Relation to connectivity and covered areain dynamic plan covering by swarm robots

The dynamic plane covering by swarm robots is a problem to make a trajectory of move multiple robots in a given field so that the trajectory covers the field, which often appears in agricultural works such as water spraying. We solve the problem by applying the swarm robot concepts in the way that a single robot called a leader moves around in the field and all the other robots called followers try to catch up the leader. The advantage of this solution is that we only need to specify a trajectory of the leader and we expect the scalability of the number of the robots. On the other hand, we have to carefully design the trajectory of the leader and the connectivity network between the followers so that all the robots are always connected and under control. This paper presents the relation between the connectivity network, the control stability, and the covered field both analytically and numerically.