相关论文: Hunter, Cauchy Rabbit, and Optimal Kakeya Sets
We consider a system of three random walkers (a `cheetah' surrounded by two `antelopes') diffusing in one dimension. The cheetah and the antelopes diffuse, but the antelopes experience in addition a deterministic relative drift velocity,…
This paper studies a stochastic robotic surveillance problem where a mobile robot moves randomly on a graph to capture a potential intruder that strategically attacks a location on the graph. The intruder is assumed to be omniscient: it…
An algorithm is presented that efficiently solves the selection problem: finding the k-th smallest member of a set. Relevant to a divide-and-conquer strategy, the algorithm also partitions a set into small and large valued subsets. Applied…
We introduce a discrete-time search game, in which two players compete to find an object first. The object moves according to a time-varying Markov chain on finitely many states. The players know the Markov chain and the initial probability…
We devise a cooperative planning framework to generate optimal trajectories for a tethered robot duo, who is tasked to gather scattered objects spread in a large area using a flexible net. Specifically, the proposed planning framework first…
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…
Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of…
Search problems at various scales involve a searcher, be it a molecule before reaction or a foraging animal, which performs an intermittent motion. Here we analyze a generic model based on such type of intermittent motion, in which the…
A Kakeya set in the linear representation $T^{*}_{2}(\mathcal{C})$, $\mathcal{C}$ a non-singular conic, is the point set covered by a set of $q+1$ lines, one through each point of $\mathcal{C}$. In this article we classify the small Kakeya…
Web crawlers are used by internet search engines to gather information about the web graph. In this paper we investigate a simple process which models such software by walking around the vertices of a graph. Once initial random vertex…
Most existing robot formation problems seek a target formation of a certain \emph{minimal} and, thus, efficient structure. Examples include the Gathering and the Chain-Formation problem. In this work, we study formation problems that try to…
We address prehensile pushing, the problem of manipulating a grasped object by pushing against the environment. Our solution is an efficient nonlinear trajectory optimization problem relaxed from an exact mixed integer non-linear trajectory…
Levy flights are known to be optimal search strategies in the particular case of revisitable targets. In the relevant situation of non revisitable targets, we propose an alternative model of bidimensional search processes, which explicitly…
A mobile agent navigating along edges of a simple connected graph, either finite or countably infinite, has to find an inert target (treasure) hidden in one of the nodes. This task is known as treasure hunt. The agent has no a priori…
Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and…
In many random search processes of interest in chemistry, biology or during rescue operations, an entity must find a specific target site before the latter becomes inactive, no longer available for reaction or lost. We present exact results…
In the symmetric rendezvous search game played on Kn (the completely connected graph on n vertices) two players are initially placed at two distinct vertices (called locations). The game is played in discrete steps and at each step each…
We introduce the Ants Nearby Treasure Search (ANTS) problem, which models natural cooperative foraging behavior such as that performed by ants around their nest. In this problem, k probabilistic agents, initially placed at a central…
The ability to cooperate with unknown partners is a central challenge in cooperative AI and widely studied in the form of zero-shot coordination (ZSC), which evaluates an algorithm by measuring the performance of independently trained…
The Levy walk in which the frequency of occurrence of step lengths follows a power-law distribution, can be observed in the migratory behavior of organisms at various levels. Levy walks with power exponents close to 2 are observed, and the…