In mathematical pursuit and escape games a pursuer (agent 1) tries to catch a target (agent 2) by closing the distance between them. Both pursuer and target can move as long as their movement is unobstructed.

The distance in traditional pursuit and escape games is taken as the Euclidean distance given in terms of the so-called L2-norm where the Pythagorean Theorem holds true. During this project, the effects of limiting one of these -agents to movement measured in the L1 norm and the addition of a finite, straight-line barrier, or obstacle, were investigated, both analytically and numerically. The earliest time in which the pursuer and target -can meet defines their dominance regions. It was found that even with lower speed (up to a ratio of 50%), an L2 target -can escape from an L1 pursuer if the target takes the “optimal” path within its dominance region. Escape is defined when the target’s dominance region becomes unbounded, meaning that it has freedom of movement in an infinite region. To define these (what is “these” referring to?), the dominance region functions were fitted to oblique asymptotes (probably would leave this sentence out entirely because you cannot explain briefly what these functions are and why you use fitting). When introducing the barrier, there are three cases for the L1 pursuer’s path: one axis of movement (AoM) blocked, both AoM blocked, and no AoM blocked. The case with single AoM and both AoM being blocked results in global change of the dominance regions, whereas the case with no AoM blocked only results in local- change.

Models of pursuit and escape are used to describe and explain real-world phenomena, including predator-prey interactions, and find applications in unmanned ground vehicle (UGV) to unmanned aerial vehicle (UAV) pursuit and target-tracking algorithms.