How fast can a low-flying unmanned aerial vehicle go through a forest without slamming into the trees? Most of today’s UAVs, otherwise known as drones, fly at slow speeds so they have enough time to avoid a collision.
But what if engineers could program UAVs to ensure they go as fast as possible while still avoiding obstacles? That’s what IEEE Senior Member Emilio Frazzoli, an associate professor of aeronautics and astronautics at MIT, and IEEE Graduate Student Member Sertac Karaman, have done. They found that given a certain density of obstacles, there is a critical speed—higher than usually considered safe—below which a UAV will likely fly collision-free. Fly it any faster and it almost certainly will smash into something.
A paper on the researchers’ work is to be presented at the IEEE Conference on Robotics and Automation, taking place from 14 to 19 May in St. Paul, Minn.
Frazzoli and Karaman discovered the speed limit in a rather unusual way: by studying the flight pattern of the goshawk, a bird of prey that flies through dense forests while making sudden changes in its path. It uses its large, fanlike tail to quickly shift direction and maneuver around branches in its way. The researchers had watched a BBC TV show in which a goshawk darted through a canopy of trees with a tiny video camera strapped to its back.
“The bird was very clearly flying at a high speed and making small corrections to its flight path without really slowing down,” Frazzoli says. But how, he wondered, was it flying so fast without colliding with branches? The answer he found would prove useful in the team’s research.
“In much of our work, we have to deal with robots moving in environments that are not completely known to them,” he adds. “For example, sensors that are typically mounted on the drones, cars, or robots can detect obstacles only up to a certain distance away. So the question arises of how to ensure that the vehicle remains safe from objects it has not ‘seen’ yet.”
The answer, until now, has been to move, drive, or fly the vehicle slow enough so that it can safely stop within the space that can be recognized by its onboard sensors.
If the goshawk could fly at speeds based only on what it could see ahead, the researchers conjectured it would have to fly a lot slower. Instead, they theorized, the bird probably uses intuition by gauging the forest’s density. Given a certain density, the hawk assumes it can fly at a certain speed and still find an opening.
But how can you program intuition into a UAV? The answer involves stochastic models based on probability theory and random variables along with percolation theory, which describes the behavior of connected clusters in a random graph. Frazzoli and Karaman came up with a differential equation to represent the position of the bird at a given location and speed.
Next, they worked out a model representing a statistical distribution of trees in a forest. The two then adjusted the model to represent varying densities of trees and then calculated the probability that a bird would collide with a tree while flying at a certain speed. After running through a number of calculations with different speeds, they found a critical speed above which the bird—or any flying object—would certainly crash. For UAVs, that is an important finding.
“Knowing the theoretical speed limit can help in setting up the specifications for a drone, or to set speed limits when flying through a certain forest,” Frazzoli says. “It was an exciting discovery. We may be the first ones to integrate percolation theory and stochastic geometry with tools and concepts from control theory and robotics.”