted sum method is equivalent to optimal control method when the players are collaborative while the trade-off method is equivalent when the players are not collaborative.