"I like interactions with the physical world, I love geometry," Kavraki says. "I like physical things." Thus she turned to practical challenges. She started to think about how robots are programmed to navigate. The problem is a tricky one. Say you want a robot to travel from point A to B, and the robot has 10 moving parts. There are a vast number of combinations in which it could use those parts to mount steps, turn corners, and so on-a number so large even a powerful computer would have trouble finding the optimal solution. Kavraki's answer was to randomly sample the range of poses open to the robot, create snapshots of the machine in motion at various stages along its path, and then connect those snapshots as efficiently as possible into a kind of road map. The computer does not search every possible combination, and may miss the best solution every now and then. But the process is fast and reliable, and that's crucial for operating robots in real time.