Well not exactly like the electronic GPS that we are all aware of, but cockroaches do have a sophisticated internal mechanism that allows them to navigate your home.
Researchers placed cockroaches inside of a maze similar to the classic experiments that used rats to navigate mazes. Once the roaches moved through the maze the researchers changed parts of the maze to see if roaches would remember where to find the end of the maze. What the researchers found was that roaches would move to the same parts of the maze that accessed the end of the maze despite the maze being changed.
This finding indicates that roaches did not rely solely on present sensory information, but they were able to recall how to navigate their environment from earlier experience. Additionally, the researchers monitored the brain activity of the roaches and discovered that the roaches have a complex neural mechanism similar to rats and even humans that allows them to navigate through complex environments. This may explain why roaches are so hard to find once we find our bug spray.
Do you think that all animals, even small brained animals, possess similar neural structures that allow them to navigate complex environments?