Abubakr Muhammad

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We consider coverage problems in sensor networks of stationary nodes with minimal geometric data. In particular, there are no coordinates and no localization of nodes. We introduce a new technique for detecting holes in coverage by means of homology, an algebraic topological invariant. The impetus for these techniques is a completion of network(More)
We consider coverage problems in robot sensor networks with minimal sensing capabilities. In particular, we demonstrate that a “blind” swarm of robots with no localization and only a weak form of distance estimation can rigorously determine coverage in a bounded planar domain of unknown size and shape. The methods we introduce come from algebraic topology.(More)
In this paper, we consider the situation where a collection of leaders dictate the motion of the followers in heterogenous multi-agent applications. In particular, the followers move according to a decentralized averaging rule, while the leaders’ motion is unconstrained. Thus, the trajectories of the leaders can be viewed as exogenous control inputs, which(More)
In this paper, we study graphs that arise from certain sensory and communication limitations on the local interactions in multi-agent systems. In particular, we show that the set of graphs that can represent formations corresponds to a proper subset of all graphs and we denote such graphs as connectivity graphs. These graphs have a special structure that(More)
In this paper, we focus on setting up a gunshot detection system with high detection performance, robustness to noise and low computational complexity. To achieve these objectives, we formulate a two-stage approach with a less costly impulsive event detection framework followed by a relatively more complex gunshot recognition stage. To improve detection(More)
Due to the limited effective range of every physical sensor, as well as potential bandwidth limitations on the communication channels, there is a need for modeling and analysis tools when studying multi-agent robot systems that take these local interactions into account. In this paper, we review some of the work done on graphs and configuration spaces, and(More)
In this paper, we study the problem of verifying dynamic coverage in mobile sensor networks using certain switched linear systems. These switched systems describe the flow of discrete differential forms on time-evolving simplicial complexes. The simplicial complexes model the connectivity of agents in the network, and the homology groups of the simplicial(More)