Cucker-smale flocking under asynchronous update dynamics

The effects of asynchronous updating of the state of the agents in a Cucker-Smale flocking model is considered in this paper. The study of asynchronous update is important because in practical implementations the agents typically have internal clocks that are not synchronized. We considered how asynchronous update will affect the time it takes to achieve flocking (flocking time) as well as how close the agents in the flock are moving (flock diameter). These factors were largely ignored in most previous works as achieving asymptotic convergence was their main focus. Furthermore, previous simulations typically assume that the agents move with the same speed. We considered the effects of achieving consensus of both the speed and the heading. Through computer simulations, we showed that both the flocking time and flock diameter increase significantly with asynchronicity. Results also showed that the diameter of the flock is substantially larger when the agents start with different speeds. These results should be taken into account when designing flocking agents in practice.