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.

On a Two Cutters and Fugitive Ship Differential Game

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.

Isaacs’ Two-on-One Pursuit-Evasion Game

The Pure Pursuit strategy is ubiquitous both in the control literature but also in real-world implementation. In this paper, we pose and solve a variant of Isaacs' Two Cutters and Fugitive Ship problem wherein the Pursuers' strategy is fixed to Pure Pursuit, thus making it an optimal control problem. The Pursuers are faster than the Evader and are endowed with a finite capture radius. All agents move with constant velocity and can change heading instantaneously. Although capture is inevitable, the Evader wishes to delay capture as long as possible. The optimal trajectories cover the entire state space. Regions corresponding to either solo capture or isochronous (dual) capture are computed and both types of maximal time-to-capture optimal trajectories are characterized.

Optimal Evasion Against Dual Pure Pursuit

The Target Guarding Problem: A real time solution for noise corrupted measurements

A two-phase evasive strategy for a pursuit-evasion problem involving two non-holonomic agents with incomplete information

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.

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Patrick Wasz

Papers

On a Two Cutters and Fugitive Ship Differential Game

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