  By introducing a predictive mechanism with small-world connections, we
propose a new motion protocol for self-driven flocks. The small-world
connections are implemented by randomly adding long-range interactions from the
leader to a few distant agents, namely pseudo-leaders. The leader can directly
affect the pseudo-leaders, thereby influencing all the other agents through
them efficiently. Moreover, these pseudo-leaders are able to predict the
leader's motion several steps ahead and use this information in decision making
towards coherent flocking with more stable formation. It is shown that drastic
improvement can be achieved in terms of both the consensus performance and the
communication cost. From the industrial engineering point of view, the current
protocol allows for a significant improvement in the cohesion and rigidity of
the formation at a fairly low cost of adding a few long-range links embedded
with predictive capabilities. Significantly, this work uncovers an important
feature of flocks that predictive capability and long-range links can
compensate for the insufficiency of each other. These conclusions are valid for
both the attractive/repulsive swarm model and the Vicsek model.
