This Micro-Mouse competition, where a robot mouse solves a maze, has been going on since 1977, and somehow, I never heard about it until today. The mice are not allowed to use any radio communication and have to do all the sensing and computation on the robot mouse.
The first phase of the competition involved finding the best algorithm to solve the maze. The best algorithm isn't depth-first-search or breadth-first-search, it's a flood-fill algorithm that optimizes the mouse movement such that it can find a path to the goal with approximately little movement, and end up, after exploring the maze both to and from the goal, knowing it found the shortest path. Actually a next step after that was finding the fastest path, which isn't necessarily the shortest path -- because the robot has to slow down to turn.
At this point, people thought the competition had been solved, but that wasn't so. In the next phase of the competition, people came up with ways of running the maze faster assuming all the competitors could figure out the optimal solution. The first was cutting diagonals. In fact algorithms were invented to optimize all turns, so the robot never makes square turns, even when there are no diagonals.
After that, people figured out way to improve the physical part of the robot: more powerful DC motors, gyroscopes to improve the robot's sense of where it is, and people carrying tape to get dust off the wheels. Because every bit of friction, or lack thereof, affects how fast the mouse can run. But even after all that, there was still one kicker yet to come: suction. People added a vacuum fan made from an inexpensive drone propeller. This holds the mouse to the maze and allows it to go much faster without flying off the maze surface on the turns.
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