Scale invariant robot behavior with fractals

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.