Self-powered shape-transforming membranes: an active matter approach to soft robotics.

We present the first example of an autonomous, extended, shape-transforming sheet made from a gel that shrinks and swells in response to the Belousov-Zhabotinsky (BZ) reaction. BZ waves traveling within the gel induce periodic flapping of the sheets. We compute the relationship between the reference Gaussian curvature and the reaction phase using the theory of non-Euclidean elasticity and show that this quantitatively predicts the evolving three-dimensional shape. We account for deviations from the purely geometric theory due to finite-thickness effects. This system demonstrates behavior reminiscent of biological organisms: autonomous shape changes of a soft slender structure powered by chemical free energy extracted from the environment. Our results constitute an important step towards the realization of autonomous soft machines.