It was also a way of pushing the boundaries of the mathematical techniques that control a machine in a relatively safe but still very real environment. “With a glider, you can test these algorithms with minimal risk to people and property,” Mr. Kochenderfer said.

In building their algorithms, Mr. Kapoor and his team relied on techniques that date back decades — something called Markov decision processes. Essentially, this is a way of identifying and responding to uncertainty.

The approach is like the one you take when looking for change in a backpack crammed with random stuff. If you just stick your hand in the bag and start rummaging around, you face enormous uncertainty. You don’t know where to grab. But if, first, you remove the larger items like books and pencils that you know aren’t coins, the change falls to the bottom and the task gets easier. That is what Microsoft’s algorithms do — in a mathematical sense. They work to limit uncertainty, to reduce the scope of the problem.

Mr. Kapoor’s team included Andrey Kolobov, a researcher who specializes in these methods.

When he joined Microsoft’s research group four years ago, Mr. Kolobov fed these ideas into the company’s Windows operating system and its Bing search engine. Back then, he was dealing with uncertainty in the digital world. Now, he’s applying them in the physical world. “The number of applications where these methods are used is growing,” Mr. Kolobov said.