Almost satisfaction of a joint connectivity condition for multi-agents in a bounded plane

In a flocking scenario of multi-agent systems, the connectivity of the group of agents is caused either by individual´s local cohesion interaction mechanism or by external boundary constraints. The latter case is particularly interesting when an individual´s cohesion ability is not reliable due to the limitation of communication range. The effect of external boundary constraints on the connectivity property of multi-agents has been intensively investigated in natural observation and engineering simulation. A theoretical analysis is given in this paper which reveals that a group of agents in a bounded plane can be almost always jointly connected and hence form a complete flock.