A cooperative Homicidal Chauffeur game

We address a pursuit-evasion problem involving an unbounded planar environment, a single evader and multiple pursuers moving along curves of bounded curvature. The problem amounts to a multi-agent version of the classic Homicidal Chauffeur problem; we identify parameter ranges in which a single pursuer is not sufficient to guarantee evader capture. We propose a novel multi-phase cooperative strategy in which the pursuers move in specific formations and confine the evader to a bounded region. The proposed strategy is inspired by the hunting and foraging behaviors of various fish species. We characterize the required number of pursuers for which our strategy is guaranteed to lead to confinement.     

On Discrete-Time Pursuit-Evasion Games With Sensing Limitations

In this paper, we address discrete-time pursuit-evasion games in the plane where every player has identical sensing and motion ranges restricted to closed disks of given sensing and stepping radii. A single evader is initially located inside a bounded subset of the environment and does not move until detected. We propose a sweep-pursuit-capture pursuer strategy to capture the evader and apply it to two variants of the game. The first involves a single pursuer and an evader in a bounded convex environment, and the second involves multiple pursuers and an evader in a boundaryless environment. In the first game, we give a sufficient condition on the ratio of sensing to stepping radius of the players that guarantees capture. In the second, we determine the minimum probability of capture, which is a function of a novel pursuer formation and independent of the initial evader location. The sweep and pursuit phases reduce both games to previously studied problems with unlimited range sensing, and capture is achieved using available strategies. We obtain novel upper bounds on the capture time and present simulation studies that address the performance of the strategies under sensing errors, different ratios of sensing to stepping radius, greater evader speed, and a different number of pursuers.      

多追捕者-单-逃跑者追逃问题实现成功捕获的约束条件

针对包含有n个追捕者及1个逃跑者的2维平面多机器人追逃问题,对实现成功捕获的约束条件进行了研究.经过理论分析得出:在机器人拥有全局视野的情况下,即使单一逃跑者性能优于每个追捕者,只要满足追捕者与逃跑者的速率比大于sin(π/n),逃跑机器人落在追捕机器人所构成的凸多边形内部且逃跑者和追捕者构成的相邻追-逃阿波罗尼奥斯圆满足两两相交(相切)这2个约束条件,则追捕者通过选择合适的追捕策略就一定可以实现成功抓捕.此外,还给出了在此约束条件下的追捕者和逃跑者的追逃策略.多组仿真实验同样证明了本文提出的约束条件是正确的.     

A Decentralized Fuzzy Learning Algorithm for Pursuit-Evasion Differential Games with Superior Evaders

In this paper, we consider multi-pursuer single-superior-evader pursuit-evasion differential games where the evader has a speed that is similar to or higher than the speed of each pursuer. A new fuzzy reinforcement learning algorithm is proposed in this work. The proposed algorithm uses the well-known Apollonius circle mechanism to define the capture region of the learning pursuer based on its location and the location of the superior evader. The proposed algorithm uses the Apollonius circle with a developed formation control approach in the tuning mechanism of the fuzzy logic controller (FLC) of the learning pursuer so that one or some of the learning pursuers can capture the superior evader. The formation control mechanism used by the proposed algorithm guarantees that the pursuers are distributed around the superior evader in order to avoid collision between pursuers. The formation control mechanism used by the proposed algorithm also makes the Apollonius circles of each two adjacent pursuers intersect or be at least tangent to each other so that the capture of the superior evader can occur. The proposed algorithm is a decentralized algorithm as no communication among the pursuers is required. The only information the proposed algorithm requires is the position and the speed of the superior evader. The proposed algorithm is used to learn different multi-pursuer single-superior-evader pursuit-evasion differential games. The simulation results show the effectiveness of the proposed algorithm.     

Maintaining strong mutual visibility of an evader moving over the reduced visibility graph

