@inproceedings{3aabb593bf4445bfa2a291960d5f071b,
title = "Morse theory and formation control",
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 paper introduces Morse theory as a tool for analyzing the number of such equilibria. A key conclusion is that for two-dimensional rigid formations of point agents, there will always be incorrect equilibria associated with any steepest descent law.",
keywords = "Formation control, Morse Theory, autonomous formations, shape control",
author = "Anderson, \{Brian D.O.\}",
year = "2011",
doi = "10.1109/MED.2011.5983133",
language = "English",
isbn = "9781457701252",
series = "2011 19th Mediterranean Conference on Control and Automation, MED 2011",
pages = "656--661",
booktitle = "2011 19th Mediterranean Conference on Control and Automation, MED 2011",
note = "2011 19th Mediterranean Conference on Control and Automation, MED 2011 ; Conference date: 20-06-2011 Through 23-06-2011",
}