We formulate the problem of an autonomous agent team facing the attack of an adversarial agent as a single-pursuer-multiple-evader pursuit-evasion game, with the assumption that the pursuer is faster than all evaders. In this game, the pursuer aims to minimize the capture time of the last surviving evader, while the evaders as a team cooperate to maximize this time. We present a gradient-based approach that quickly computes the controls for the evaders as a team under an open-loop formulation that is conservative towards the evader team by deriving analytical formulas. We demonstrate the advantage of the gradient-based approach by comparing performance both in computation time and in optimality with the iterative open-loop method studied in our previous work. Multiple heuristics have been designed to deal with the inherent intractability of evaluating all possible capture sequences. Extensive simulations have been performed, with results discussed.

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