In this paper, we address the problem of determining whether a mobile robot, called the pursuer, is able to maintain strong mutual visibility (a visibility notion between regions over a convex partition of the environment) of an antagonist agent, called the evader. We frame the problem as a non cooperative game. We consider the case in which the pursuer and the evader move at bounded speed, traveling in a known polygonal environment with or without holes, and in which there are no restrictions as to the distance that might separate the agents. Unlike our previous efforts (Murrieta-Cid et al. in Int J Robot Res 26:233–253, 2007), we give special attention to the combinatorial problem that arises when searching for a solution through visiting several locations in an environment with obstacles. In this paper we take a step further, namely, we assume an antagonistic evader who moves continuously and unpredictably, but with a constraint over its set of admissible motion policies, as the evader moves in the shortest-path roadmap, also called the reduced visibility graph (RVG). The pursuer does not know which among the possible paths over the RVG the evader will choose, but the pursuer is free to move within all the environment. We provide a constructive method to solve the decision problem of determining whether or not the pursuer is able to maintain strong mutual visibility of the evader. This method is based on an algorithm that computes the safe areas (areas that keep evader surveillance) at all times. We prove decidability of this problem, and provide a complexity measure to this evader surveillance game; both contributions hold for any general polygonal environment that might or not contain holes. All our algorithms have been implemented and we show simulation results.     

Coordinated pursuer control using particle filters for autonomous search-and-capture

In a real-world pursuit-evasion (PE) game, the pursuers often have a limited field-of-view of the evaders and thus are required to search for and detect the evaders before capturing them. This paper presents a unified framework and control algorithm using particle filters (PFs) for the coordination of multiple pursuers to search for and capture multiple evaders given the ability of PF to estimate highly non-Gaussian densities prevalent in search problems. The pursuer control problem is formulated as a stochastic control problem where global objectives function of both searching and capturing are common. To take the evaders’ actions into account, an action measure (AM) is defined over the evaders’ PDs is used to represent the probability that the evader may transit each state in the PD. The global objective functions for search and capture are then decomposed into local objective functions for unification through objective priority weights. Coordination between the pursuers takes place through the multi-sensor update where the observation likelihoods of all pursuers are used in the PF update stage. The control actions of each pursuer are then determined individually, based on the updated PDs given the objective weights, action measures as well as evader importance weights in the case of multiple evaders. The proposed algorithm is tested in three scenarios for its effectiveness. In addition, a parametric study on the average capture time against the initial variances of the target state uncertainty is conducted to test for robustness. Results show that the pursuers are able to capture all the evaders in each case with the capture time for the second and last scenario differing by only 2.9% implying firstly that under the proposed algorithm, the capture time is not proportional to the increase in the number of evaders and also suggested robustness and potential scalability of the proposed algorithm.     

Evasion strategies of a three-player lifeline game

This study examines a multi-player pursuit-evasion game, more specifically, a three-player lifeline game in a planar environment, where a single evader is tasked with reaching a lifeline prior to capture. A decomposition method based on an explicit policy is proposed to address the game qualitatively from two main aspects: (1) the evader’s position distribution to guarantee winning the game (i.e., the escape zone), which is based on the premise of knowing the pursuers’ positions initially, and (2) evasion strategies in the escape zone. First, this study decomposes the three-player lifeline game into two two-player sub-games and obtains an analytic expression of the escape zone by constructing a barrier, which is an integration of the solutions of two sub-games. This study then explicitly partitions the escape zone into several regions and derives an evasion strategy for each region. In particular, this study provides a resultant force method for the evader to balance the active goal of reaching the lifeline and the passive goal of avoiding capture. Finally, some examples from a lifeline game involving more than one pursuer are used to verify the effectiveness and scalability of the evasion strategies.     

Multiple capture in Pontryagin’s almost periodic example

This paper considers Pontryagin’s generalized nonstationary example with several participants under the same dynamic and inertial capabilities of the players, in which the set of admissible control actions is a convex compact set and the terminal sets are convex compact sets. We obtain sufficient conditions for the multiple capture of one evader by a group of pursuers under the assumption that some functions associated with the initial data and game parameters are almost periodic. Each pursuer cannot make a capture more than once before being eliminated from the game. Such a situation may happen when the evader must be “terminated” but contact between the pursuer and the evader does not guarantee termination.     

A cooperative pursuit-evasion game in wireless sensor and actor networks

This paper studies the problem of the pursuit-evasion game under the wireless sensor and actor networks (WSANs). In order to plan paths for pursuers to capture an evader in the pursuit-evasion game, a novel multi-step cooperative strategy is presented. Under this strategy, the pursuit-evasion game is studied in two stages. In the first stage we assume that the evader is always static in the workplace, and in the second stage the evader will move once it senses the existence of pursuers. A Daisy-Chain Formation algorithm and a sliding mode-based method are presented to control the pursuit. Based on Lyapunov stability theory, the proposed algorithm is proved to be convergent. At last, simulation results are provided to demonstrate the effectiveness of the proposed method.     

