Pursuit-evasion Game Research Articles

Towards the design of an intelligent aerospace pursuit-evasion game

Towards the design of an intelligent aerospace pursuit-evasion game

Nonlinear Control for Spacecraft Pursuit-Evasion Game Using the State-Dependent Riccati Equation Method

Spacecraft pursuit-evasion game is formulated as a two-player zero-sum differential game. The Hill reference frame is used to describe the dynamics of the game. The goal is to derive feedback control law which forms a saddle point solution to the game. Both spacecraft use continuous-thrust engines. The linear quadratic differential game theory is applied to derive a linear control law. This theory is extended to derive a nonlinear control law using the state-dependent Riccati equation method. A state-dependent coefficient matrix is developed for this purpose. Various scenarios are considered for comparing the performance of the linear and nonlinear laws. In all the scenarios, the efficacy of the nonlinear control law is found to be superior to that of the linear control law with computation cost similar to the linear law.

Mayer control problem with probabilistic uncertainty on initial positions

In this paper we introduce and study an optimal control problem in the Mayer's form in the space of probability measures on Rn endowed with the Wasserstein distance. Our aim is to study optimality conditions when the knowledge of the initial state and velocity is subject to some uncertainty, which are modeled by a probability measure on Rd and by a vector-valued measure on Rd, respectively. We provide a characterization of the value function of such a problem as unique solution of an Hamilton–Jacobi–Bellman equation in the space of measures in a suitable viscosity sense. Some applications to a pursuit-evasion game with uncertainty in the state space is also discussed, proving the existence of a value for the game.

Mobile agents path planning based on an extension of Bug-Algorithms and applied to the pursuit-evasion game

Mobile agents path planning based on an extension of Bug-Algorithms and applied to the pursuit-evasion game

Fractional Calculus Guidance Algorithm in a Hypersonic Pursuit-Evasion Game

<p class="p1">Aiming at intercepting a hypersonic weapon in a hypersonic pursuit-evasion game, this paper presents a fractional calculus guidance algorithm based on a nonlinear proportional and differential guidance law. First, under the premise of without increasing the complexity degree of the guidance system against a hypersonic manoeuvering target, the principle that the differential signal of the line-of-sight rate is more sensitive to the target manoeuver than the line-of-sight rate is employed as the guidelines to design the guidance law. A nonlinear proportional and differential guidance law (NPDG) is designed by using the differential derivative of the line-of-sight rate from a nonlinear tracking differentiator. By using the differential definition of fractional calculus, on the basis of the NPDG, a fractional calculus guidance law (FCG) is proposed. According to relative motions between the interceptor and target, the guidance system stability condition with the FCG is given and quantitative values are also proposed for the parameters of the FCG. Under different target manoeuver conditions and noisy conditions, the interception accuracy and robustness of these two guidance laws are analysed. Numerical experimental results demonstrate that the proposed guidance algorithms effectively reduce the miss distance against target manoeuvers. Compared with the NPDG, a stronger robustness of the FCG is shown under noisy condition.</p>

Pursuit-evasion game of many players with coordinate-wise integral constraints on a convex set in the plane

We study a differential game of many pursuers and one evader in the plane. It is assumed that the pursuers and evader move is allowed within a non empty closed convex set in the plane. Control functions of players are subject to coordinate-wise integral constraints. The game is over when the state of the evader y coincides with that of a pursuer x i , i = {1, ... , m } at given time t i (unspecified), i.e. , x i ( t i ) = y ( t i ). We obtain conditions under which the game is over in finite time, no matter where the players start from. Moreover, we construct winning for the pursuers.

An Introduction to Lazy Cops and Robbers on Graphs

SummaryCops and Robbers is a classic pursuit—evasion game played on graphs. A new variant, Lazy Cops and Robbers, allows only one cop to move at a time, making the game’s mechanics more akin to chess. We investigate and describe a few examples, showing that on some graphs lazy cops can be as effective as ordinary cops, but on other graphs they are not (and sometimes they are much worse). Some examples are based on the cops and robber moving like particular chess pieces. We also mention related results and pose some open problems.

The capture time of a planar graph

This paper examines the capture time of a planar graph in a variant of the pursuit-evasion games, called cops and robbers game. Since any planar graph is 3-cop-win, we study the capture time of a planar graph G of n vertices using three cops, which is denoted by $$capt_3(G)$$ . We present a new capture strategy and show that $$capt_3(G) \le 2n$$ . This is the first result on $$capt_3(G)$$ .

