True 3-D displays for avionics and mission crewstations
Elizabeth A. Sholler, Frederick M. Meyer, et al.
SPIE AeroSense 1997
We consider the problem of patrolling-i.e. ongoing exploration of a network by a decentralized group of simple memoryless robotic agents. The model for the network is an undirected graph, and our goal, beyond complete exploration, is to achieve close to uniform frequency of traversal of the graph's edges. A simple multi-agent exploration algorithm is presented and analyzed. It is shown that a single agent following this procedure enters, after a transient period, a periodic motion which is an extended Eulerian cycle, during which all edges are traversed an identical number of times. We further prove that if the network is Eulerian, a single agent goes into an Eulerian cycle within 2|E|D steps, |E| being the number of edges in the graph and D being its diameter. For a team of κ agents, we show that after at most 2(1 + 1/κ)|E|D steps the numbers of edge visits in the network are balanced up to a factor of two. In addition, various aspects of the algorithm are demonstrated by simulations.
Elizabeth A. Sholler, Frederick M. Meyer, et al.
SPIE AeroSense 1997
Karthik Visweswariah, Sanjeev Kulkarni, et al.
IEEE International Symposium on Information Theory - Proceedings
Robert Manson Sawko, Malgorzata Zimon
SIAM/ASA JUQ
Sonia Cafieri, Jon Lee, et al.
Journal of Global Optimization