The
northern goshawk is one of nature’s diehard thrill-seekers. The
formidable raptor preys on birds and small mammals, speeding through
tree canopies and underbrush to catch its quarry. With reflexes that
rival a fighter pilot’s, the goshawk zips through a forest at high
speeds, constantly adjusting its flight path to keep from colliding with
trees and other obstacles.
While
speed is a goshawk’s greatest asset, researchers at MIT say the bird
must observe a theoretical speed limit if it wants to avoid a crash. The
researchers found that, given a certain density of obstacles, there
exists a speed below which a bird—and any other flying object—has a fair
chance of flying collision-free. Any faster, and a bird or aircraft is
sure to smack into something, no matter how much information it has
about its environment. A paper detailing the results has been accepted
to the IEEE Conference on Robotics and Automation.
These
findings may not be news to the avian world, but Emilio Frazzoli, an
associate professor of aeronautics and astronautics at MIT, says knowing
how fast to fly can help engineers program unmanned aerial vehicles
(UAVs) to fly at high speeds through cluttered environments such as
forests and urban canyons.
Frazzoli
is part of an interdisciplinary team that includes biologists at
Harvard University, who are observing flying behaviors in goshawks and
other birds, and roboticists at MIT, who are engineering birdlike UAVs.
With Frazzoli’s mathematical contributions, the team hopes to build
fast, agile UAVs that can move through cluttered environments—much like a
goshawk streaking through the forest.
Speedy intuition
Most
UAVs today fly at relatively slow speeds, particularly if navigating
around obstacles. That’s mainly by design: Engineers program a drone to
fly just fast enough to be able to stop within the field of view of its
sensors.
“If
I can only see up to five meters, I can only go up to a speed that
allows me to stop within five meters,” Frazzoli says. “Which is not very
fast.”
If
the northern goshawk flew at speeds purely based on what it could
immediately see, Frazzoli conjectures that the bird would not fly as
fast. Instead, the goshawk likely gauges the density of trees, and
speeds past obstacles, knowing intuitively that, given a certain forest
density, it can always find an opening through the trees.
Frazzoli points out that a similar intuition exists in downhill skiing.
“When
you go skiing off the path, you don’t ski in a way that you can always
stop before the first tree you see,” Frazzoli says. “You ski and you see
an opening, and then you trust that once you go there, you’ll be able
to see another opening and keep going.”
Frazzoli
says that in a way, robots may be programmed with this same speedy
intuition. Given some general information about the density of obstacles
in a given environment, a robot could conceivably determine the maximum
speed below at it can safely fly.
Forever flying
Toward
this end, Frazzoli and PhD student Sertac Karaman developed
mathematical models of various forest densities, calculating the maximum
speed possible in each obstacle-filled environment.
The
researchers first drew up a differential equation to represent the
position of a bird in a given location at a given speed. They then
worked out what’s called an ergodic model representing a statistical
distribution of trees in the forest—similar to those commonly used by
ecologists to characterize the density of a forest. In an ergodic
forest, while the size, shape and spacing of individual trees may vary,
their distribution in any given area is the same as any other area. Such
models are thought to be a fair representation of most forests in the
world.
Frazzoli
and Karaman adjusted the model to represent varying densities of trees,
and calculated the probability that a bird would collide with a tree
while flying at a certain speed. The team found that, for any given
forest density, there exists a critical speed above which there is no
“infinite collision-free trajectory.” In other words, the bird is sure
to crash. Below this speed, a bird has a good chance of flying without
incident.
“If
I fly slower than that critical speed, then there is a fair possibility
that I will actually be able to fly forever, always avoiding the
trees,” Frazzoli says.
The
team’s work establishes a theoretical speed limit for any given
obstacle-filled environment. For UAVs, this means that no matter how
good robots get at sensing and reacting to their environments, there
will always be a maximum speed they will need to observe to ensure
survival.
The
researchers are now seeing if the theory bears out in nature. Frazzoli
is collaborating with scientists at Harvard, who are observing how birds
fly through cluttered environments—in particular, whether a bird will
choose not to fly through an environment that is too dense. The team is
comparing the birds’ behavior with what Frazzoli’s model can predict. So
far, Frazzoli says preliminary results in pigeons are “very
encouraging.”
In
the coming months, Frazzoli also wants to see how close humans can come
to such theoretical speed limits. He and his students are developing a
first-person flying game to test how well people can navigate through a
simulated forest at high speeds.
“What
we want to do is have people play, and we’ll just collect statistics,”
Frazzoli says. “And the question is, how close to the theoretical limit
can we get?”