On a Characterization of Evasion Strategies for Pursuit-Evasion Games on Graphs

We give a characterization of robber-win strategies for general pursuit-evasion games with one evader and any finite number of pursuers on a finite graph. We also give an algorithm that solves robber-win games.

A Two-on-One Linear Pursuit–Evasion Game with Bounded Controls

A linearized engagement with two pursuers versus a single evader is considered, in which the adversaries’ controls are bounded and have first-order dynamics and the pursuers’ intercept times are equal. Wishing to formulate the engagement as a zero-sum differential game, a suitable cost function is proposed and validated, and the resulting optimization problem and its solution are presented. Construction and analysis of the game space is shown, and the players’ closed-form optimal controls are derived for the case of two “strong” pursuers. The results are compared to those of a 1-on-1 engagement with a “strong” pursuer, and it is shown that the addition of a second pursuer enlarges the capture zone and introduces a new singular zone to the game space, in which the pursuers can guarantee equal misses, regardless of the evader’s actions. Additionally, it is concluded that in the regular zones the closed-form optimal pursuit strategies are unchanged compared to two 1-on-1 engagements, whereas the optimal evasion strategy is more complex. Several simulations are performed, illustrating the adversaries’ behavior in different regions of the game space.

Visibility graphs, dismantlability, and the cops and robbers game

We study versions of cop and robber pursuit–evasion games on the visibility graphs of polygons, and inside polygons with straight and curved sides. Each player has full information about the other player's location, players take turns, and the robber is captured when the cop arrives at the same point as the robber. In visibility graphs we show the cop can always win because visibility graphs are dismantlable, which is interesting as one of the few results relating visibility graphs to other known graph classes. We extend this to show that the cop wins games in which players move along straight line segments inside any polygon and, more generally, inside any simply connected planar region with a reasonable boundary. Essentially, our problem is a type of pursuit–evasion using the link metric rather than the Euclidean metric, and our result provides an interesting class of infinite cop-win graphs.

A Comprehensive Differential Game Theoretic Solution to a Game of Two Cars

In this paper, a pursuit-evasion game involving two non-holonomic agents is examined using the theory of differential games. It is assumed that the two players move on the Euclidean plane with fixed but different speeds and they each have a lower bound on their achievable turn radii. Both players steer at each instant by choosing their turn radii value and directions of turn. By formulating the game as a game of kind, we characterize the regions of initial conditions that lead to capture as well as the regions that lead to evasion, when both the players play optimally. The game is then formulated as a game of degree to obtain time-optimal paths for the pursuer and evader inside a capture region. Besides, all possible scenarios are considered for both players that differ in speed ratios and maneuverability constraints. Solutions are provided for those cases using appropriate simulation parameters, which aid in understanding the characteristics of the game of two cars under a wide range of constraints.

A Model-Based Approach to Optimizing Ms. Pac-Man Game Strategies in Real Time

This paper presents a model-based approach for computing real-time optimal decision strategies in the pursuit-evasion game of Ms. Pac-Man. The game of Ms. Pac-Man is an excellent benchmark problem of pursuit-evasion game with multiple, active adversaries that adapt their pursuit policies based on Ms. Pac-Man's state and decisions. In addition to evading the adversaries, the agent must pursue multiple fixed and moving targets in an obstacle-populated environment. This paper presents a novel approach by which a decision-tree representation of all possible strategies is derived from the maze geometry and the dynamic equations of the adversaries or ghosts. The proposed models of ghost dynamics and decisions are validated through extensive numerical simulations. During the game, the decision tree is updated and used to determine optimal strategies in real time based on state estimates and game predictions obtained iteratively over time. The results show that the artificial player obtained by this approach is able to achieve high game scores, and to handle high game levels in which the characters speeds and maze complexity become challenging even for human players.

