### Optimization and Systems Theory Seminar

Friday, April 2, 2004, 11.00-12.00, Room 3721, Lindstedtsvägen 25

**Professor
Clyde F. Martin**

Department of Mathematics

Texas Tech. University

Lubbock, Texas, USA

####
How many robots can talk at the same time?

Suppose we are given a mob of robots that cannot communicate with each
other if they are closer together than r meters and that their
communications systems only have a range of R meters. For tactical
purposes it is often convenient that every robot be able to
communicate directly with every other robot in the mob. The question
arises of how many robots can be used and still meet these distance
constraints. The problem can be directly phrased as a min-max
optimization problem but as such is nontrivial to solve. However, it
is clearly closely related to the problem of circle packing. The
circle packing problem has been studied for many years and,
interestingly, is not solved in any precise sense. The circle packing
problem is dual, in some sense, to the communication problem. The
circle packing problem is usually stated as *"Determine the smallest
circle in which n unit circles can be places without overlap"*. We
will show in this talk that given known results from the circle
packing problem satisfactory answers can be obtained for the
communications problem.

This is joint work with Magnus Egerstedt.

Calendar of seminars

*Last update: March 17, 2004 by
Anders Forsgren.
*