Simple local rules, complex global behavior
Much of swarm robotics takes direct inspiration from biology. An ant colony can efficiently find a short path between its nest and a food source even though no single ant has any map, any global plan, or any understanding of the colony's overall situation. Each ant just follows simple local rules, like reinforcing pheromone trails that other ants have already used successfully. Flocks of birds and schools of fish show the same pattern: no bird is 'in charge' or has a picture of the whole flock's shape, yet the group moves as a coherent, coordinated whole.
This is the core idea of emergence: sophisticated, useful group-level behavior arising from many individuals independently following simple rules based only on local information, with no individual needing the global picture. It's a fundamentally different design philosophy than centralized planning. Instead of computing a group behavior and dictating it to every robot, you design the local rule and let the group behavior appear as a consequence.