Wireless Sensor and Actuator Networks: Algorithms and Protocols for Scalable Coordination and Data Communication

9.10 CLUSTERING ROBOT SWARMS

A self-organized robot aggregation model was studied in Correll and Martinoli (2007b). The study is inspired by swarms of German cockroaches. Cockroaches move randomly through the arena and eventually stop and aggregate into clusters of different sizes. In each cluster, a cockroach can sense the presence of at least one other cockroach. Those clusters are not persistent and cockroaches might resume moving and leave the cluster. The average time for a cockroach to rest within a cluster increases while the size of the cluster increases (Jeanson et al., 2004).

Let p^leave(j) and p^join(j) denote the probability a cockroach/robot leaves and joins a cluster of size j, respectively. These values are observed in Jeanson et al. (2004). Let p_c denote the probability that a robot encounters another one at every time step of length T. p_c is estimated as follows: p_c = (1/A_total)v_rw_dT, where A_total is the area of the arena, v_r the average speed of an individual, w_d the individual's detection width, that is, communication range of the robot. Therefore, the behavior of robots can be modeled as the Markov process. The average number of robots N_j(k + 1) in an aggregation of size j at time k + 1, is as follows:

The first term N_j(k) is the average number of robots in an aggregation of size j at time k. The second term indicates that a searching robot encounters one of the ...