Cooperative Multiple Pursuers against a Single Evader

This paper considers a pursuit-evasion game for non-holonomic systems where a group of pursuers attempts to capture an evader in a bounded connected domain. The problem is challenging because all vehicles have the same maneuvering capability in terms of speed and turn radius constraint. The paper initially discusses a simple approach for holonomic systems that is based on the minimization of the safe-reachable area (the area containing the set of points to where an evader can travel without being caught). This idea is then extended to develop a pursuit-evasion strategy for non-holonomic systems. However, solving such a problem is computationally intractable. Therefore, we propose a computationally efficient algorithm to obtain approximate solutions. This paper also proposes an alternative approach to obtain a simple yet effective solution to the cooperative pursuit problem that is based on missile guidance laws. As there is no analytical proof of capture, we empirically evaluate the performance of the algorithms and perform a comparative study using solutions obtained from umpteen simulations. A total of four different cooperative pursuit strategies and three different evader strategies are taken into account for the comparative study. In the process, an evader strategy which is superior to that based on the optimization of safe-reachable area is also identified.     

Relay pursuit of a maneuvering target using dynamic Voronoi diagrams

This paper addresses the problem of the pursuit of a maneuvering target by a group of pursuers distributed in the plane. This pursuit problem is solved by associating it with a Voronoi-like partitioning problem that characterizes the set of initial positions from which the target can be intercepted by a given pursuer faster than any other pursuer from the same group. In the formulation of this partitioning problem, the target does not necessarily travel along prescribed trajectories, as it is typically assumed in the literature, but, instead, it can apply an “evading” strategy in an effort to delay or, if possible, escape capture. We characterize an approximate solution to this problem by associating it with a standard Voronoi partitioning problem. Subsequently, we propose a relay pursuit strategy, that is, a special group pursuit scheme such that, at each instant of time, only one pursuer is assigned the task of capturing the maneuvering target. During the course of the relay pursuit, the pursuer–target assignment changes dynamically with time based on the (time varying) proximity relations between the pursuers and the target. This proximity information is encoded in the solution of the Voronoi-like partitioning problem. Simulation results are presented to highlight the theoretical developments.     

Scalable and practical pursuit-evasion with networked robots

In this paper, we consider the design and implementation of practical pursuit-evasion games with networked robots, where a communication network provides sensing-at-a-distance as well as a communication backbone that enables tighter coordination between pursuers. We first develop, using the theory of zero-sum games, an algorithm that computes the minimal completion time strategy for pursuit-evasion when pursuers and evaders have same speed, and when all players make optimal decisions based on complete knowledge. Then, we extend this algorithm to when evader are significantly faster than pursuers. Unfortunately, these algorithms do not scale beyond a small number of robots. To overcome this problem, we design and implement a partition algorithm where pursuers capture evaders by decomposing the game into multiple multi-pursuer single-evader games. We show that the partition algorithm terminates, has bounded capture time, is robust, and is scalable in the number of robots. We then describe the design of a real-world mobile robot-based pursuit evasion game. We validate our algorithms by experiments in a moderate-scale testbed in a challenging office environment. Overall, our work illustrates an innovative interplay between robotics and communication.     

复杂三维多面体环境中空地协作追逃问题

结合无人机(UAV)的空中移动和无人车(UGV)的地面移动特点,本文提出了一种UAV/UGV空地协作系统,并且针对其在复杂地形中的追逃问题,提出了一种复杂三维多面体环境中UAV/UGV空地协作追逃策略.首先介绍了UAV/UGV空地协作系统的结构与协作追逃问题描述.接着将边界值问题(BVP)改进并离散化作为博弈走法生成器.然后,针对逃方已知追方位置,而追方只具备直线视野(LOS)的不利条件,分析了最坏情况.逃方策略在保证最大生存条件下尽可能获得博弈胜利.追方策略根据逃方状态分成3种情况进行讨论:逃方处于追方的视野范围内、逃方刚刚消失于追方视野以及追方完全丢失逃方的情况.最后,对比仿真结果说明了本文算法的有效性,并分析了追逃结果的影响因素.由于地形是非凸的并且充满障碍,因此该策略虽不能保证追方一定能够胜利,但在最坏情况下是最优的.     

The problem of optimal approach in locally Euclidean spaces

A differential game of optimal approach with simple motions when players move in locally Euclidean spaces is studied. The game-end moment is fixed, and the game payment is a distance between the pursuer and the evader at the game-end moment. The value of game is obtained in the explicit form for any initial positions of players. Moreover, the differential game of optimal approach for the denumerable number of pursuers and one evader in the Euclidean space is solved. All pursuers are controlled by one parameter.     

