Abstract

Given a large number (the flock) of moving physical objects (birds, robots, or otherwise), we investigate physically reasonable mechanisms of influencing their orbits in such a way that they move along a prescribed course and in a prescribed andfixed configuration (or in formation). Each agent is programmed to see the position and velocity of a certain number of others. To be able to fly in formation, an agent tries to match the mean position and velocity of his neighbours to his own. A linear feedback is used to ensure stability of the coherent flight patterns. We analyse in detail how the communication graph affects the coherence of the stable flight patterns and give a characterisation of these stable flight patterns. We do the same if in addition the flight of the flock is guided by one or more leaders. We then use this theory to develop some applications. Examples of these are: flight guided by external controls, flocks of flocks, and some results about flocks whose formation is always oriented along the line of flight (such as geese).