A drone can hear the shape of a room

With a speaker and four microphones, drones can echolocate like bats

Mathematicians at Purdue University in West Lafayette, Indiana, have found that drones can determine position with echolocation.

The signal-processing research has potential applications for people, underwater vehicles and even cars, said Mireille “Mimi” Boutin, a Purdue University associate professor of mathematics and electrical and computer engineering.

Boutin and Gregor Kemper, a professor of algorithmic algebra in the Department of Mathematics at the Technical University of Munich, have worked to reconstruct the wall configuration of rooms by using echoes picked up by microphones on the drone.

Mathematicians found a method to hear the shape of a room using four microphones mounted on a drone. Pictured: Mireille Boutin. (Photo: Purdue University)

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 — much like bats use echolocation to orient themselves with their surroundings.

The challenge is to determine which distance corresponds to which wall, a process called echosorting. Sorting the echoes accurately ensures that all the walls heard are truly there. This way, the algorithm used does not produce “ghost” walls.

The research is directly related to two complementary problems in engineering: localization (determining where you are in an environment) and mapping (determining the shape of your environment).

The research, which uses methods from commutative algebra, proves that it’s possible for a minimal setup of four microphones arranged in a non-planar shape, along with a loudspeaker emitting a singal signal, to reconstruct a room.

The microphones and loudspeaker could be mounted on a moving car, a robot navigating in an indoor environment, or an underwater vehicle exploring a wreck in the ocean. Some of these situations put restrictions on rotations and translations that can be applied to the microphone configuration. The impact of such restrictions on the reconstruction problem will also be studied in future work.

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

Citation. “A Drone Can Hear the Shape of a Room,” by Mireille Boutin and Gregor Kemper, SIAM Journal on Applied Algebra and Geometry, 4(1), 123–140, Published online Feb. 6, 2020, https://doi.org/10.1137/19M1248534.