Differential Game Strategies in Pursuit-Evasion Dynamics

Differential games provide a rigorous mathematical framework for analysing conflict and cooperation in dynamic systems, particularly those featuring pursuers and evaders. Originating in classical work on two‐player zero‐sum games, this field considers each agent’s control inputs within differential equations that govern motion. Optimal strategies emerge from solving a value function—often characterised by a Hamilton–Jacobi–Isaacs equation—that balances interception objectives against evasion efforts. Recent decades have seen advances in geometric methods, such as Apollonius curves and spheres, enabling closed‐form solutions in low‐dimensional settings. Concurrently, computational techniques have matured: grid‐based solvers, level‐set methods and more recently deep reinforcement learning architectures have been applied to high‐dimensional and stochastic scenarios. Applications span robotics swarms conducting cooperative tracking, autonomous vehicles evading hazards, and spacecraft performing interception under orbital perturbations. The global significance of these developments lies in their capacity to inform secure navigation, resource‐efficient guidance and resilient decision‐making in uncertain and adversarial environments.

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Technical terms

Differential game: A mathematical framework in which opposing players select control functions within differential equations to optimise conflicting objectives.

Pursuit–evasion dynamics: The strategic interaction between agents attempting interception (pursuers) and those seeking to avoid capture (evaders) within a dynamic system.

Apollonius sphere: A geometric locus representing all points satisfying a constant ratio of distances to two moving agents, used to determine interception conditions in three dimensions.

Hamilton–Jacobi–Isaacs equation: A partial differential equation that characterises the value function of a differential game, capturing optimal control and counter‐control strategies.

Deep reinforcement learning: A computational approach employing neural networks to learn optimal control policies through iterative interaction with an environment.

References

1. Multiplayer Reach–Avoid Differential Games in 3D Space Inspired by Harris’ Hawks’ Cooperative Hunting Tactics. Research (2023).
2. Orbital Interception Pursuit Strategy for Random Evasion Using Deep Reinforcement Learning. Space Science & Technology (2023).
3. Game Tree Search-based Impulsive Orbital Pursuit–Evasion Game with Limited Actions. Space Science & Technology (2024).