Topological locomotion

We investigate how the propagation of the topological domain walls through a metamaterial based on the squares rotating mechanism can be harnessed to generate locomotion. First, we add internal elastic constraints to transform the system into a bi-stable system, with the two energy minima being the two symmetry-related rotated phases. Such metamaterial supports topological solitons that take the deformed metamaterial from one static equilibrium position to another one. Remarkably, our results indicate that by combining the propagation of such finite-width topological solitons with angle-dependent friction (that can be easily realized by putting the system on wheels) we can realize a crawler.