One brain versus many: the centralized approach
A centralized coordination architecture has a single decision-maker, either a central server or one designated robot, that receives state information from every robot in the fleet and makes all the assignment and coordination decisions. Because it sees everything at once, it can compute solutions that are efficient and close to globally optimal, assigning tasks and paths in a way that minimizes total travel distance or balances load across the fleet in ways no individual robot could figure out on its own with only local information.
The cost of that global view is fragility and scaling pressure. If the central coordinator fails, loses power, or loses communication with the fleet, the entire system can grind to a halt, since no robot has the authority or information to keep making coordinated decisions on its own. And as more robots join the fleet, both the communication bandwidth needed to report every robot's state and the computation needed to solve the joint assignment problem grow quickly, so centralized approaches tend to hit a ceiling.