Singular surfaces in multi-agent connectivity maintenance games

In this paper, we analyze a connectivity maintenance problem that arises when two mobile autonomous agents navigate in an environment containing obstacles. Using the Rician fading model for the communication channel, we address the problem for the case when the motion strategies for one of the agents is adversarial in nature. We investigate a specific kind of singular surface that appears in the solution to the underlying pursuit-evasion game, namely the dispersal surface. We present construction of the projection of several dispersal surfaces for various obstacle geometries by fixing the initial position of the evader. Finally, we present numerical simulations for specific environments containing obstacles.