Feedback Strategies for a Reach-Avoid Game With a Single Evader and Multiple Pursuers

Jayakumar, S.; Bakolas, Efstathios

doi:10.1109/tcyb.2019.2914869

Cited by 53 publications

(23 citation statements)

References 22 publications

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“…Definition 1 (Apollonius Circle): For 0 < γ < 1 and any given pair of points (x P , x E ) ∈ R 4 , where x P = (x P , y P ) ∈ R 2 and x E = (x E , y E ) ∈ R 2 , the Apollonius circle between x P and x E , which is denoted as A(x P , x E ; γ), is defined as the set of points z ∈ R 2 that satisfy z − x E = γ z − x P , that is, (14) where the center function C : R 4 → R 2 and the radius function R : R 4 → R are respectively given by…”

Section: Game Of Kindmentioning

confidence: 99%

“…In [11]- [13], the authors show that in fact the classical differential game approach is still applicable in the multiplayer border-defense games. The case when the differential game approach is not applicable due to information asymmetry (i.e., the pursuers are aware of neither the location of the target area nor the evader's optimal strategies) was discussed in [14].…”

Section: Introductionmentioning

confidence: 99%

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Optimal Strategies for Guarding a Compact and Convex Target Set: A Differential Game Approach

Lee,

Bakolas

2021

Preprint

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We revisit the two-player planar target-defense game posed in [1], a special class of pursuit-evasion games in which the pursuer (or defender) strives to defend a stationary target area from the evader (or intruder) who desires to reach it, if possible, or approach it as close as possible. In this paper, the target area is assumed to be a compact and convex set. Unlike classical two-player pursuit-evasion games, this game involves two subgames: a capture game and an escape game. In the capture game, where capture is assured, the evader attempts to minimize the distance between her final position and the target area whereas the pursuer tries to maximize the same distance. In the escape game, where capture is not guaranteed, the evader attempts to maximize the distance between herself and the pursuer at the moment that she reaches the target for the first time. Our solution approach is based on Isaacs classical method in differential games. We first identify the barrier surface that demarcates the state space of the game into two subspaces, each of which corresponds to the two aforementioned subgames, by means of geometric arguments. Thereafter, we derive the optimal strategies for the players in each subspace. We show that, as long as the target area is compact and convex, the value of the game in each subspace is always continuously differentiable, and the proposed optimal strategies correspond to the unique saddle-point state-feedback strategies for the players. We illustrate our proposed solutions by means of numerical simulations.

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Section: Game Of Kindmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Strategies for Guarding a Compact and Convex Target Set: A Differential Game Approach

Lee,

Bakolas

2021

Preprint

Self Cite

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“…This problem was further investigated in [34] as a reachability game, and the defender tried to intercept the pursuer as far as possible from the evader. The strategy proposed in [35] allowed a single evader to reach the target's location against a group of pursuers. The asset guarding game was revisited in [36] from the perspective of a real-time implementation for the optimal solution.…”

Section: Introductionmentioning

confidence: 99%

Three-agent Time-constrained Cooperative Pursuit-Evasion

Sinha,

Kumar,

Mukherjee

2021

Preprint

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This paper considers a pursuit-evasion scenario among three agents-an evader, a pursuer, and a defender.We design cooperative guidance laws for the evader and the defender team to safeguard the evader from an attacking pursuer. Unlike differential games, optimal control formulations, and other heuristic methods, we propose a novel perspective on designing effective nonlinear feedback control laws for the evader-defender team using a time-constrained guidance approach. The evader lures the pursuer on the collision course by offering itself as bait. At the same time, the defender protects the evader from the pursuer by exercising control over the engagement duration. Depending on the nature of the mission, the defender may choose to take an aggressive or defensive stance. Such consideration widens the applicability of the proposed methods in various three-agent motion planning scenarios such as aircraft defense, asset guarding, search and rescue, surveillance, and secure transportation. We use a fixed-time sliding mode control strategy to design the control laws for the evaderdefender team and a nonlinear finite-time disturbance observer to estimate the pursuer's maneuver. Finally, we present simulations to demonstrate favorable performance under various engagement geometries, thus vindicating the efficacy of the proposed designs.

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“…In the literature, the Hamilton-Jacobi-Isaacs approach is ideal for general low-dimensional differential games [32][33][34]. However, the Hamilton-Jacobi-Isaacs approach cannot be directly applied to the multiplayer reach-avoid game due to the increasing dimension of the joint state space and the complexity of terminal conditions with the number of players [31,35]. Also, the analytical solutions for the games are often unavailable because of the unwieldiness of partial differential equations.…”

mentioning

confidence: 99%

“…Also, the analytical solutions for the games are often unavailable because of the unwieldiness of partial differential equations. So far, many seminal works have been put forward about multiplayer reach-avoid games with various approaches that overcome the shortcomings of the classic HJI approach [25][26][27][28][29][30][31]. For example, In [25], the authors obtained the barrier by integrating the HJI partial differential equations.…”

mentioning

confidence: 99%

Reach‐avoid games with two heterogeneous defenders and one attacker

Chen

2021

IET Control Theory & Appl

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This article addresses a reach-avoid game with two heterogeneous defenders and one attacker in a bounded, convex domain consisting of a target region and a play region. The attacker aims to reach the target region before being captured by any defenders, while the defenders strive to capture the attacker in advance. A simple geometric method is introduced that only considers the position relation between the reaching regions of the players and the boundary of the target region to construct the barrier of the two-player version reach-avoid game analytically. Next, based on the speed ratio between the defenders, the necessary and sufficient conditions suitable for the general game setups to judge which defender contributes to the barrier and decompose the problem into several two-player version subproblems are given. Then, the barrier of the original game is constructed analytically by combining these subproblems in all possible situations. The method provided an analytical expression of the barrier and has essentially no computation burden. Thus, the method is suitable for online applications. And solutions given in this work can be extended to general multiplayer situations and the game with complex setups for further research.

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Feedback Strategies for a Reach-Avoid Game With a Single Evader and Multiple Pursuers

Cited by 53 publications

References 22 publications

Optimal Strategies for Guarding a Compact and Convex Target Set: A Differential Game Approach

Optimal Strategies for Guarding a Compact and Convex Target Set: A Differential Game Approach

Three-agent Time-constrained Cooperative Pursuit-Evasion

Reach‐avoid games with two heterogeneous defenders and one attacker

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