Khan Pham

Bio: Khan Pham is an academic researcher from Air Force Research Laboratory. The author has contributed to research in topics: Pursuer & Differential game. The author has an hindex of 1, co-authored 1 publications receiving 5 citations.

Two-an-One Pursuit with a Non-Zero Capture Radius

Abstract: In this paper, we revisit the “Two Cutters and Fugitive Ship” differential game that was addressed by Isaacs, but move away from point capture. We consider a two-on-one pursuit-evasion differential game with simple motion and pursuers endowed with circular capture sets of radius l > 0. The regions in the state space where only one pursuer effects the capture and the region in the state space where both pursuers cooperatively and isochronously capture the evader are characterized, thus solving the Game of Kind. Concerning the Game of Degree, the algorithm for the synthesis of the optimal state feedback strategies of the cooperating pursuers and of the evader is presented.

On a Two Cutters and Fugitive Ship Differential Game

Abstract: Isaacs’ Two Cutters and Fugitive Ship differential game is revisited. In this letter, it is assumed that the three players, that is, the two cutters and the fugitive ship have equal speeds, but the cutters have a non-zero capture radius. The state space region where capture is guaranteed, notwithstanding the fact that the cutters are not faster than the fugitive ship, is delineated, and the protagonists’ optimal state feedback strategies are synthesized.

Isaacs’ Two-on-One Pursuit-Evasion Game

Abstract: We consider Isaacs’ pursuit-evasion differential game in the Euclidean plane where two pursuers, say cutters, chase a fugitive ship. All move with simple motion, the speeds of the cutters each being greater than that of the fugitive ship, the evader. Coincidence with either one, or both pursuers, is capture, and time of capture is the payoff/cost. The solution of the Game of Kind is provided and the intuitively appealing geometric method used to solve the Two Cutters and Fugitive Ship Game of Degree is justified. This opens the door to employing the geometric method to design operationally relevant group pursuit/swarm attack tactics.

An Analytic Study of Pursuit Strategies

Abstract: The Two-on-One pursuit-evasion differential game is revisited where the holonomic players have equal speed, and the two pursuers are endowed with a circular capture range ` > 0. Then, the case where the pursuers’ capture ranges are unequal, `1 > `2 ≥ 0, is analyzed. In both cases, the state space region where capture is guaranteed is delineated and the optimal feedback strategies are synthesized. Next, pure pursuit is considered whereupon the terminal separation between a pursuer and an equal-speed evader less than the pursuer’s capture range ` > 0. The case with two pursuers employing pure pursuit is considered, and the conditions for capturability are presented. The pure pursuit strategy is applied to a target-defense scenario and conditions are given that determine if capture of the attacker before he reaches the target is possible. Lastly, three-on-one pursuit-evasion is considered where the three pursuers are initially positioned in a fully symmetric configuration. The evader, situated at the circumcenter of the three pursuers, is slower than the pursuers. We analyze collision course and pure pursuit guidance and provide evidence that conventional strategy for “optimal” evasive maneuver is incorrect.