Formation Control and Obstacle Avoidance for Multi-Agent Systems Based on Virtual Leader-Follower Strategy

This paper investigates the formation control and obstacle avoidance problem for multi-agent systems (MASs), which aims to coordinate the pursuer agents to capture a mobile target. The target appears at a location randomly and its movement obeys Reactive Rabbit Model. The pursuers and the mobile target can be modeled as a Pursuit-Evasion Game (PEG). During the movement, not all of the pursuer agents can obtain the real-time information of the target. Moreover, the obstacle avoidance makes the formation of pursuer agents a big challenge to encircle the mobile target. In order to tackle these two problems, the formation control and obstacle avoidance algorithm is presented in this paper based on a novel virtual leader-follower strategy and potential functions. The obstacle avoidance problem can then be solved by constructing a velocity potential. The numerical analysis and simulation demonstrate the effectiveness of the proposed algorithm.

Pursuit-evasion games: a tractable framework for antijamming games in aerial attacks

We solve a communication problem between a UAV and a set of receivers, in the presence of a jamming UAV, using differential game theory tools. We propose a new approach in which this kind of games can be approximated as pursuit-evasion games. The problem is posed in terms of optimizing capacity, and it is solved in two ways: firstly, a surrogate function approach is used to approximate it as a pursuit-evasion game; secondly, the game is solved without that approximation. In both cases, Isaacs equations are used to find the solution. Finally, both approaches are compared in terms of relative distance and complexity.

Multiple-Pursuer/One-Evader Pursuit–Evasion Game in Dynamic Flowfields

In this paper, a reachability-based approach is adopted to deal with the pursuit–evasion differential game between one evader and multiple pursuers in the presence of dynamic environmental disturbances (for example, winds or sea currents). Conditions for the game to be terminated are given in terms of reachable set inclusions. Level set equations are defined and solved to generate the forward reachable sets of the pursuers and the evader. The time-optimal trajectories and the corresponding optimal strategies are subsequently retrieved from these level sets. The pursuers are divided into active pursuers, guards, and redundant pursuers according to their respective roles in the pursuit–evasion game. The proposed scheme is implemented on problems with both simple and realistic time-dependent flowfields, with and without obstacles.

The pursuit-evasion game on the 1-skeleton graph of a regular polyhedron. I

We consider a game between a group of n pursuers and one evader moving with the same maximum velocity along the 1-skeleton graph of a regular polyhedron. The goal of the paper is finding, for each regular polyhedron M, a number N(M) with the following properties: if n ź N(M), the group of pursuers wins, while if n

Pursuit-evasion in a two-dimensional domain

In a pursuit-evasion game, a team of pursuers attempt to capture an evader. The players alternate turns, move with equal speed, and have full information about the state of the game. We consider the most restrictive capture condition: a pursuer must become colocated with the evader to win the game. We prove two general results about this adversarial motion planning problem in geometric spaces. First, we show that one pursuer has a winning strategy in any compact CAT(0) space. This complements a result of Alexander, Bishop and Ghrist, who provide a winning strategy for a game with positive capture radius. Second, we consider the game played in a compact domain in Euclidean two-space with piecewise analytic boundary and arbitrary Euler characteristic. We show that three pursuers always have a winning strategy by extending recent work of Bhadauria, Klein, Isler and Suri from polygonal environments to our more general setting.

Revisiting the two-side optimization problem in satellite pursuit-evasion

In the present paper two-side optimization problem where the intercepting satellite pursuits the target satellite was studied. In the pursuit-evasion game the continuous thruster and the simple central gravity with J2 perturbation were involved for two satellites. With applying the functional extremum condition, the optimal control outputs of both side satellites were obtained by building the systems Hamilton function. Further, the two side optimal problem was transformed to the TPBVP, which contributed the solution with the mixed numerical method. Finally, the proposed method was validated by the numerical simulation, where the optimal interception and escaping trajectories were illustrated.

Positive Alexander Duality for Pursuit and Evasion

Considered is a class of pursuit-evasion games, in which an evader tries to avoid detection. Such games can be formulated as the search for sections to the complement of a coverage region in a Euclidean space over time. Prior results give homological criteria for evasion in the general case that are not necessary and sufficient. This paper provides a necessary and sufficient positive cohomological criterion for evasion in the general case. The principal tools are (1) a refinement of the Cech cohomology of a coverage region with a positive cone encoding spatial orientation, (2) a refinement of the Borel--Moore homology of the coverage gaps with a positive cone encoding time orientation, and (3) a positive variant of Alexander Duality. Positive cohomology decomposes as the global sections of a sheaf of local positive cohomology over the time axis; we show how this decomposition makes positive cohomology computable using techniques of computational polyhedral geometry and linear programming.