Numerical model of the locomotion of oscillating ‘robots’ with frictional anisotropy on differently-structured surfaces

Abstract

In engineering materials, surface anisotropy is known in certain textured patterns that appear during the manufacturing process. In biology, there are numerous examples of mechanical systems which combine anisotropic surfaces with the motion, elicited due to some actuation using muscles or stimuli-responsive materials, such as highly ordered cellulose fiber arrays of plant seeds. The systems supplemented by the muscles are rather fast actuators, because of the relatively high speed of muscle contraction, whereas the latter ones are very slow, because they generate actuation depending on the daily changes in the environmental air humidity. If the substrate has ordered surface profile, one can expect certain statistical order of potential trajectories (depending on the order of the spatial distribution of the surface asperities). If not, the expected trajectories can be statistically rather random. The same presumably holds true for the artificial miniature robots that use actuation in combination with frictional anisotropy. In order to prove this hypothesis, we developed numerical model helping us to study abovementioned cases of locomotion in 2D space on an uneven terrain. We show that at extremely long times, these systems tends to behave according to the rules of ballistic diffusion. Physically, it means that their motion tends to be associated with the “channels” of the patterned substrate. Such a motion is more or less the same as it should be in the uniform space. Such asymptotic behavior is specific for the motion in model regular potential and would be impossible on more realistic (and complex) fractal reliefs. However, one can expect that in any kind of the potential with certain symmetry (hexagonal or rhombic, for example), where it is still possible to find the ways, the motion along fixed direction during long (or even almost infinite) time intervals is possible.