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TECHNICAL PAPERS

Stable Cooperative Vehicle Distributions for Surveillance

[+] Author and Article Information
Jorge Finke

Department of Electrical and Computer Engineering, The Ohio State University, Columbus, Ohio 43212finkej@ece.osu.edu

Kevin M. Passino

Department of Electrical and Computer Engineering, The Ohio State University, Columbus, Ohio 43212passino@ece.osu.edu

www.ece.osu.edu/∼passino/kmp-pubs.html

J. Dyn. Sys., Meas., Control 129(5), 597-608 (Jan 17, 2007) (12 pages) doi:10.1115/1.2767656 History: Received April 15, 2006; Revised January 17, 2007

A mathematical model for the study of the behavior of a spatially distributed group of heterogeneous vehicles is introduced. We present a way to untangle the coupling between the assignment of any vehicle’s position and the assignment of all other vehicle positions by defining general sensing and moving conditions that guarantee that even when the vehicles’ motion and sensing are highly constrained, they ultimately achieve a stable emergent distribution. The achieved distribution is optimal in the sense that the proportion of vehicles allocated over each area matches the relative importance of being assigned to that area. Based on these conditions, we design a cooperative control scheme for a multivehicle surveillance problem and show how the vehicles’ maneuvering and sensing abilities, and the spatial characteristics of the region under surveillance, affect the desired distribution and the rate at which it is achieved.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Suitability functions for an area with ℓ=2.5km and vehicles at speed v=15m∕s; T=100m with (left) and without (right) intra-area coordination strategies. Each data point represents 60 simulation runs with varying target pop-up locations. The error bars are sample standard deviations from the mean.

Grahic Jump Location
Figure 2

Suitability functions si(xi) for three fully connected nodes with x¯=x̱=1, w̱=w¯=0, εc=7, and C=36. Under perfect sensing conditions, the IFD distribution is reached when all agents are distributed in such a way that at state x neighboring nodes i such that i∊I(x) have suitability levels that do not differ by more than M. After the IFD is reached, there is no movement of agents between nodes. For the example shown in the plot, while agents distribute themselves over nodes 1 and 2, node 3 remains at the minimum agent capacity εc at the desired distribution. Node i=3 is called a truncated node. The suitability level s3(εc) is too low to be chosen by any agent. Note also that there may exist different distributions of the total agent capacity that correspond to neighboring suitability levels of nodes i∊I(x) differing by at most M. The light-colored vertical bands represent all possible distributions of agent capacity for which the IFD pattern is achieved. We denote the set of all such distributions by Xd and will describe it mathematically in Sec. 3. The dark-colored vertical bars illustrate a particular distribution x′=[7,12,17]T, and its resultant suitability levels satisfy the IFD pattern (note that x′=[7,11,18]T and x′=[7,10,19]T would also result in suitability levels that satisfy the IFD pattern).

Grahic Jump Location
Figure 3

Two possible IFD realizations for vehicles traveling at constant speed v=15m∕s and T=800m deployed in a region divided into four areas with ℓ=2.5km and connected by a line topology

Grahic Jump Location
Figure 4

Effects of implementing a synchronous and partially asynchronous iterative methods to try to reduce the effects of the sensing noise w on the mission performance with 20 vehicles at constant speed v=15m∕s and T=800m; no cooperative sensing (left), agreement strategy (middle), averaging strategy (right)

Grahic Jump Location
Figure 5

Effects of implementing a synchronous and partially asynchronous iterative methods on reaching an IFD realization; no cooperative sensing (square), agreement strategy (circle), averaging strategy (triangle). Each data point represent 50 simulation runs with varying target pop-up locations. The error bars are sample standard deviations from the mean.

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