Reach-Avoid Games With Two Defenders and One Attacker: An Analytical Approach

Area of Science:

• Control Theory
• Game Theory
• Robotics

Background:

• Reach-avoid games involve complex state-space analysis.
• Multiplayer games often rely on computationally intensive numerical methods.
• Existing methods struggle with real-time applications due to complexity.

Purpose of the Study:

• To develop an analytical method for constructing the barrier in a two-defender, one-attacker reach-avoid game.
• To define and characterize defender dominance regions (DDR) and attacker dominance regions (ADR).
• To derive optimal strategies for players based on payoff functions and initial states.

Main Methods:

• Utilizing an attack region method to analytically construct the barrier.
• Employing Voronoi diagrams and Apollonius circles for barrier formulation.
• Considering practical payoff functions to determine optimal player strategies.

Main Results:

• The barrier analytically divides the state space into DDR and ADR.
• For initial states in DDR, defenders guarantee interception; in ADR, the attacker succeeds.
• Optimal strategies are derived, showing ADR subdivision based on player strategies.

Conclusions:

• The proposed analytical method provides an exact barrier formulation, overcoming limitations of numerical approaches.
• This method is suitable for real-time updates in complex reach-avoid games.
• The study offers precise strategies for players within their respective dominance regions.