In this article, we investigate and derive optimal strategies for the pursuit-evasion problem of two players with damped double integrator dynamics. The pursuer is assumed to have a greater acceleration and attempt to capture the evader as quickly as possible, while the evader wants to avoid or delay the capture. Different from the problems with single integrator dynamics, optimal strategies for such a problem are not intuitive. To solve this problem, we exploit both geometrical methods and differential games. Specifically, we first illustrate some properties of the optimal strategies, using which isochrones of the players are constructed. Then, by exploring the geometrical characteristics of the isochrones of the two players, we derive the target point directly without using the explicit formula of the intersections of isochrones. We propose an algorithm to determine the capture time, which is exactly the value function of the game, and finally the optimal strategies are derived subsequently. To prove the optimality of the proposed strategies, differential games and Hamilton-Jacobi-Isaacs (HJI) equation are used, where we show that the proposed value function is the solution to the HJI equation under our proposed strategies. Moreover, we apply our results to the game with one pursuer and multiple evaders, and some useful results are given. Finally, we carry out various simulations to show the optimality and effectiveness of our proposed strategies.

With the in-depth integration of research across multiple disciplines, such as biomimetics, robotics, and sensing technology, significant advancements have been made in swarm robotics technology, which has been applied in areas including drone swarms, mobile robot swarms, and underwater robot swarms. However, due to the limitations of underwater communication technologies, underwater robot swarms have lagged behind aerial and ground swarms in their development. This paper primarily explores the applications and advancements of swarm intelligence (SI) in multiple underwater robot swarms. Inspired by the behavior of animal swarms, researchers have translated this concept into the design and control strategies of underwater robot swarms. This approach draws on the self-organization, robustness, and adaptability inherent in collective behaviors, significantly enhancing the performance of underwater robot swarms. This paper provides a comprehensive review of the current research status of bio-inspired swarming of multiple underwater robots, including the design and classification of swarm underwater robots, SI algorithms and their applications in multiple underwater robots, and communication mechanisms for underwater robots. Furthermore, this paper highlights critical technical challenges that need to be addressed in research, along with proposed solutions, and discusses the vast application prospects of bio-inspired underwater swarming in military and civilian fields, providing clear directions for future research.

This paper introduces an innovative hierarchical model with a leader to facilitate navigation of a swarm of underwater robots, inspired by the collective behaviours observed in natural animal groups, such as schools of fish and flocks of birds. In this model, the leader robot carries a comprehensive set of navigation information, while the other robots are stratified based on the relative distances between them and follow the leader during the navigation process. The model incorporates repulsion and attraction forces to enable clustering and collision avoidance among the robots. Initial simulation results confirm the scalability of the model and its robustness against noise, while further simulations demonstrate that the proposed layered strategy effectively manages polyline and circular trajectory navigation and guides the robotic group around obstacles while maintaining the group’s structural stability and efficiency. In addition, the decentralised nature of the model and its minimal communication requirements make it highly suitable for practical underwater tasks. This research not only provides an effective and deployable solution for the cooperative synchronisation of underwater robots but also offers valuable insights for understanding and designing other types of robotic swarm systems.

Conventional aquatic robots are typically constrained by fixed morphology and single-mode locomotion, limiting adaptability to unstructured environments. Inspired by the diverse fin-driven locomotion strategies of natural fish, we present a self-reconfigurable robotic fish swarm system capable of operating across a wide range of aquatic conditions and tasks. Each robotic fish unit features autonomous physical assembly and disassembly capabilities by electropermanent magnets, enabling both connection and intermodule communication, allowing the swarm to dynamically reconfigure its morphology. Systematic evaluation reveals that swarm configurations substantially outperform individual units in various locomotion performance, including stability, maneuverability, swimming speed, energy efficiency, and multimodal locomotion ability. The swarm also demonstrates collaborative capabilities in navigating through complex environments, manipulating obstacles, and transporting objects, both in laboratory and outdoor aquatic settings. This work provides a framework for aquatic robots to adapt to unstructured environments and complex tasks, contributing to the advancement of multifunctional, reconfigurable robotic systems.

In the domain of multiplayer pursuit–evasion games, it is crucial to address the practical aspects of the players' heterogeneity, the distributed control manner, and the pursuers' goal of minimum makespan. However, the three topics have received limited attention in existing literature, both separately and in combination. In this article, we address the multiplayer pursuit–evasion game integrating these key topics, where the pursuers with simple motions strive to capture as many evaders, characterized by damped double integrators, as possible, meanwhile minimizing the task makespan. To this end, we establish an overall framework and sequentially tackle four key issues, leading to an effective solution to the entire problem. We first propose a novel isochron-based method to derive the capture condition and acquire the optimal pursuit and evasion strategies. Then, we enhance the usability of the capture condition by geometrically deriving the analytical form of the pursuer's winning region with respect to a given evader. Third, leveraging the concept of winning regions, we determine the lower boundary of pursuers' sensing range, ensuring sufficient information acquisition for evader allocation while avoiding selection conflicts. Finally, we propose a fully distributed allocation algorithm for each pursuer allowing the pursuer team to converge to the optimal evader allocation. By combining these contributions, we successfully provide an effective solution to the entire problem. Various simulations are conducted to show the effectiveness of our proposed methods.

In this article, we study a pursuit–evasion game between two players with heterogeneous kinematics, where the pursuer is with damped double-integrator dynamics and the evader is with single-integrator dynamics. The pursuer aims at capturing the evader as soon as possible, while the evader wants to avoid or delay the capture. Traditional methods to solve pursuit–evasion games rely on the Hamilton–Jacobi–Isaacs (HJI) equations and retrogressive path equations, which are very complicated and nonintuitive, thus failing to obtain a complete solution. To overcome these challenges, we develop an intuitive isochron-based method to thoroughly analyze all possible situations of the game and a concise geometric approach to calculate the optimal strategies, providing a complete solution to this game. Specifically, the isochron-based method effectively leverages three main factors: the players' motion capability, the pursuer's capture capability, and the players' states. Based on these, we analyze the players' superiority and the geometrical features of their isochrones and the intersections, thus acquiring concise conditions that determine the game's outcome. For the success-capture cases, we propose a new geometric approach to calculate the target points of the players and then obtain the closed-loop state feedback optimal pursuit and evasion strategies. We then get the corresponding value function and provide a validation using the HJI equation. For the success-evasion cases, we exploit the intersection of the players' isochrones to design some effective evasion strategies, which ensure that the evader can always avoid or delay the capture. Finally, some numerical simulations are carried out to validate the effectiveness and applicability of our results.