scholarly journals DIFFERENTIAL GAME WITH A LIFELINE FOR THE INERTIAL MOVEMENTS OF PLAYERS

2021 ◽  
Vol 7 (2) ◽  
pp. 94
Author(s):  
Bahrom T. Samatov ◽  
Ulmasjon B. Soyibboev
Keyword(s):  
Euclidean Space ◽  
Differential Game ◽  
Pursuit Problem ◽  
Solvability Conditions ◽  
Pursuit Evasion ◽  
Attainability Domain ◽  
Evasion Problem ◽  
Pursuit Strategy

In this paper, we study the well-known problem of Isaacs called the "Life line" game when movements of players occur by acceleration vectors, that is, by inertia in Euclidean space. To solve this problem, we investigate the dynamics of the attainability domain of an evader through finding solvability conditions of the pursuit-evasion problems in favor of a pursuer or an evader. Here a pursuit problem is solved by a parallel pursuit strategy. To solve an evasion problem, we propose a strategy for the evader and show that the evasion is possible from given initial positions of players. Note that this work develops and continues studies of Isaacs, Petrosjan, Pshenichnii, Azamov, and others performed for the case of players' movements without inertia.

Minmax fuzzy deterministic policy gradient for zero-sum differential game: Take pursuit-evasion problem as example

2021 ◽  
pp. 1-14
Author(s):  
Wei Liao ◽  
Xiaohui Wei ◽  
Jizhou Lai
Keyword(s):  
Differential Game ◽  
Fuzzy Inference ◽  
Q Value ◽  
Inference System ◽  
State Action ◽  
Pursuit Evasion ◽  
Novel Structure ◽  
Policy Gradient ◽  
Evasion Problem ◽  
Zero Sum

A novel actor-critic algorithm is introduced and applied to zero-sum differential game. The proposed novel structure consists of two actors and a critic. Different actors represent the control policies of different players, and the critic is used to approximate the state-action utility function. Instead of neural network, the fuzzy inference system is applied as approximators for the actors and critic so that the specific practical meaning can be represented by the linguistic fuzzy rules. Since the goals of the players in the game are completely opposite, the actors for different players are simultaneously updated in opposite directions during the training. One actor is updated updated toward the direction that can minimize the Q value while the other updated toward the direction that can maximize the Q value. A pursuit-evasion problem with two pursuers and one evader is taken as an example to illustrate the validity of our method. In this problem, the two pursuers the same actor and the symmetry in the problem is used to improve the replay buffer. At the end of this paper, some confrontations between the policies with different training episodes are conducted.

SOLUTION OF SIMPLE PURSUIT-EVASION PROBLEM WHEN EVADER MOVES ON A GIVEN CURVE

2010 ◽  
Vol 12 (03) ◽  
pp. 223-238 ◽  
Author(s):  
ATAMURAT SH. KUCHKAROV
Keyword(s):  
Differential Game ◽  
Sufficient Conditions ◽  
Initial Position ◽  
Necessary And Sufficient Conditions ◽  
Phase Constraint ◽  
Simple Motion ◽  
Pursuit Evasion ◽  
Evasion Problem ◽  
Necessary And Sufficient

We investigate a simple motion pursuit-evasion differential game of one Pursuer and one Evader. Maximal speeds of the players are equal. The Evader moves along a given curve without self-intersection. There is no phase constraint for the Pursuer. Necessary and sufficient conditions to complete pursuit from both fixed initial position and all initial positions are obtained.

scholarly journals PURSUIT AND EVASION DIFFERENTIAL GAMES IN HILBERT SPACE

2010 ◽  
Vol 12 (03) ◽  
pp. 239-251 ◽  
Author(s):  
GAFURJAN I. IBRAGIMOV ◽  
RISMAN MAT HASIM
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Differential Games ◽  
Differential Game ◽  
Infinite System ◽  
System Of Differential Equations ◽  
Pursuit Problem ◽  
Pursuit And Evasion ◽  
Evasion Problem ◽  
Total Resource

We consider pursuit and evasion differential game problems described by an infinite system of differential equations with countably many Pursuers in Hilbert space. Integral constraints are imposed on the controls of players. In this paper an attempt has been made to solve an evasion problem under the condition that the total resource of the Pursuers is less then that of the Evader and a pursuit problem when the total resource of the Pursuers greater than that of the Evader. The strategy of the Evader is constructed.

