Everyone knows what it’s like for an airplane to land: The slow maneuvering into an approach pattern, the long descent, and the brakes slamming on as soon as the plane touches down, which seems to just barely bring it to a rest a mile later. Birds, however, can switch from barreling forward at full speed to lightly touching down on a target as narrow as a telephone wire. Why can’t an airplane be more like a bird, asked MIT researchers, who have demonstrated a new control system that allows a foam glider with only a single motor on its tail to land on a perch, just like a pet parakeet.
The work could have important implications for the design of robotic planes, greatly improving their maneuverability and potentially allowing them to recharge their batteries simply by alighting on power lines, according to researchers.
Birds can land so precisely because they take advantage of a complicated aerodynamic phenomenon called “stall,” a natural brake that lets them stop quickly within short distances. When an airplane is in flight, its wings are either parallel to the ground or, when it’s changing altitude or banking, a few degrees off. Within that narrow range of angles, the airflow over the plane’s wings is smooth and regular, like the flow of water around a small, smooth stone in a creek bed.
A bird approaching its perch, however, will tilt its wings back at a much sharper angle. Instantly, the airflow over the wings becomes turbulent, and vortices — whirlwinds — form behind the wings. The effects of the vortices are hard to predict: If a plane tilts its wings back too far, it can fall out of the sky. Hence the name “stall.”
The smooth airflow over the wings of a normally operating plane is well-understood mathematically; as a consequence, engineers are highly confident that plane will respond to the pilot’s commands as intended. But stall is an exponentially more complicated phenomenon: No one has yet found a precise way to describe it mathematically, and even the best approximations are enormously time-consuming to compute.
To develop their perching glider, MIT Associate Professor Russ Tedrake, a member of the Computer Science and Artificial Intelligence Laboratory, and Rick Cory, a PhD student in Tedrake’s lab who defended his dissertation this spring, took a two-pronged approach. The first step was to develop their own mathematical model of a glider in stall, which allows them to calculate an initial flight plan before the glider is launched. “It gets this nominal trajectory,” Cory explains. “It says, ‘If this is a perfect model, this is how it should fly.’” But, he adds, “because the model is not perfect, if you play out that same solution, it completely misses.”
So a separate control system takes over once the glider is in the air. The heart of that system is what Tedrake describes as a library of trajectories: Sensors report on the glider’s position, and the control system looks up a trajectory that will take it to the perch.
Of course, if the library had to record a separate trajectory for every possible point in space, it would be too large to store or search. So the control system also includes algorithms that look at the glider’s position and then nudge it onto the nearest stored trajectory. The addition of these algorithms, Tedrake explains, makes the trajectories look like funnels: They have wide mouths that encompass a range of possible starting positions, but they all lead to the same target.
Because the algorithms have to be executed on the fly, they drastically simplify the complex mathematics of stall. But by using techniques developed at MIT’s Laboratory for Information and Decision Systems, Tedrake and Cory were able to mathematically determine the range of conditions under which those simplifications would work — the width of the funnels’ mouths. Cory describes this approach in his dissertation, which earned him Boeing’s 2010 Engineering Student of the Year Award.
The measure of air resistance against a body in flight is known as the “drag coefficient.” A cruising plane tries to minimize its drag coefficient, but when it’s trying to slow down, it tilts its wings back in order to increase drag. Ordinarily, it can’t tilt back too far, for fear of stall. But because Cory and Tedrake’s control system takes advantage of stall, the glider, when it’s landing, has a drag coefficient that’s four to five times that of other aerial vehicles.
For some time, the U.S. Air Force has been interested in the possibility of unmanned aerial vehicles that could land in confined spaces and has been funding and monitoring research in the area. “What Russ and Rick and their team is doing is unique,” says Gregory Reich of the Air Force Research Laboratory. “I don’t think anyone else is addressing the flight control problem in nearly as much detail.” Reich points out, however, that in their experiments, Cory and Tedrake used data from wall-mounted cameras to gauge the glider’s position, and the control algorithms ran on a computer on the ground, which transmitted instructions to the glider. “The computational power that you may have on board a vehicle of this size is really, really limited,” Reich says. Even though the MIT researchers’ course correction algorithms are simple, they may not be simple enough.
Tedrake’s lab, however, has already begun to address the problem of moving the glider’s location sensors onboard, and although Cory will be moving to California to take a job researching advanced robotics techniques for Disney, he hopes to continue collaborating with Tedrake. “I visited the Air Force, and I visited Disney, and they actually have a lot in common,” Cory says. “The Air Force wants an airplane that can land on a power line, and Disney wants a flying Tinker Bell that can land on a lantern. But the technology’s similar.”
For more information: MIT.edu