Search Results (63)

A Stackelberg equilibrium–based Model Reference Adaptive Control (MSE) method is proposed for spacecraft Pursuit–Evasion (PE) games with incomplete information and sequential decision making under a non–zero–sum framework. First, the spacecraft PE dynamics under $J_2$ perturbation are mapped to a dynamic Stackelberg game model. Next, the Riccati equation solves the equilibrium problem, deriving the evader’s optimal control strategy. Finally, a model reference adaptive algorithm enables the pursuer to dynamically adjust its control gains. Simulations show that the MSE strategy outperforms Nash Equilibrium (NE) and Single–step Prediction Stackelberg Equilibrium (SSE) methods, achieving 25.46% faster convergence than SSE and 39.11% lower computational cost than NE. Full article

Pursuit–evasion games are a fundamental framework for advancing autonomous decision-making and cooperative control in multi-UAV systems. However, the application of reinforcement learning to pursuit–evasion games involving fixed-wing UAVs remains challenging due to constraints, such as minimum velocity, limited turning radius, and high-dimensional continuous action spaces. To address these issues, this paper proposes a method that integrates automatic curriculum learning with multi-agent proximal policy optimization. A self-play mechanism is introduced to simultaneously train both pursuers and evaders, enabling dynamic and adaptive encirclement strategies. In addition, a reward structure specifically tailored for the encirclement task was designed to guide the pursuers in gradually achieving the encirclement of the evader while ensuring their own safety. To further improve training efficiency and convergence, this paper develops a subgame curriculum learning framework that progressively exposes agents to increasingly complex scenarios, facilitating experience accumulation and skill transfer. The simulation results demonstrate that the proposed approach improves learning efficiency and cooperative pursuit performance under realistic fixed-wing UAV dynamics. This work provides a practical and scalable solution for multiple fixed-wing UAV pursuit–evasion missions in complex environments. Full article

This paper proposes an inner–outer loop computational framework to address the morphology optimization and pursuit–evasion control problem for space modular robots. First, a morphological design space considering the functional characteristics of different modules is designed. Then, an elite genetic algorithm is applied to evolve the morphology within this space, and a proximal policy optimization algorithm is applied to control the space modular robot with evolved morphology. Considering symmetry, centrality, module cost, and average cumulative reward, a comprehensive morphological assessment is proposed to evaluate the morphology. And the assessment result serves as the fitness of evolution. In addition, by implementing the algorithm on the JAX framework for parallel computing, the computational efficiency was significantly enhanced, allowing the entire optimization process within 17.3 h. Comparative simulation results verify the effectiveness and superiority of the proposed computational framework. Full article

For the satellite orbit pursuit–evasion game problem, this paper proposes a multi-stage optimization-based solution aimed at improving the confrontation strategies between task satellites and target satellites in complex space environments. The approach divides the satellite pursuit–evasion game into two phases: the “approach phase” and the “sustained phase”. It dynamically optimizes the trajectories and strategies of the task and target satellites to achieve adaptive orbit control and behavior optimization. To enhance the global search capability and local convergence of the algorithm, this paper employs the Zebra Optimization Algorithm, introducing a multi-population cooperative evolution mechanism, and integrates differential game theory to improve the stability and reliability of the game strategies. Simulation results demonstrate that the proposed method effectively enhances task efficiency under multiple constraints, dynamically adjusts the strategies of both the pursuer and the evader, and provides an efficient, scalable solution applicable to satellite pursuit–evasion games in complex space environments. Full article

This paper investigates Mean Field Game methods to solve missile interception strategies in three-dimensional space, with a focus on analyzing the pursuit–evasion problem in many-to-many scenarios. By extending traditional missile interception models, an efficient solution is proposed to avoid dimensional explosion and communication burdens, particularly for large-scale, multi-missile systems. The paper presents a system of stochastic differential equations with control constraints, describing the motion dynamics between the missile (pursuer) and the target (evader), and defines the associated cost function, considering proximity group distributions with other missiles and targets. Next, Hamilton–Jacobi–Bellman equations for the pursuers and evaders are derived, and the uniqueness of the distributional solution is proved. Furthermore, using the $ϵ$-Nash equilibrium framework, it is demonstrated that, under the MFG model, participants can deviate from the optimal strategy within a certain tolerance, while still minimizing the cost. Finally, the paper summarizes the derivation process of the optimal strategy and proves that, under reasonable assumptions, the system can achieve a uniquely stable equilibrium, ensuring the stability of the strategies and distributions of both the pursuers and evaders. The research provides a scalable solution to high-risk, multi-agent control problems, with significant practical applications, particularly in fields such as missile defense systems. Full article

