Related papers: Evasion Paths in Mobile Sensor Networks

Consider a mobile sensor network, in which each sensor covers a ball. Sensors do not know their locations, but can detect if the covered balls overlap. An intruder cannot pass undetected between overlapping sensors. An evasion path exists…

Suppose one wants to monitor a domain with sensors, each sensing a small ball-shaped region, but the domain is hazardous enough that one cannot control the placement of the sensors. A prohibitively large number of randomly placed sensors…

Given a compact manifold $X$ with boundary and a submersion $f : X \rightarrow Y$ whose restriction to the boundary of $X$ has isolated critical points with distinct critical values and where $Y$ is $[0,1]$ or $S^1$, the connected…

The evasion paths problem asks when a dynamically changing space can be navigated: imagine guards are patrolling a region, for instance, and we need to stay outside their view. We use the Bousfield-Kan spectral sequence for homotopy inverse…

In this paper we study the dynamic aspects of the coverage of a mobile sensor network resulting from continuous movement of sensors. As sensors move around, initially uncovered locations are likely to be covered at a later time. A larger…

This paper studies, for the first time, the trajectory planning problem in adversarial environments, where the objective is to design the trajectory of a robot to reach a desired final state despite the unknown and arbitrary action of an…

To the coverage problem of sensor networks, V. de Silva and R. Ghrist (2007) developed several approaches based on (persistent) homology theory. Their criteria for the coverage are formulated on the Rips complexes constructed by the…

The classical setting of optimal control theory assumes full knowledge of the process dynamics and the costs associated with every control strategy. The problem becomes much harder if the controller only knows a finite set of possible…

We consider a task of surveillance-evading path-planning in a continuous setting. An Evader strives to escape from a 2D domain while minimizing the risk of detection (and immediate capture). The probability of detection is path-dependent…

We consider a class of pursuit-evasion problems where an evader enters a directed acyclic graph and attempts to reach one of the terminal nodes. A pursuer enters the graph at a later time and attempts to capture the evader before it reaches…

In this paper, we extend the recent body of work on planning under uncertainty to include the fact that sensors may not provide any measurement owing to misdetection. This is caused either by adverse environmental conditions that prevent…

Effective communication is crucial for deploying robots in mission-specific tasks, but inadequate or unreliable communication can greatly reduce mission efficacy, for example in search and rescue missions where communication-denied…

In previous work, empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here…

The optimal control of a "blind" pursuer searching for an evader moving on a road network and heading at a known speed toward a set of goal vertices is considered. To aid the "blind" pursuer, certain roads in the network have been…

Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing the phase space dynamics of time-series data. Persistent homology effectively identifies global topological features, such as loops…

In this paper we consider the question of sensor network coverage for a 2-dimensional domain. We seek to compute the probability that a set of sensors fails to cover given only non-metric, local (who is talking to whom) information and a…

We study the design of sampling trajectories for stable sampling and the reconstruction of bandlimited spatial fields using mobile sensors. The spectrum is assumed to be a symmetric convex set. As a performance metric we use the path…

Pursuit-evasion is a multi-agent sequential decision problem wherein a group of agents known as pursuers coordinate their traversal of a spatial domain to locate an agent trying to evade them. Pursuit evasion problems arise in a number of…

In this paper, we study the problem of map matching with travel time constraints. Given a sequence of $k$ spatio-temporal measurements and an embedded path graph with travel time costs, the goal is to snap each measurement to a close-by…

In practice, wireless networks are deployed over finite domains, the level of mobility is different at different locations, and user mobility is correlated over time. All these features have an impact on the temporal properties of…