Related papers: Escaping a Polygon
This paper investigates a pursuit-evasion problem involving three agents: a pursuer, an evader, and a defender. Cooperative guidance laws are developed for the evader-defender team that guarantee interception of the pursuer by the defender…
In this paper we study a linear pursuit differential game described by an infinite system of first-order differential equations in Hilbert space. The control functions of players are subject to geometric constraints. The pursuer attempts to…
We study a finite-horizon differential game of pursuit-evasion like, between a single player and a mass of agents. The player and the mass directly control their own evolution, which for the mass is given by a first order PDE of transport…
This paper investigates the application of game-theoretic principles combined with advanced Kalman filtering techniques to enhance maritime target tracking systems. Specifically, the paper presents a two-player, imperfect information,…
This paper explores a multi-agent containment problem, where a fast evader, modeled having constant speed and using constant heading, attempts to escape a circular containment region that is orbited by a slower pursuer with a nonzero…
We consider an autonomous navigation problem, whereby a traveler aims at traversing an environment in which an adversary tries to set an ambush. A two players zero sum game is introduced. Players' strategies are computed as random path…
This paper studies a variant of multi-player reach-avoid game played between intruders and defenders. The intruder team tries to score by sending as many intruders as possible to the target area, while the defender team tries to minimize…
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…
In this paper, we address a pursuit-evasion game involving multiple players by utilizing tools and techniques from reinforcement learning and matrix game theory. In particular, we consider the problem of steering an evader to a goal…
In this article an $n$-pursuer versus $m$-evader reach-avoid differential game in 3D space is studied. A team of evaders aim to reach a stationary target while avoiding capture by a team of pursuers. The multiplayer scenario is formulated…
Consider a two-player game repeated N times. Player 1 can choose between two styles (for interpretability, offensive and defensive), whereas Player 2 uses a single fixed style. Let X N\,:= \#wins -\#losses for Player 1 after N games, and…
In this paper we investigate a differential game in which countably many dynamical objects pursue a single one. All the players perform simple motions. The duration of the game is fixed. The controls of a group of pursuers are subject to…
We present two zero-sum games modeling situations where one player attacks (or hides in) a finite dimensional nonempty compact set, and the other tries to prevent the attack (or find him). The first game, called patrolling game, corresponds…
Sublinear time complexity is required by the massively parallel computation (MPC) model. Breaking dynamic programs into a set of sparse dynamic programs that can be divided, solved, and merged in sublinear time. The rectangle escape problem…
This paper addresses a multi-pursuer single-evader pursuit-evasion game where the free-moving evader moves faster than the pursuers. Most of the existing works impose constraints on the faster evader such as limited moving area and moving…
We consider concurrent games played by two-players on a finite-state graph, where in every round the players simultaneously choose a move, and the current state along with the joint moves determine the successor state. We study a…
Given a two-dimensional polygonal space, the multi-robot visibility-based pursuit-evasion problem tasks several pursuer robots with the goal of establishing visibility with an arbitrarily fast evader. The best known complete algorithm for…
In classical works on a planar differential pursuit-evasion game with a faster pursuer, the intercept point resulting from the equilibrium strategies lies on the Apollonius circle. This property was exploited for the construction of the…
We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…