Construction of Barrier in a Fishing Game With Point Capture

Area of Science:

• Robotics
• Control Theory
• Game Theory

Background:

• Pursuit-evasion games are critical in robotics and autonomous systems.
• The
• fishing game
• ]
• The
• fishing game
• presents a unique challenge with a faster evader and two pursuers.

Purpose of the Study:

• To define the winning conditions for both evader and pursuers in the fishing game.
• To develop an explicit policy for constructing the barrier separating winning regions.
• To solve optimal control strategies for minimum time capture or escape.

Main Methods:

• Decomposition of the fishing game into two subgames: included angle and relative distances.
• Analysis of capture or escape possibilities within each subgame.
• Fusion of games of kind and degree by solving optimal control problems.

Main Results:

• Analytical forms of the barrier separating player-specific winning regions.
• Optimal control strategies for minimum time pursuit or evasion.
• Derived upper bounds for player winning times.

Conclusions:

• The developed method provides a clear strategy for determining outcomes in the fishing game.
• Explicit policies and optimal control strategies enhance the understanding of pursuit-evasion dynamics.
• This research contributes to the design of autonomous systems capable of complex navigation and interception tasks.