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EETE APRIL 2013

ELECTRONICS IN ROBOTICS Fine-tuning legged robots’ dynamics on granular media By Julien Happich Largely inspired by nature’s most efficient solutions to locomotion problems, a team of researchers from the Georgia Institute of Technology have combined theory and experiment to better understand and predict how small legged-robots can move on and interact with complex granular materials such as sand. Dubbed “terradynamics”, this new field of research provides the equations to describe and predict how small animals and robots can move on granular and unstable terrain. Comparable to what has been done to predict the motion of animals and vehicles through the air or water, terradynamics could allow designers to optimize legged robots operating in complex environments for search-and-rescue missions, space exploration or other tasks. “We now have the tools to understand the movement of legged vehicles over loose sand in the same way that scientists and engineers have had tools to understand aerodynamics and hydrodynamics,” said Daniel Goldman, a professor in the School of Physics at the Georgia Institute of Technology. “We are at the beginning of tools that will allow us to do the design and simulation of legged-robots to not only predict their performance, but also to optimize designs and allow us to create new concepts.” Existing techniques for describing locomotion on surfaces are complex and can’t take into account the intrusion of legs into a granular surface. To improve and simplify the understanding, Goldman and collaborators Chen Li and Tingnan Zhang examined the motion of a small legged robot as it moved on granular media. Using a 3-D printer, they created legs in a variety of shapes and used them to study how different configurations affected the robot’s speed along a track bed. They then measured granular force laws from experiments to predict forces on legs, and created simulation to predict the robot’s motion. A key finding is that the forces applied to independent elements of the robot legs can be simply summed together to provide a reasonably accurate measure of the net force on a robot moving through granular media. This technique, known as linear superposition, works surprisingly well for legs moving in diverse kinds of granular media. “We discovered that Chen Li observes as a robotic arm rotates a model c-shaped leg through poppy seeds to measure ground reaction forces. (Georgia Tech Photo: Gary Meek) the force laws affecting this motion are generic in a diversity of granular media, including poppy seeds, glass beads and natural sand,” said Li, who is now a Miller postdoctoral fellow at the University of California at Berkeley. “Based on this generalization, we developed a practical procedure for non-specialists to easily apply terradynamics in their own studies using just a single force measurement made with simple equipment they can buy off the shelf, such as a penetrometer.” For more complicated granular materials, although the terradynamics approach still worked well, an additional factor – perhaps the degree to which particles resemble a sphere – may be required to describe the forces with equivalent accuracy. Beyond understanding the basic physics principles involved, the researchers also learned that convex legs made in the shape of the letter “C” worked better than other variations. “As long as the legs are convex, the robot generates large lift and small body drag, and thus can run fast,” Goldman said. “When the limb shape was changed to flat or concave, the performance dropped. This information is important for optimizing the energy efficiency of legged robots.” According to the researchers, terradynamics yields simulations that are not only as accurate as the established discrete element method (DEM) simulation, but also much more computationally efficient, taking seconds instead of weeks. The six-legged experimental robot was just 13 centimeters long and weighed about 150 grams. “From a biological perspective, this opens up a new area,” said Goldman, who has studied a variety of animals to learn how their locomotion may assist robot designers. “These are the kinds of tools that can help understand why lizards have feet and bodies of certain shapes. The problems associated with movement in sandy environments are as important to many animals as they are to robots.” Georgia Tech graduate student Tingnan Zhang and postdoctoral fellow Chen Li compare experimental data and computer simulations. (Georgia Tech Photo: Gary Meek) A simulation of a bio-inspired legged robot running on the surface of another planet using c-shaped legs. (Credit: Tingnan Zhang) www.electronics-eetimes.com Electronic Engineering Times Europe April 2013 35


EETE APRIL 2013
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