Curve-straight probabilistic engagement zones (CSPEZ) quantify the spatial regions an evader should avoid to reduce capture risk from a turn-rate-limited pursuer following a curve-straight path with uncertain parameters including position, heading, velocity, range, and maximum turn rate. This paper presents methods for generating evader trajectories that minimize capture risk under such uncertainty. We first derive an analytic solution for the deterministic curve-straight basic engagement zone (CSBEZ), then extend this formulation to a probabilistic framework using four uncertainty-propagation approaches: Monte Carlo sampling, linearization, quadratic approximation, and neural-network regression. We evaluate the accuracy and computational cost of each approximation method and demonstrate how CSPEZ constraints can be integrated into a trajectory-optimization algorithm to produce safe paths that explicitly account for pursuer uncertainty.

This paper presents a novel strategy for a multi-agent pursuit-evasion game involving multiple faster pursuers with heterogenous speeds and a single slower evader. We define a geometric region, the evader's safe-reachable set, as the intersection of Apollonius circles derived from each pursuer-evader pair. The capture strategy is formulated as a zero-sum game where the pursuers cooperatively minimize the area of this set, while the evader seeks to maximize it, effectively playing a game of spatial containment. By deriving the analytical gradients of the safe-reachable set's area with respect to agent positions, we obtain closed-form, instantaneous optimal control laws for the heading of each agent. These strategies are computationally efficient, allowing for real-time implementation. Simulations demonstrate that the gradient-based controls effectively steer the pursuers to systematically shrink the evader's safe region, leading to guaranteed capture. This area-minimization approach provides a clear geometric objective for cooperative capture.

Computing worst-case robust strategies in pursuit-evasion games (PEGs) is time-consuming, especially when real-world factors like partial observability are considered. While important for general security purposes, real-time applicable pursuit strategies for graph-based PEGs are currently missing when the pursuers only have imperfect information about the evader's position. Although state-of-the-art reinforcement learning (RL) methods like Equilibrium Policy Generalization (EPG) and Grasper provide guidelines for learning graph neural network (GNN) policies robust to different game dynamics, they are restricted to the scenario of perfect information and do not take into account the possible case where the evader can predict the pursuers' actions. This paper introduces the first approach to worst-case robust real-time pursuit strategies (R2PS) under partial observability. We first prove that a traditional dynamic programming (DP) algorithm for solving Markov PEGs maintains optimality under the asynchronous moves by the evader. Then, we propose a belief preservation mechanism about the evader's possible positions, extending the DP pursuit strategies to a partially observable setting. Finally, we embed the belief preservation into the state-of-the-art EPG framework to finish our R2PS learning scheme, which leads to a real-time pursuer policy through cross-graph reinforcement learning against the asynchronous-move DP evasion strategies. After reinforcement learning, our policy achieves robust zero-shot generalization to unseen real-world graph structures and consistently outperforms the policy directly trained on the test graphs by the existing game RL approach.

We consider a scenario where a team of two unmanned aerial vehicles (UAVs) pursue an evader UAV within an urban environment. Each agent has a limited view of their environment where buildings can occlude their field-of-view. Additionally, the pursuer team is agnostic about the evader in terms of its initial and final location, and the behavior of the evader. Consequently, the team needs to gather information by searching the environment and then track it to eventually intercept. To solve this multi-player, partially-observable, pursuit-evasion game, we develop a two-phase neuro-symbolic algorithm centered around the principle of bounded rationality. First, we devise an offline approach using deep reinforcement learning to progressively train adversarial policies for the pursuer team against fictitious evaders. This creates $k$-levels of rationality for each agent in preparation for the online phase. Then, we employ an online classification algorithm to determine a "best guess" of our current opponent from the set of iteratively-trained strategic agents and apply the best player response. Using this schema, we improved average performance when facing a random evader in our environment.

This paper proposes a cooperative integrated estimation-guidance framework for simultaneous interception of a non-maneuvering target using a team of unmanned autonomous vehicles, assuming only a subset of vehicles are equipped with dedicated sensors to measure the target's states. Unlike earlier approaches that focus solely on either estimation or guidance design, the proposed framework unifies both within a cooperative architecture. To circumvent the limitation posed by heterogeneity in target observability, sensorless vehicles estimate the target's state by leveraging information exchanged with neighboring agents over a directed communication topology through a prescribed-time observer. The proposed approach employs true proportional navigation guidance (TPNG), which uses an exact time-to-go formulation and is applicable across a wide spectrum of target motions. Furthermore, prescribed-time observer and controller are employed to achieve convergence to true target's state and consensus in time-to-go within set predefined times, respectively. Simulations demonstrate the effectiveness of the proposed framework under various engagement scenarios.

