Seminar Details
2011-11-22 (14.00) : Morse Theory and Formation Control
At Euler building
Organized by Mathematical Engineering
Speaker :
Brian D O ANDERSON (Australian
National University)
Abstract :
Formation shape control for a collection of point agents is concerned
with devising decentralized control laws which will ensure that the
formation will move so that certain inter-agent distances assume
prescribed values. A number of algorithms based on steepest descent of
an error function have been suggested for various problems, and all
display the existence of incorrect equilibria, though often the
equilibria are saddle points or unstable. This talk introduces Morse
theory as a tool for analyzing the number of such equilibria.
Initially a simpler problem is reviewed: that of navigating a point
agent using a steepest descent law to a point in a closed
two-dimensional region containing obstacles. A key conclusion is that
for both the navigation problem and for the formation shape control
problem, there will always be incorrect equilibria associated with any
steepest descent law.