Reach-avoid games for players with damped double integrator dynamics

2025/05/17 by Mengxin Lyu, Ruiliang Deng, Lyu, Mengxin +5 · 1 citation
Computer Science · Engineering · #Adaptive Dynamic Programming Control #Extremum Seeking Control Systems #FOS: Electrical engineering #Guidance and Control Systems #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2505.11951

openalex publication_date 2025/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates a reach-avoid game between two players with damped double integrator dynamics. An optimal state-feedback strategy is derived using a differential game framework combined with geometric analysis. To facilitate the analysis, we introduce the concept of multiple reachable region by characterizing the motion of players with damped double integrator dynamics. Based on this, a new type of the attackers dominance region is introduced. We show that distinct strategies are required depending on the location of the terminal position within different areas of the attacker's dominance region. Furthermore, we prove that the proposed strategies satisfy the necessary condition for optimality. Numerical simulations are provided to illustrate the conclusions.

Citations

• Pursuit Winning Strategies for Reach-Avoid Games with Polygonal Obstacles
• Defending a Static Target Point with a Slow Defender
• One Apollonius Circle is Enough for Many Pursuit-Evasion Games
• Perimeter-defense Game between Aerial Defender and Ground Intruder
• The Complete Differential Game of Active Target Defense
• Matching-Based Capture Strategies for 3D Heterogeneous Multiplayer Reach-Avoid Differential Games
• Perimeter-defense Game on Arbitrary Convex Shapes
• Construction of the Barrier for Reach-Avoid Differential Games in Three-Dimensional Space with Four Equal-Speed Players
• Markov Chains with Maximum Return Time Entropy for Robotic Surveillance
• Multi-Vehicle Collision Avoidance via Hamilton-Jacobi Reachability and Mixed Integer Programming
• Escape Regions of the Active Target Defense Differential Game

Cited by

• Pursuit-Evasion Between a Velocity-Constrained Double-Integrator Pursuer and a Single-Integrator Evader

Related

• Escape Regions of the Active Target Defense Differential Game
• Defender-Attacker-Target Game: Open-Loop Solution
• The Complete Differential Game of Active Target Defense
• Defending a Static Target Point with a Slow Defender
• Construction of the Barrier for Reach-Avoid Differential Games in Three-Dimensional Space with Four Equal-Speed Players