Optimality of Motion Camouflage Under Escape Uncertainty

Motion camouflage can be a useful tactic for a pursuer attempting to conceal their true trajectory from their target. Many previous studies determine optimal trajectories subject to motion camouflage constraints, but these analyses do not address when it is optimal to use, nor do they account for the pursuer's inability to predict if and when the target will try to escape. We present an optimal control framework to determine when the pursuer should use motion camouflage amidst uncertainty in the target's escape attempt time. Focusing on the illustrative problem of a male hover fly pursuing a female hover fly for mating, we model the female fly's escape response as the result of a non-homogeneous Poisson point process with a biologically informed rate function, and we obtain and numerically solve two Hamilton-Jacobi-Bellman (HJB) PDEs which encode the pursuer's optimal trajectories. Our numerical experiments and statistics illustrate when it is optimal to use motion camouflage pursuit tactics under varying degrees of the target's visual acuity and tolerance to the pursuer's presence.