June 2013

The fascination of nature informing technology continues. I have reported periodically on robotics and locomotion in sand, most recently after my personal encounter with the ‘sand swimmer,’ *Scincus albifasciatus laterimaculatus.*Much of this extraordinary work is done by researchers at the ‘CRAB lab’ at Georgia Tech, and their cleverness doesn’t stop. Take a look at this recent report from Phys.Org - and make sure you watch the video!

Terradynamics: Technique could help designers predict how legged robots
will move on granular surfaces

This is a simulation of a bio-inspired legged robot running
on the surface of Mars using c-shaped legs. Georgia Tech researchers are
studying how legged robots move on granular materials such as sand. Credit:
Tingnan Zhang

Using a combination of theory and experiment, researchers have developed a
new approach for understanding and predicting how small legged robots – and
potentially also animals – move on and interact with complex granular materials
such as sand.

The research could help create and advance the field of “terradynamics” – a
name the researchers have given to the science of legged animals and vehicles
moving on granular and other complex surfaces. Providing equations to describe
and predict this type of movement – comparable to what has been done to predict
the motion of animals and vehicles through the air or water – could allow
designers to optimize legged robots operating in complex environments for
search-and-rescue missions, space exploration or other tasks.

Using a combination of theory and experiment, Georgia Tech
researchers have developed a new approach for understanding and predicting how
small legged robots – and potentially also animals – move on and interact with
complex granular materials such as sand. Credit: Inertia Films

“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.”

Robots such as the Mars Rover have depended on wheels for moving in complex
environments such as sand and rocky terrain. Robots envisioned for autonomous
search-and-rescue missions also rely on wheels, but as the vehicles become
smaller, designers may need to examine alternative means of locomotion, Goldman
said.

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.

The key insight, according to Goldman, was that the forces applied to
independent elements of the robot legs could be simply summed together to
provide a reasonably accurate measure of the net force on a robot moving through
granular media. That technique, known as linear superposition, worked
surprisingly well for legs moving in diverse kinds of granular media.

“We discovered that 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.”

Georgia Tech professor Daniel Goldman and postdoctoral
fellow Chen Li watch a robot traverse a track bed of poppy seeds as part of a
study into how animals and robots move on granular surfaces. Credit: Gary
Meek

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.”

Aerodynamic designers have long used a series of equations known as
Navier-Stokes to describe the movement of vehicles through the air. Similarly,
these equations also allow hydrodynamics designers to know how submarines and
other vehicles move through water. “Terradynamics” could provide designers with
an efficient technique for understanding motion through media that flows around
legs of terrestrial animals and robots.

“Using terradynamics, our simulation is not only as accurate as the
established discrete element method (DEM) simulation, but also much more
computationally efficient,” said Zhang, who is a graduate student in Goldman’s
laboratory. “For example, to simulate one second of robot locomotion on a
granular bed of five million poppy seeds takes the DEM simulation a month using
computers in our lab. Using terradynamics, the simulation takes only 10
seconds.”

The six-legged experimental robot was just 13 centimeters long and weighed
about 150 grams. Robots of that size could be used in the future for
search-and-rescue missions, or to scout out unknown environments such as the
surface of Mars. They could also provide biologists with a better understanding
of how animals such as sand lizards run and kangaroo rats hop on granular media.

“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.”

Beyond optimizing the design of future small robots, the work could also lead
to a better understanding of the complex environment through which they will
have to move.

“We think that the kind of approach we are taking allows us to ask questions
about the physics of granular materials that no one has asked before,” Goldman
added. “This may reveal new features of granular materials to help us create
more comprehensive models and theories of motion. We are now beginning to get
the rules of how vehicles move through these materials.”

More information: Chen Li, Tingnan Zhang, Daniel I. Goldman. “A Terradynamics
of Legged Locomotion on Granular Media,” Science (2013):
dx.doi.org/10.1126/science.1229163

The research was supported by the National Science Foundation Physics of
Living Systems, the Army Research Office, the Army Research Laboratory, the
Burroughs Wellcome Fund and the Miller Institute for Basic Research in Science
of the University of California, Berkeley.

Provided by Georgia Institute of Technology

[If you visit CRAB Lab’s list of press releases, you will find endless further wonders, including work on how baby turtles move through sand.] SIGNATURE

Originally published at: https://throughthesandglass.typepad.com/through_the_sandglass/2013/06/index.html