Personal use of this material is permitted. Abstract-- Motivated by the problem of pursuit-evasion, we present a motion planning framework that combines energy-based diffusion models with artificial potential fields for robust real time trajectory generation in complex environments. Our approach processes obstacle information directly from point clouds, enabling efficient planning without requiring complete geometric representations. The framework employs classifier-free guidance training and integrates local potential fields during sampling to enhance obstacle avoidance. In dynamic scenarios, the system generates initial trajectories using the diffusion model and continuously refines them through potential field-based adaptation, demonstrating effective performance in pursuit-evasion scenarios with partial pursuer observability. This paper is motivated by the problem of using robots to guide crowds to safety in scenarios involving rapidly evolving threats, such as an active shooter or a forest fire.

Effectively positioning pursuers in pursuit-evasion games without prior knowledge of evader locations remains a significant challenge. A novel approach that combines game-theoretic control theory with Graph Neural Networks is introduced in this work. By conceptualizing pursuer configurations as strategic arrangements and representing them as graphs, a Graph Characteristic Space is constructed via multi-objective optimization to identify Pareto-optimal configurations. A Graph Convolutional Network (GCN) is trained on these Pareto-optimal graphs to generate strategically effective initial configurations, termed "hot starts". Empirical evaluations demonstrate that the GCN-generated hot starts provide a significant advantage over random configurations. In scenarios considering multiple pursuers and evaders, this method hastens the decline in evader survival rates, reduces pursuer travel distances, and enhances containment, showcasing clear strategic benefits.

Adversarial environments require agents to navigate a key strategic trade-off: acquiring information enhances situational awareness, but may simultaneously expose them to threats. To investigate this tension, we formulate a PursuitEvasion-Exposure-Concealment Game (PEEC) in which a pursuer agent must decide when to communicate in order to obtain the evader's position. Each communication reveals the pursuer's location, increasing the risk of being targeted. Both agents learn their movement policies via reinforcement learning, while the pursuer additionally learns a communication policy that balances observability and risk. We propose SHADOW (Strategic-communication Hybrid Action Decision-making under partial Observation for Warfare), a multi-headed sequential reinforcement learning framework that integrates continuous navigation control, discrete communication actions, and opponent modeling for behavior prediction. Empirical evaluations show that SHADOW pursuers achieve higher success rates than six competitive baselines. Our ablation study confirms that temporal sequence modeling and opponent modeling are critical for effective decision-making. Finally, our sensitivity analysis reveals that the learned policies generalize well across varying communication risks and physical asymmetries between agents.

This paper addresses a critical aerial defense challenge in contested airspace, involving three autonomous aerial vehicles -- a hostile drone (the pursuer), a high-value drone (the evader), and a protective drone (the defender). We present a cooperative guidance framework for the evader-defender team that guarantees interception of the pursuer before it can capture the evader, even under highly dynamic and uncertain engagement conditions. Unlike traditional heuristic, optimal control, or differential game-based methods, we approach the problem within a time-constrained guidance framework, leveraging true proportional navigation based approach that ensures robust and guaranteed solutions to the aerial defense problem. The proposed strategy is computationally lightweight, scalable to a large number of agent configurations, and does not require knowledge of the pursuer's strategy or control laws. From arbitrary initial geometries, our method guarantees that key engagement errors are driven to zero within a fixed time, leading to a successful mission. Extensive simulations across diverse and adversarial scenarios confirm the effectiveness of the proposed strategy and its relevance for real-time autonomous defense in contested airspace environments.

--This paper introduces the concept of trajectory encryption in cooperative simultaneous target interception, wherein heterogeneity in guidance principles across a team of unmanned autonomous systems is leveraged as a strategic design feature. By employing a mix of heterogeneous time-to-go formulations leading to a cooperative guidance strategy, the swarm of vehicles is able to generate diverse trajectory families. This diversity expands the feasible solution space for simultaneous target interception, enhances robustness under disturbances, and enables flexible time-to-go adjustments without predictable detouring. From an adversarial perspective, heterogeneity obscures the collective interception intent by preventing straightforward prediction of swarm dynamics, effectively acting as an encryption layer in the trajectory domain. Simulations demonstrate that the swarm of heterogeneous vehicles is able to intercept a moving target simultaneously from a diverse set of initial engagement configurations. Cooperative intercept missions, once limited to large-scale interceptor systems, are also being realized using agile teams of small drones.