Control of antagonistic swarm dynamics via Lyapunov's method

We consider hostile conflicts between two multi‐agent swarms. First, we investigate the complex nature of a single pursuer attempting to intercept a single evader (1P‐1E), and establish some rudimentary rules of engagement. We elaborate on the stability repercussions of these rules. Second, we extend the modelling and stability analysis to multi‐agent swarms with conflicting interests. The present document considers only swarms with equal membership strengths for simplicity. This effort is based on a set of suggested momenta deployed on individual agents. Because pursuers and evaders differ in the influences that they exert on one another, we emphasize asymmetry in momenta between the two types of swarm members. The proposed centralized control law evolves from a Lyapunov concept. Swarm interactions are modelled in two phases: the approach phase during which the two swarms act like individuals in the 1P‐1E interaction; and the individual pursuit phase where each pursuer is assigned to an evader. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A Mixed Integer Linear Programming approach to pursuit evasion problems with optional connectivity constraints

In this paper, we address the multi pursuer version of the pursuit evasion problem in polygonal environments. By discretizing the problem, and applying a Mixed Integer Linear Programming (MILP) framework, we are able to address problems requiring so-called recontamination and also impose additional constraints, such as connectivity between the pursuers. The proposed MILP formulation is less conservative than solutions based on graph discretizations of the environment, but still somewhat more conservative than the original underlying problem. It is well known that MILPs, as well as multi pursuer pursuit evasion problems, are NP-hard. Therefore we apply an iterative Receding Horizon Control (RHC) scheme where a number of smaller MILPs are solved over shorter planning horizons. The proposed approach is implemented in Matlab/Cplex and illustrated by a number of solved examples.     

To a nonstationary group pursuit problem with phase constraints

We consider two linear nonstationary pursuit-evasion problems with one evader and a group of pursuers under the conditions that the players have equal dynamic abilities and that the evader cannot leave a certain set. We prove that if the number of pursuers is less than the space dimension, then the evader can avoid capture in the interval [t ₀,∞).     

Simple Group Pursuit Subject to Phase Constraints and Data Delay

The problem of the simple pursuit of a single evader by a group of pursuers subject to phase constraints is considered. It is assumed that the pursuers receive information about the evader’s control and affect the control system with a time delay. Sufficient conditions for the solvability of the pursuit problem are obtained.     

Anticipated velocity based guidance strategy for wheeled mobile evader amidst stationary and moving obstacles in bounded environment

This paper is concerned with a class of pursuit‐evasion game problems amidst stationary and moving obstacles in a bounded environment. We concentrate on evader's strategy taking into account the following challenges: (i) pursuer and evader are nonholonomic wheeled mobile robots and the evader is slower than the pursuer; (ii) pursuer follows a proportional navigation law; and (iii) geometry of the environment is not known to the players, a priori. We propose an efficient evader‐centric anticipated velocity based guidance strategy. Pursuer's trajectory is anticipated at each step by the evader using quadratic polynomial interpolation. The aim of the evader is to escape interception with the pursuer for maximum possible time. To deal with static obstacles, a technique based on a well‐known tangent bug algorithm is presented. While dealing with dynamic obstacles, a recently introduced reciprocal orientation method is employed to avoid collision in situations when the dynamic obstacle also cooperates in the process. In case dynamic obstacles do not participate in the process of collision avoidance, a well‐known velocity obstacle method is employed for planning safe collision‐free paths. Efficiency of the proposed algorithms is analyzed with respect to the interception time and the distance traveled by the players. Copyright © 2014 John Wiley & Sons, Ltd.     

Pursuit evasion game with costly information

In this paper we study a pursuit evasion game in which information is costly. The pursuer has to pay, i.e. lose some time, whenever he wants information on the evader's position. Therefore the capture will be done in successive stages. The pursuer gets information, then moves using an open loop control, and so on. We characterize the setC ₁ of the initial states that the pursuer can capture in one stage whatever the evader does. This set is taken as a new target for an other stage. In this way we characterize the setC _n of the initial states the pursuer can capture inn stages in the worst case. We also give a pursuer's strategy that minimizes the total duration of the game, as opposed to the number of stages.This research has been supported in part by the French Direction des Recherches et Etudes Techniques (DRET).