Pursuit-evasion games in dynamic flow fields via reachability set analysis

Sun, Wei; Tsiotras, Panagiotis; Lolla, Tapovan; Subramani, Deepak N.; Lermusiaux, Pierre F. J.

doi:10.23919/acc.2017.7963664

Cited by 16 publications

(10 citation statements)

References 27 publications

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“…Reachability-based approached are presented in [4] using Hamilton-Jacobi-Isaac's formulation to compute the reachable set of a continuous dynamic differential game. However, [5] argued that solutions of HJI equations are not readily available from the practical point of view especially for the problems with multiple agents and non-trivial dynamics, thus proposed conditions for the game to be terminated in terms of reachable sets inclusion. Numerical solutions to differential games by a sequence of finite state Markov games has been presented in [6] where players are assumed to be moving at constant speed.…”

Section: Introductionmentioning

confidence: 99%

Pursuit-evasion Game for Nonholonomic Mobile Robots With Obstacle Avoidance using NMPC

Sani

Robu

Hably

2020

2020 28th Mediterranean Conference on Control and Automation (MED)

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In this work, non-cooperative competitive games between two unmanned ground robots using Nonlinear Model Predictive Control (NMPC) while incorporating obstacle avoidance techniques are studied. The objective of the first player (pursuer) is to minimize the relative distance and orientation between itself and the second player (evader) while avoiding obstacles, whereas the evader does the opposite. The Pursuit-Evasion Game (PEG) being a typical class of a differential game is formulated as a zero-sum game with two homogeneous players in five different game scenarios. The objective function of each player is formulated as a double optimization problem and is solved separately using NMPC techniques. The optimal trajectory of each player is computed iteratively by considering the best response of the opponent player. The level of information is assumed to be symmetric. Simulations of various scenarios show the winning possibility of each player.

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Section: Introductionmentioning

confidence: 99%

Pursuit-evasion Game for Nonholonomic Mobile Robots With Obstacle Avoidance using NMPC

Sani

Robu

Hably

2020

2020 28th Mediterranean Conference on Control and Automation (MED)

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“…Level set schemes have however been shown to be very efficient at solving these governing planning equations [17][18][19][20][21], more so than graph search schemes [22]. They have been used onboard real ocean vehicles at sea [23] and employed to solve pursuit-evasion games [24] as reviewed in Section 3.…”

Section: Path Planning Games In Marine Domainmentioning

confidence: 99%

“…This section reviews the major contributions about pursuit-evasion games. In [24], a reachability-based approach is proposed to deal with the pursuit-evasion differential game between two players in the presence of dynamic environmental disturbances (e.g., winds, sea currents). In [33], the authors extend the previous work to the case of multiple pursuers.…”

Section: Pursuit-evasion Gamesmentioning

confidence: 99%

Game Theory for Unmanned Vehicle Path Planning in the Marine Domain: State of the Art and New Possibilities

Cococcioni

Fiaschi

Lermusiaux

2021

JMSE

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Thanks to the advent of new technologies and higher real-time computational capabilities, the use of unmanned vehicles in the marine domain has received a significant boost in the last decade. Ocean and seabed sampling, missions in dangerous areas, and civilian security are only a few of the large number of applications which currently benefit from unmanned vehicles. One of the most actively studied topic is their full autonomy; i.e., the design of marine vehicles capable of pursuing a task while reacting to the changes of the environment without the intervention of humans, not even remotely. Environmental dynamicity may consist of variations of currents, the presence of unknown obstacles, and attacks from adversaries (e.g., pirates). To achieve autonomy in such highly dynamic uncertain conditions, many types of autonomous path planning problems need to be solved. There has thus been a commensurate number of approaches and methods to optimize this kind of path planning. This work focuses on game-theoretic approaches and provides a wide overview of the current state of the art, along with future directions.

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“…Let T o = inf{t ∈ R : R − e (e 0 , R p , t) = ∅}. It is shown in [24], for pursuer and evader which can turn instantaneously, that such a condition is indeed necessary and sufficient for capture if we consider open-loop strategies and capture occurs at T o . However, the claim does not hold if we consider feedback strategies for the pursuer and evader.…”

Section: Analysis Using Reachability Setsmentioning

confidence: 99%

“…Reachable sets have been used for analyzing differential games since [8,17]. Recently reachable sets have been used to derive feedback strategies under varying flow fields for various types of pursuers and evaders [24,25] and also in multi-player pursuit-evasion games [13,15,18]. In this paper we analyze the relation between feedback min − max strategies and reachable sets.…”

Section: Introductionmentioning

confidence: 99%

A computationally efficient feedback solution for a particular case of the game of two cars

Chaudhari

Chourasia

Chakraborty

2019

2019 18th European Control Conference (ECC)

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In this paper, a time-optimal feedback solution to the game of two cars, for the case where the pursuer is faster and more agile than the evader, is presented. The concept of continuous subsets of the reachable set is introduced to characterize the time-optimal pursuit-evasion game under feedback strategies. Using these subsets it is shown that, if initially the pursuer is distant enough from the evader, then the feedback saddle point strategies for both the pursuer and the evader are coincident with one of the common tangents from the minimum radius turning circles of the pursuer to the minimum radius turning circles of the evader. Using geometry, four feasible tangents are identified and the feedback min − max strategy for the pursuer and the max − min strategy for the evader are derived by solving a 2 × 2 matrix game at each instant. Insignificant computational effort is involved in evaluating the pursuer and evader inputs using the proposed feedback control law and hence it is suitable for real-time implementation. The proposed law is validated further by comparing the resulting trajectories with those obtained by solving the differential game using numerical techniques.

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Pursuit-evasion games in dynamic flow fields via reachability set analysis

Abstract: Pursuit-evasion games in dynamic flow fields via reachability set analysis The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters.

Cited by 16 publications

References 27 publications

Pursuit-evasion Game for Nonholonomic Mobile Robots With Obstacle Avoidance using NMPC

Pursuit-evasion Game for Nonholonomic Mobile Robots With Obstacle Avoidance using NMPC

Game Theory for Unmanned Vehicle Path Planning in the Marine Domain: State of the Art and New Possibilities

A computationally efficient feedback solution for a particular case of the game of two cars

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