Guaranteed strategies for escaping encirclement

Resumo

This paper considers a conflict situation on the plane as follows. A fast evader E has to break out the encirclement of slow pursuers P_j1,...,jn = {P_j1,..., P_jn }, n ≥ 3, with a miss distance not smaller than r ≥ 0. First, we estimate the minimum guaranteed miss distance from E to a pursuer P_a, a ∈ {j₁,..., j_n}, when the former moves along a given straight line. Then the obtained results are used to calculate the guaranteed estimates to a group of two pursuers P_b,c = {P_b, P_c}, b, c ∈ {j₁,..., j_n}, b ≠ c, when E maneuvers by crossing the rectilinear segment P_bP_c, and the state passes to the domain of the game space where E applies a strategy under which the miss distance to any of the pursuers is not decreased. In addition, we describe an approach to the games with a group of pursuers P_j1,...jn, n ≥ 3, in which E seeks to break out the encirclement by passing between two pursuers P_b and P_c, entering the domain of the game space where E can increase the miss distance to all pursuers by straight motion. By comparing the guaranteed miss distances with r for all alternatives b, c ∈ {j₁,..., j_n}, b ≠ c, and a ∉ {b, c}, it is possible to choose the best alternative and also to extract the histories of the game in which the designed evasion strategies guarantee a safe break out from the encirclement.