  Robots deployed at orders of magnitude different size scales, and that retain
the same desired behavior at any of those scales, would greatly expand the
environments in which the robots could operate. However it is currently not
known whether such robots exist, and, if they do, how to design them. Since
self similar structures in nature often exhibit self similar behavior at
different scales, we hypothesize that there may exist robot designs that have
the same property. Here we demonstrate that this is indeed the case for some,
but not all, modular soft robots: there are robot designs that exhibit a
desired behavior at a small size scale, and if copies of that robot are
attached together to realize the same design at higher scales, those larger
robots exhibit similar behavior. We show how to find such designs in simulation
using an evolutionary algorithm. Further, when fractal attachment is not
assumed and attachment geometries must thus be evolved along with the design of
the base robot unit, scale invariant behavior is not achieved, demonstrating
that structural self similarity, when combined with appropriate designs, is a
useful path to realizing scale invariant robot behavior. We validate our
findings by demonstrating successful transferal of self similar structure and
behavior to pneumatically-controlled soft robots. Finally, we show that biobots
can spontaneously exhibit self similar attachment geometries, thereby
suggesting that self similar behavior via self similar structure may be
realizable across a wide range of robot platforms in future.