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 A VISIBILITY-BASED PURSUIT-EVASION PROBLEM

1999 ◽  
Vol 09 (04n05) ◽  
pp. 471-493 ◽  
Author(s):  
LEONIDAS J. GUIBAS ◽  
JEAN-CLAUDE LATOMBE ◽  
STEVEN M. LAVALLE ◽  
DAVID LIN ◽  
RAJEEV MOTWANI
Keyword(s):  
Finite Graph ◽  
Initial Position ◽  
Moving Target ◽  
Multiply Connected ◽  
Pursuit Evasion ◽  
Minimum Number ◽  
Evasion Problem ◽  
Free Spaces ◽  
Simply Connected ◽  
Motion Strategy

This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually "see" an evader that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. This problem was first introduced by Suzuki and Yamashita. Our study of this problem is motivated in part by robotics applications, such as surveillance with a mobile robot equipped with a camera that must find a moving target in a cluttered workspace. A few bounds are introduced, and a complete algorithm is presented for computing a successful motion strategy for a single pursuer. For simply-connected free spaces, it is shown that the minimum number of pursuers required is Θ( lg  n). For multiply-connected free spaces, the bound is [Formula: see text] pursuers for a polygon that has n edges and h holes. A set of problems that are solvable by a single pursuer and require a linear number of recontaminations is shown. The complete algorithm searches a finite graph that is constructed on the basis of critical information changes. It has been implemented and computed examples are shown.

Collaboration Strategy Simulation of Multi-Agents for Pursuit-Evasion in Wireless Sensor Networks

2010 ◽  
Vol 29-32 ◽  
pp. 2238-2242
Author(s):  
Li Xin Guo ◽  
Lei Ping Zhao
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Wireless Sensor ◽  
Field Boundary ◽  
Pursuit Evasion ◽  
Continuous Map ◽  
Evasion Strategy ◽  
Statistical Results ◽  
Pursuit Strategy ◽  
Multi Agents

In this study, we used Cricket equipments based on wireless sensor networks to study the pursuit-evasion strategy of multi-robots in a continuous map. In order to improve the efficiency, two new pursuit-evasion strategies were proposed. To meet the need of a continuous map, a greedy algorithm was utilized to deal with boundary problem when a pursuer or an evader was near the field boundary. The statistical results show the converging-attack pursuit strategy outperforms in pursuing the evader with different escaping strategies, such as randomly moving, active escaping strategy and vector-wards escaping strategy. The vector-wards escaping strategy is also effective in delaying the capture of evaders.

scholarly journals On pursuit-evasion differential game problem in a Hilbert space

2020 ◽  
Vol 5 (6) ◽  
pp. 7467-7479
Author(s):  
Jamilu Adamu ◽  
◽  
Kanikar Muangchoo ◽  
Abbas Ja’afaru Badakaya ◽  
Jewaidu Rilwan ◽  
...  
Keyword(s):  
Hilbert Space ◽  
Differential Game ◽  
Game Problem ◽  
Pursuit Evasion

scholarly journals Two-Stage Pursuit Strategy for Incomplete-Information Impulsive Space Pursuit-Evasion Mission Using Reinforcement Learning

Aerospace ◽  
2021 ◽  
Vol 8 (10) ◽  
pp. 299
Author(s):  
Bin Yang ◽  
Pengxuan Liu ◽  
Jinglang Feng ◽  
Shuang Li
Keyword(s):  
Reinforcement Learning ◽  
Incomplete Information ◽  
Trajectory Optimization ◽  
Game Problem ◽  
Gradient Algorithm ◽  
Two Stage ◽  
Pursuit Evasion ◽  
Evasion Game ◽  
Close Distance ◽  
Pursuit Strategy

This paper presents a novel and robust two-stage pursuit strategy for the incomplete-information impulsive space pursuit-evasion missions considering the J2 perturbation. The strategy firstly models the impulsive pursuit-evasion game problem into a far-distance rendezvous stage and a close-distance game stage according to the perception range of the evader. For the far-distance rendezvous stage, it is transformed into a rendezvous trajectory optimization problem and a new objective function is proposed to obtain the pursuit trajectory with the optimal terminal pursuit capability. For the close-distance game stage, a closed-loop pursuit approach is proposed using one of the reinforcement learning algorithms, i.e., the deep deterministic policy gradient algorithm, to solve and update the pursuit trajectory for the incomplete-information impulsive pursuit-evasion missions. The feasibility of this novel strategy and its robustness to different initial states of the pursuer and evader and to the evasion strategies are demonstrated for the sun-synchronous orbit pursuit-evasion game scenarios. The results of the Monte Carlo tests show that the successful pursuit ratio of the proposed method is over 91% for all the given scenarios.

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