Construction of Barrier in a Three-Player Pursuit-Evasion Game

2016 ◽  
Vol 04 (01) ◽  
pp. 41-49 ◽  
Author(s):  
Xinxing Li ◽  
Zhihong Peng ◽  
Wenzhong Zha ◽  
Jie Chen
Keyword(s):  
Explicit Form ◽  
Optimal Strategies ◽  
The State ◽  
Capture Zone ◽  
Pursuit Evasion ◽  
Evasion Game ◽  
Target Set ◽  
Turning Radius ◽  
Minimum Turning Radius

This paper addresses a particular pursuit-evasion game with two pursuers with slower speed but smaller minimum turning radius and a faster evader with bigger minimum turning radius. This is a game of kind, and what interests us is how to construct the barrier that separates the state zone into capture zone and escape zone, and what the optimal strategies for the players are on the barrier. Under some mild assumptions, we give the explicit form of the barrier near the BUP (i.e., the boundary of the usable part on the boundary of the target set) by using Isaacs’ method, and a procedure to construct the barrier when the retrogressive time is big enough by determining the optimal strategies for the players on the BUP. Then we prove that the optimal strategies remain unchanged near some special parts on the BUP, and we give two examples to illustrate these situations.

scholarly journals A Stochastic Characterization of the Capture Zone in Pursuit-Evasion Games

Games ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 54
Author(s):  
Simone Battistini
Keyword(s):  
Optimal Strategies ◽  
Capture Zone ◽  
Pursuit Evasion ◽  
Guidance Strategies ◽  
Stochastic Characterization ◽  
Evasion Game ◽  
Multi Agent ◽  
Planning Problems ◽  
Insight Into

Pursuit-evasion games are used to define guidance strategies for multi-agent planning problems. Although optimal strategies exist for deterministic scenarios, in the case when information about the opponent players is imperfect, it is important to evaluate the effect of uncertainties on the estimated variables. This paper proposes a method to characterize the game space of a pursuit-evasion game under a stochastic perspective. The Mahalanobis distance is used as a metric to determine the levels of confidence in the estimation of the Zero Effort Miss across the capture zone. This information can be used to gain an insight into the guidance strategy. A simulation is carried out to provide numerical results.

scholarly journals A Simplified Pursuit-evasion Game with Reinforcement Learning

2021 ◽  
Vol 65 (2) ◽  
pp. 160-166
Author(s):  
Gabor Paczolay ◽  
Istvan Harmati
Keyword(s):  
Linear Programming ◽  
Reinforcement Learning ◽  
Programming Problem ◽  
Collision Avoidance ◽  
Linear Programming Problem ◽  
The State ◽  
State Information ◽  
Pursuit Evasion ◽  
Pursuit And Evasion ◽  
Evasion Game

In this paper we visit the problem of pursuit and evasion and specifically, the collision avoidance during the problem. Two distinct tasks are visited: the first is a scenario when the agents can communicate with each other online, meanwhile in the second scenario they have to only rely on the state information and the knowledge about other agents' actions. We propose a method combining the already existing Minimax-Q and Nash-Q algorithms to provide a solution that can better take the enemy as well as friendly agents' actions into consideration. This combination is a simple weighting of the two algorithms with the Minimax-Q algorithm being based on a linear programming problem.

scholarly journals PURSUIT-EVASION DIFFERENTIAL GAMES WITH THE GRÖNWALL TYPE CONSTRAINTS ON CONTROLS

2020 ◽  
Vol 6 (2) ◽  
pp. 95
Author(s):  
Bahrom T. Samatov ◽  
Gafurjan Ibragimov ◽  
Iroda V. Khodjibayeva
Keyword(s):  
Differential Games ◽  
Differential Game ◽  
Optimal Strategy ◽  
Optimal Strategies ◽  
The State ◽  
Differential Constraints ◽  
Quality Problem ◽  
Pursuit Evasion ◽  
Optimal Pursuit ◽  
Pursuit Strategy

A simple pursuit-evasion differential game of one pursuer and one evader is studied. The players' controls are subject to differential constraints in the form of the integral Grönwall inequality. The pursuit is considered completed if the state of the pursuer coincides with the state of the evader. The main goal of this work is to construct optimal strategies for the players and find the optimal pursuit time. A parallel approach strategy for Grönwall-type constraints is constructed and it is proved that it is the optimal strategy of the pursuer. In addition, the optimal strategy of the evader is constructed and the optimal pursuit time is obtained. The concept of a parallel pursuit strategy (\(\Pi\)-strategy for short) was introduced and used to solve the quality problem for "life-line" games by L.A.Petrosjan. This work develops and expands the works of Isaacs, Petrosjan, Pshenichnyi, and other researchers, including the authors.

scholarly journals Predictive pursuit-evasion game control method for approaching space non-cooperative target

2020 ◽  
Vol 53 (2) ◽  
pp. 14882-14887
Author(s):  
Yuan Chai ◽  
Jianjun Luo ◽  
Mingming Wang ◽  
Min Yu
Keyword(s):  
Control Method ◽  
Pursuit Evasion ◽  
Evasion Game

scholarly journals Collaborative Pursuit-Evasion Strategy of UAV/UGV Heterogeneous System in Complex Three-Dimensional Polygonal Environment

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Xiao Liang ◽  
Honglun Wang ◽  
Haitao Luo
Keyword(s):  
Visual Field ◽  
Heterogeneous System ◽  
Three Dimensional ◽  
Unmanned Ground Vehicle ◽  
Worst Case ◽  
Ground Vehicle ◽  
Pursuit Evasion ◽  
Evasion Game ◽  
Evasion Strategy ◽  
Aerial Vehicle

The UAV/UGV heterogeneous system combines the air superiority of UAV (unmanned aerial vehicle) and the ground superiority of UGV (unmanned ground vehicle). The system can complete a series of complex tasks and one of them is pursuit-evasion decision, so a collaborative strategy of UAV/UGV heterogeneous system is proposed to derive a pursuit-evasion game in complex three-dimensional (3D) polygonal environment, which is large enough but with boundary. Firstly, the system and task hypothesis are introduced. Then, an improved boundary value problem (BVP) is used to unify the terrain data of decision and path planning. Under the condition that the evader knows the position of collaborative pursuers at any time but pursuers just have a line-of-sight view, a worst case is analyzed and the strategy between the evader and pursuers is studied. According to the state of evader, the strategy of collaborative pursuers is discussed in three situations: evader is in the visual field of pursuers, evader just disappears from the visual field of pursuers, and the position of evader is completely unknown to pursuers. The simulation results show that the strategy does not guarantee that the pursuers will win the game in complex 3D polygonal environment, but it is optimal in the worst case.

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