In this paper, we adopt the fuzzy actor–critic learning (FACL) and model predictive control (MPC) algorithms to solve the pursuit–evasion game (PEG) of quadrotors. FACL is used for perception, decision-making, and predicting the trajectories of agents, while MPC is utilized to address the flight control and target optimization of quadrotors. Specifically, based on the information of the opponent, the agent obtains its own game strategy by using the FACL algorithm. Based on the reference input from the FACL algorithm, the MPC algorithm is used to develop altitude, translation, and attitude controllers for the quadrotor. In the proposed hierarchical framework, the FACL algorithm provides real-time reference inputs for the MPC controller, enhancing the robustness of quadrotor control. The simulation and experimental results show that the proposed hierarchical control algorithm effectively realizes the PEG of quadrotors. Full article

With the rapid development of perception, decision-making, and control technologies, pursuit–evasion (PE) games with unmanned surface vehicles (USVs) have become an interesting research topic in military implementations and civilian areas. In this paper, we provide an overview of recent advances in the PE games with USVs. First, the motion model of USVs and successful criteria for PE games are presented. Next, some challenging issues in PE games with USVs are briefly discussed. Then, recent results on one-pursuer one-evader, multiple-pursuer one-evader, and multiple-pursuer multiple-evader with USVs are reviewed in detail. Finally, several theoretical and technical issues are suggested to direct future research, including target prediction, dynamic task allocation, brain-inspired decision-making, safe control, and PE experiments. Full article

Imagine using mobile guards to defend the vertices of a graph G from a sequence of attacks subject to the conditions that after each attack: (i) each guard either remains in place or moves to an adjacent vertex; (ii) the configuration of guards forms a Roman-dominating set; and (iii) there is at least one guard on each attacked vertex. We show that it is always possible to defend the vertices of a tree with n vertices using at most $⌈{\displaystyle \frac{5n}{6}}⌉$ guards and that this bound is tight. Full article

Real-time dynamic capture of a single moving target is one of the most crucial and representative tasks in UAV capture problems. This paper proposes a multi-UAV real-time dynamic capture strategy based on a differential game model to address this challenge. In this paper, the dynamic capture problem is divided into two parts: pursuit and capture. First, in the pursuit–evasion problem based on differential games, the capture UAVs and the target UAV are treated as adversarial parties engaged in a game. The current pursuit–evasion state is modeled and analyzed according to varying environmental information, allowing the capture UAVs to quickly track the target UAV. The Nash equilibrium solution in the differential game is optimal for both parties in the pursuit–evasion process. Then, a collaborative multi-UAV closed circular pipeline control method is proposed to ensure an even distribution of capture UAVs around the target, preventing excessive clustering and thereby significantly improving capture efficiency. Finally, simulations and real-flight experiments are conducted on the RflySim platform in typical scenarios to analyze the computational process and verify the effectiveness of the proposed method. Results indicate that this approach effectively provides a solution for multi-UAV dynamic capture and achieves desirable capture outcomes. Full article

This paper investigates three-dimensional pursuit problems in noncooperative stochastic differential games. By introducing a novel polynomial value function capable of addressing high-dimensional dynamic systems, the forward–backward stochastic differential equations (FBSDEs) for optimal strategies are derived. The uniqueness of the value function under bounded control inputs is rigorously established as a theoretical foundation. The proposed methodology constructs optimal closed-loop feedback strategies for both pursuers and evaders, ensuring state convergence and solution uniqueness. Furthermore, the Lebesgue measure of the barrier surface is computed, enabling the design of strategies for scenarios involving multiple pursuers and evaders. To validate its applicability, the method is applied to missile interception games. Simulations confirm that the optimal strategies enable pursuers to consistently intercept evaders under stochastic dynamics, demonstrating the robustness and practical relevance of the approach in pursuit–evasion problems. Full article

