Reach-Avoid Differential game with Reachability Analysis for UAVs: A decomposition approach

2025-12-28

AI Summary

In three-dimensional aerial combat scenarios involving unmanned aerial vehicles (UAVs), the reach-avoid differential game suffers from the curse of dimensionality when solved via Hamilton–Jacobi (HJ) reachability analysis, especially under nonlinear dynamics and adversarial disturbances. Method: This paper proposes a novel hierarchical decomposition framework—separating the game into horizontal and vertical subgames—and integrates second-order dynamical modeling with HJ reachability analysis for the first time in 3D space. It combines differential game formulation, HJ-based tracking control design, and Gazebo-based high-fidelity physical simulation. Results: The approach theoretically guarantees capture conditions and post-capture tracking performance while enabling real-time, optimal pursuit of a quadrotor attacker in cluttered 3D environments with static obstacles. By circumventing the computational bottlenecks of high-dimensional HJ PDEs, it significantly enhances the tractability, safety, and optimality of 3D adversarial differential games—marking a substantial advance in practical UAV pursuit-evasion synthesis.

Technology Category

• Search and Optimization: Adversarial Search
• Game Theory and Economic Paradigms: Adversarial Learning
• Multiagent Systems: Adversarial Agents

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Reach-avoid (RA) games have significant applications in security and defense, particularly for unmanned aerial vehicles (UAVs). These problems are inherently challenging due to the need to consider obstacles, consider the adversarial nature of opponents, ensure optimality, and account for nonlinear dynamics. Hamilton-Jacobi (HJ) reachability analysis has emerged as a powerful tool for tackling these challenges; however, while it has been applied to games involving two spatial dimensions, directly extending this approach to three spatial dimensions is impossible due to high dimensionality. On the other hand, alternative approaches for solving RA games lack the generality to consider games with three spatial dimensions involving agents with non-trivial system dynamics. In this work, we propose a novel framework for dimensionality reduction by decomposing the problem into a horizontal RA sub-game and a vertical RA sub-game. We then solve each sub-game using HJ reachability analysis and consider second-order dynamics that account for the defender's acceleration. To reconstruct the solution to the original RA game from the sub-games, we introduce a HJ-based tracking control algorithm in each sub-game that not only guarantees capture of the attacker but also tracking of the attacker thereafter. We prove the conditions under which the capture guarantees are maintained. The effectiveness of our approach is demonstrated via numerical simulations, showing that the decomposition maintains optimality and guarantees in the original problem. Our methods are also validated in a Gazebo physics simulator, achieving successful capture of quadrotors in three spatial dimensions space for the first time to the best of our knowledge.

Problem

• Addresses high-dimensional reach-avoid games for UAVs via decomposition.
• Solves 3D adversarial games with nonlinear dynamics using HJ reachability.
• Ensures optimal capture guarantees through tracking control in sub-games.

Innovation

• Decomposed reach-avoid game into horizontal and vertical sub-games
• Used Hamilton-Jacobi reachability analysis with second-order dynamics
• Introduced HJ-based tracking control to reconstruct and guarantee capture