Mathematicians equip drone with speaker and microphones to make it echolocate like bats

March 11, 2020 | AUVSI News

Mathematicians have discovered that a drone equipped with microphones and a speaker—with the help of algebra and geometry—can echolocate similarly to how bats use echolocation to orient themselves with their surroundings.

According to Purdue University associate professor of mathematics and electrical and computer engineering Mireille “Mimi” Boutin, this signal processing research could have potential applications for people, underwater vehicles and even cars.

“Many engineering applications require a lot of math, and sometimes you need to use tools from areas of mathematics that are considered abstract – in this case, methods from commutative algebra,” Boutin explains.

“It’s considered a very abstract part of mathematics, but it applies to a very practical engineering problems. This shows just how unclear the boundary between applied and abstract math can be, and that engineering is truly a multidisciplinary discipline.”

Using echoes picked up by microphones on the drone, Boutin, along with Gregor Kemper, a professor of algorithmic algebra in the Department of Mathematics at the Technical University of Munich, reconstructed the wall configuration of rooms. According to the researchers, when a microphone hears an echo, the time difference between the moment the sound was produced and the time it was heard is recorded. That time difference shows the distance traveled by the sound after bouncing on a wall.

The challenge, researchers explain, is to determine which distance corresponds to which wall, which is a process called echosorting. By sorting the echoes accurately, one can make sure that all walls that are heard are truly there, which ensures that the algorithm does not produce “ghost” walls.

The research is directly related to two complementary problems in engineering: localization and mapping. The research conducted by Boutin and Kemper proves that it’s possible for a minimal setup of four microphones arranged in a non-planar shape, along with just a loudspeaker emitting one signal, to reconstruct a room.

The next steps will be to consider other scenarios, which could include instances when the movement of the drone is restricted, or when the drone listens to the echoes of consecutive sounds as it is moving.

Practically, there are several ways this echolocation research could be applied, including a device of this kind potentially being carried by a person, affixed to a car, or even used underwater. Having more signal input would prevent solely relying on one type of input, and would ultimately improve the chances that objects could be detected more accurately and in a wider variety of conditions.