metric vs topological maps

These are two very different ways for a robot to write down the world. A metric map is like a precise architect's blueprint: it records actual distances and shapes in real units, so the robot knows the desk is 2.3 metres straight ahead and the wall runs exactly here. A topological map is more like a subway diagram: it forgets the exact distances and instead remembers the places that matter and which ones connect to which — kitchen links to hallway, hallway links to living room. One captures precise geometry; the other captures connectivity, the bare structure of how places hang together.

Each style is good at something the other is bad at. A metric map lets a robot squeeze through a narrow doorway or park a wheel within a centimetre, because it knows the exact measurements — but it is heavy to store, slow to search across a whole building, and it drifts: tiny measurement errors pile up over long distances until the far end of the map no longer lines up with reality. A topological map is wonderfully light and easy to reason over for long-haul planning ("to reach the lobby, go kitchen → hallway → stairs"), and it shrugs off that drift because it never claimed exact distances in the first place — but on its own it cannot tell the robot precisely how to steer between two doorways.

Because of this trade-off, real robots usually blend the two into a hybrid map: a topological skeleton of connected places for big-picture planning, with a small, accurate metric patch stored inside each place for the fine, careful manoeuvring that happens once you arrive. Think of it as a city subway map for deciding the route, plus a detailed street map of just the block you step out onto.