Theoretical speed above which birds and drones are sure to crash found.
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.
Researchers at MIT 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.
Emilio Frazzoli, an associate professor of aeronautics and astronautics at MIT, said that 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.
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 said.
"Which is not very fast," he said.
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 said.
"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," he said.
According to Frazzoli, in a wayrobots 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.
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.
They 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 said.
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.
A paper detailing the results of the study has been accepted to the IEEE Conference on Robotics and Automation. ( ANI )
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