Mathematics

Micro-organisms propel themselves in viscous environments by the periodic, nonreciprocal beating of slender appendages known as flagella. Active materials have been widely exploited to mimic this form of locomotion. However, the realization of such coordinated beating in biomimetic flagella requires complex actuation modulated in space and time. We prove through experiments on polyelectrolyte hydrogel samples that directed undulatory locomotion of a soft robotic swimmer can be achieved by untethered actuation from a uniform and static electric field. A minimal mathematical model is sufficient to reproduce, and thus explain, the observed behavior. The periodic beating of the swimming hydrogel robot emerges from flutter instability thanks to the interplay between its active and passive reconfigurations in the viscous environment. Interestingly, the flutter-driven soft robot exhibits a form of electrotaxis whereby its swimming trajectory can be controlled by simply reorienting the electric field. Our findings trace the route for the embodiment of mechanical intelligence in soft robotic systems by the exploitation of flutter instability to achieve complex functional responses to simple stimuli. While the experimental study is conducted on millimeter-scale hydrogel swimmers, the design principle we introduce requires simple geometry and is hence amenable for miniaturization via micro-fabrication techniques. We believe it may also be transferred to a wider class of soft active materials.