In pursuit–evasion scenarios, the pursuer typically possesses a lethal zone. If the evader effectively utilizes perceptual information, they can narrowly escape the lethal zone while minimizing energy consumption, thereby avoiding excessive and unnecessary maneuvers. Based on optimal control theory, we propose a guidance law for achieving critical safe miss distance evasion under bounded control. First, we establish the zero-effort miss (ZEM) state equation for the evader, while approximating disturbances from the pursuer. Next, we formulate an optimal control problem with energy consumption as the objective function and the ZEM at the terminal time as the terminal constraint. Subsequently, we design an iterative algorithm that combines the homotopy method and Newton’s iteration to solve the optimal control problem, applying Pontryagin’s Maximum Principle. The simulation results indicate that the designed iterative method converges effectively; through online updates, the proposed guidance law can successfully achieve critical safe miss distance evasion. Compared to programmatic maneuvering and norm differential game guidance law, this approach not only stabilizes the evader’s evasion capabilities but also significantly reduces energy consumption. Full article

The game of pursuit–evasion has always been a popular research subject in the field of Unmanned Aerial Vehicles (UAVs). Current evasion decision making based on reinforcement learning is generally trained only for specific pursuers, and it has limited performance for evading unknown pursuers and exhibits poor generalizability. To enhance the ability of an evasion policy learned by reinforcement learning (RL) to evade unknown pursuers, this paper proposes a pursuit UAV attitude estimation and pursuit strategy identification method and a Model Reference Policy Adaptation (MRPA) algorithm. Firstly, this paper constructs a Markov decision model for the pursuit–evasion game of UAVs that includes the pursuer’s attitude and trains an evasion policy for a specific pursuit strategy using the Soft Actor–Critic (SAC) algorithm. Secondly, this paper establishes a novel relative motion model of UAVs in pursuit–evasion games under the assumption that proportional guidance is used as the pursuit strategy, based on which the pursuit UAV attitude estimation and pursuit strategy identification algorithm is proposed to provide adequate information for decision making and policy adaptation. Furthermore, a Model Reference Policy Adaptation (MRPA) algorithm is presented to improve the generalizability of the evasion policy trained by RL in certain environments. Finally, various numerical simulations imply the precision of pursuit UAV attitude estimation and the accuracy of pursuit strategy identification. Also, the ablation experiment verifies that the MRPA algorithm can effectively enhance the performance of the evasion policy to deal with unknown pursuers. Full article

Aiming to address the problem of pursuit and interception for spacecraft using multiple evasion strategies, a pursuit strategy involving the use of an interactive multiple-model filter (IMM) in a pursuit–evasion game is considered, where the Evader adopts a switchable evasion strategy based on a linear quadratic method and zero-effort miss method. In this case, an improved interactive multiple-model feedback-learning filter method based on a long short-term memory network (LSTM-IMML) is proposed to estimate the Evader’s strategy mode, with the resulting estimation allowing the Pursuer to then switch its own strategy to the appropriate pursuit strategy to intercept the Evader. Also, the improved interactive multiple-model feedback learning filter can feed back the fusion estimation of the last-time state to the next-time state to improve estimation accuracy. An LSTM-based probability estimation network is designed to accurately estimate the probability of different modes. The proposed LSTM-IMML method can be used in the pursuit–evasion game when the Evader is able to switch its evasion strategy. The simulation results show that the LSTM-IMML method has better state estimation accuracy, and the mode probability estimation of the Evader is more exact and stable. Full article

This paper proposed an innovative guidance strategy, denoted as NMPC-IM, which integrates the Insensitive Mechanism (IM) with Nonlinear Model Predictive Control (NMPC) for Unmanned Aerial Vehicle (UAV) pursuit-evasion scenarios, with the aim of effectively intercepting maneuvering targets with consideration of input constraints while minimizing average energy expenditure. Firstly, the basic principle of IM is proposed, and it is transformed into an additional cost function in NMPC. Secondly, in order to estimate the states of maneuvering target, a fixed-time sliding mode disturbance observer is developed. Thirdly, the UAV’s interception task is formulated into a comprehensive Quadratic Programming (QP) problem, and the NMPC-IM guidance strategy is presented, which is then improved by the adjustment of parameters and determination of maximum input. Finally, numerical simulations are carried out to validate the effectiveness of the proposed method, and the simulation results show that the NMPC-IM guidance strategy can decrease average energy expenditure by mitigating the impact of the target’s maneuverability, optimizing the UAV’s trajectory during the interception process. Full article