Optimal Strategies in Multiplayer Reach-Avoid Games With Different Speed Ratios

Area of Science:

• Robotics
• Game Theory
• Control Theory

Background:

• Reach-avoid games are crucial for autonomous systems.
• Analyzing games with differing player speeds and capture radii presents challenges.
• Existing numerical methods have limitations in computational complexity and real-time application.

Purpose of the Study:

• To develop geometric methods for analyzing reach-avoid games with heterogeneous speeds.
• To construct optimal analytical strategies and defensive barriers.
• To enable precise, real-time calculations for nonpoint capture scenarios.

Main Methods:

• Geometric analysis of state space division into defensive and offensive advantage regions.
• Development of optimal strategies based on payoff functions and player positions.
• Construction of barriers and calculation of unique optimal target points.

Main Results:

• Demonstration of optimal analytical strategies for various speed ratios.
• Identification of a unique optimal target point within the offensive advantage region.
• Validation of constructed barriers' effectiveness in multiplayer simulations.

Conclusions:

• The proposed geometric method provides precise and real-time solutions for reach-avoid games.
• This approach overcomes limitations of traditional numerical methods.
• The findings are applicable to complex, multiplayer defensive scenarios.