One Apollonius Circle is Enough for Many Pursuit-Evasion Games

Abstract

This paper investigates obstacle-free simple motion pursuit-evasion problems where the pursuer is faster and game termination is point capture. It is well known that the interior of the Apollonius Circle (AC) is the evader's dominance region, however, it was unclear whether the evader could reach outside the initial AC without being captured. We construct a pursuit strategy that guarantees the capture of an evader within an arbitrarily close neighborhood of the initial AC. The pursuer strategy is derived by reformulating the game into a nonlinear control problem, and the guarantee holds against any admissible evader strategy. Our result implies that the evader can freely select the capture location, but only inside the initial AC. Therefore, a class of problems, including those where the payoff is determined solely based on the location of capture, are now trivial.

A lionfish-inspired predation strategy in planar structured environments *

“…Pursuit and evasion are well-studied topics with applications in missile guidance [14], biological predation [9,10,21], and engineered systems [17,20,22,23]. Pure pursuit [14] is characterized by having a pursuer P heading directly towards an evader E along their line-of-sight vector, i.e.…”

“…For biologists, predator-prey interactions inform the structure of ecosystems [1][2][3] and characterize the pursuit and evasive behaviors of predators and prey [1,[4][5][6][7][8][9][10][11][12][13]. Engineers and mathematicians use these interactions to develop dynamic and kinematic models for missile guidance [14] and differential games [15,16] and to derive pursuit and evasion strategies for robotic systems [17][18][19][20][21][22][23][24].…”

“…The points of intersection between the pursuit and evasion trajectories lie on the Appollonius circle which contain positions where the pursuer and evader are projected coincide. The circle's center and radius correspond to the positions where capture is guaranteed [20,24,27]. The method of Appollonius circle assumes pursuit of a faster non-maneuvering evader, whereas [14] assumes the evader is non-maneuvering and is slower than the pursuer.…”

Accelerating Fuzzy Actor–Critic Learning via Suboptimal Knowledge for a Multi-Agent Tracking Problem

“…Therefore, in view of the above shortcomings, this study introduced the Apollonius circle to give the guided policy from the perspective of geometric planning on the basis of the original FACL [39]. By integrating the guided policy into the network of reinforcement learning, the prior information is utilized, and the policy that copes with the escaping target, which may suddenly turn, can be adjusted quickly.…”