The mathematical theory of rigidity was originally developed for
structural engineering and Constraint based Computer Aided design. In
recent years, it has been applied to problems in control theory and
location of objects in random networks. This talk will summarize some
basic combinatorial and geometric results and their application to control
theory and location of agents within a network.
We will focus on a few sample problems: coordinating a collection of
moving agents, such with measured distances between certain pairs. Which
patterns of measurements will let us hold the pattern? Which new
measurements do you need to hold a pattern when one agent drops out?
Results from rigidity will be applied or refined to address these
questions, including questions of control where distances are directed
(one of a pair responds to this distance). Results in the plane, and
partial results / unsolved problems in 3-space will be described.
The talk draws on joint work with a larger community of researchers,
including the groups of A. Stephen Morse and Y. Richard Yang at Yale.