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We consider an autonomous navigation problem, whereby a traveler aims attraversing an environment in which an adversary tries to set an ambush. A twoplayers zero sum game is introduced. Players' strategies are computed as randompath distributions, a realization of which is the path chosen by the traveler.A parallel is drawn between the discrete problem, where the traveler moves on anetwork, and the continuous problem, where the traveler moves in the plane.Analytical optimal policies are derived. Using assumptions from the Minimal Cut- Maximal Flow literature, the optimal value of the game is shown to be relatedto the maximum flow on the environment in both the discrete and the continuouscases, when the reward function for the ambusher is uniform. A linear programis introduced that allows for the computation of optimal policies, compatiblewith non-uniform reward functions. In order to relax the assumptions for thecomputation of the players' optimal strategies of the continuous game, anetwork is created, inspired by recently introduced sampling based motionplanning techniques, and the linear program is adapted for continuousconstraints.

Discrete and Continuous ambush games: optimal policies and approximate solutions