Locomotion of elastic sheets driven by curvature incompatibility

Locomotion of slender bodies on curved surfaces arises across scales, from migrating cells and tissues to cm-scale organisms. Some of these bodies harness changes in their curvature to propel themselves through space. We study this mode of motion experimentally in two systems: mm-scale active gels floating on a two-dimensional curved fluid–fluid interface (a meniscus), and a 10 cm elastic cart confined to a one-dimensional curved rail. In both cases, external stimulation induces periodic modulation of the body’s intrinsic curvature, producing motion along the non-uniformly curved substrate. Yet each system is unique: the active gel moves autonomously and changes both its position and orientation, whereas the cart’s dynamics involve inertia and exhibit richer behaviors, such as period-doubling and the onset of chaos.

We develop a minimal theoretical model in which locomotion emerges from geometric incompatibility between the body’s time-dependent intrinsic curvature and the local curvature of the substrate. Spatial and angular energy gradients generate tangential forces and torques driving translation and rotation. Experiments with sheets of fixed intrinsic curvature and numerical integration of the governing equations validate the model’s predictions. Together, these results reveal a universal mechanism by which geometric frustration in active elastic materials can generate self-propelled motion across length scales.