Snapping has enabled diverse unique functionalities, including amplified force and fast response, [15] high-speed motion (crawling, [16] swimming, [16,17] and jumping [18][19][20][21] ), physical intelligence, [22] and mechanical memory operation. [23] Among different soft active materials, anisotropic smart materials such as liquidcrystal polymers (LCPs) [24][25][26] have recently attracted growing interest in untethered actuation and motion [27][28][29][30] due to their two-way shape memory effects. LCPs can reversibly shrink or elongate by shifting between the nematic and the isotropic states in response to thermal, photo-, or chemical stimulations. [31,32] Light or heatinduced snapping is reported in various LCPs-based bistable soft active structures such as doubly clamped buckled strips, [6,[33][34][35] cylindrical shells, [36] twisted ribbons, [22] and circular bilayered rings. [37] However, snapping in most studies (not limited to LCPs) is not self-sustained without either manually changing the mechanical or stimuliresponsive actuation inputs [6,[16][17][18][19][20][21]33] or imposing external physical constraints. [22,34,35] This largely hinders their potential applications for untethered and autonomous motion in soft robots. Achieving self-sustained snapping under constant external stimuli remains challenging and yet largely unexplored, because it needs to repeatedly store and release the strain energy for autonomous reversible switch between two stable states in response to constant external stimuli.Here, we report leveraging wavy ring geometry for achieving self-sustained snapping and autonomous motion in a library of freestanding liquid-crystal elastomers (LCEs) rings in response to constant heat or light. In contrast to doubly clamped buckled strips, [6,[33][34][35] a circular elastic ring can undergo snapping instabilities under simple mechanical forces such as bending or twisting without the need of external physical constraints, [38,39] since the closed-loop ring shape imposes an intrinsic geometric constraint. We show that the snapping behavior and snapping-induced motion can be programmed by the geometric asymmetries during fabrication for autonomous periodic dancing or crawling motions on a hot surface or under infrared light. The highly symmetric LCE wavy ring can achieve steady-state, periodic dancinglike motions via snapping-induced non-stopping flipping. To achieve directional motion, we explore the strategy of introducing geometric asymmetries to break the symmetric shape Harnessing snapping, an instability phenomenon observed in nature (e.g., Venus flytraps), for autonomy has attracted growing interest in autonomous soft robots. However, achieving self-sustained snapping and snappingdriven autonomous motions in soft robots remains largely unexplored. Here, harnessing bistable, ribbon ring-like structures for realizing self-sustained snapping in a library of soft liquid-crystal elastomer wavy rings under constant thermal and photothermal actuation are reported. The self-sustained snapping ...

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