Robots

This is another conversation Gudrun had during the British
Applied Mathematics Colloquium which took place 5th – 8th April
2016 in Oxford.


Since 2002 Anette Hosoi has been Professor of Mechanical
Engineering at MIT (in Cambridge, Massachusetts). She is also a
member of the Mathematical Faculty at MIT. After undergraduate
education in Princeton she changed to Chicago for a Master's and
her PhD in physics.


Anette Hosoi wanted to do fluid dynamics even before she had any
course on that topic. Then she started to work as Assistant
Professor at MIT where everyone wanted to build robots. So she
had to find an intersection between fluid and roboters. Her first
project were Robo-snailes with her student Brian Chan. Snails
move using a thin film of fluid under their foot (and muscles).
Since then she has been working on the fascinating boundary of
flow and biomechanics.


At the BAM Colloquium she was invited for a plenary lecture on
"Marine Mammals and Fluid Rectifiers: The Hydrodynamics of Hairy
Surfaces". It started with a video of Boston dynamics which
showed the terrific abilities some human-like robots have today.
Nevertheless, these robots are rigid systems with a finite number
of degrees of freedom. Anette Hosoi is working in control and
fluid mechanics and got interested in soft systems in the context
of robots of a new type. Soft systems are a completely new way to
construct robots and for that one has to rethink everything from
the bottom up.You are a dreamer she was told for that more than
once.


For example Octopuses (and snails) move completely different to
us and most animals the classcallly designed robots with two,
four or more legs copy. At the moment the investigation of those
motions is partially triggered by the plausible visualization in
computer games and in animated movie sequences. A prominent
example for that is the contribution of two mathematicians at
UCLA to represent all interactions with snow in the animated
movie Frozen. The short verison of their task was to get the
physics right when snow falls off trees or people fall into snow
- otherwise it just doesn't look right.


To operate robots which are not built with mechanical devices but
use properties of fluids to move one needs valves and pumps to
control flow. They should be cheap and efficient and without any
moving parts (since moving parts cause problems). A first famous
example for such component is a fluid rectifier which was
patented by Nicola Tesla in the 1920ies. His device relied on
inertia. But in the small devices as necessary for the new robots
there are no inertia. For that Anette Hosoi and her group need to
implement new mechnisms. A promising effect is elasticity -
especially in channels. Or putting hair on the boundary of
channels. Hair can cause asymmetric behaviour in the system. In
one direction it bends easily with the flow while in the opposite
direction it might hinder flow.


While trying to come up with clever ideas for the new type of
robots the group found a topic which is present (almost)
everywhere in biology - which means a gold mine for research and
open questions. Of course hair is interacting with the flow and
not just a rigid boundary and one has to admit that in real life
applications the related flow area usually is not small (i.e. not
negligible in modelling and computations). Mathematically spoken,
the model needs a change in the results for the boundary layer.
This is clear from the observations and the sought after
applications. But it is clear from the mathematical model as
well. At the moment they are able to treat the case of low
Reynolds number and the linear Stokes equation which of course,
is a simplification. But for that case the new boundary
conditions are not too complicated and can be treated similar as
for porous media (i.e. one has to find an effective
permeability). Fortunately even analytic solutions could be
calculated.


As next steps it would be very interesting to model plunging
hairy surfaces into fluids or withdrawing hairy surfaces from
fluids (which is even more difficult). This would have a lot of
interesting applications and a first question could be to find
optimal hair arrangements. This would mean to copy tricks of bat
tongues like people at Brown University are doing.

References

I. E. Block Community Lecture: Razor Clams to Robots: The
Mathematics Behind Biologically Inspired Design , A. Hosoi at
SIAM Annual meeting, 2013.

B. Chan, N.J. Balmforth and A.E. Hosoi: Building a better
snail: Lubrication and adhesive locomotion, Phys. Fluids, 17,
113101, 2005.