Exploring bodies of water on their surface allows robots to efficiently communicate and harvest energy from the sun. On the water surface, however, robots often face highly unstructured environments, cluttered with plant matter, animals, and debris. We report a fast (5.1 cm/s translation and 195 °/s rotation), centimeter-scale swimming robot with high maneuverability and autonomous untethered operation. Locomotion is enabled by a pair of soft, millimeter-thin, undulating pectoral fins, in which traveling waves are electrically excited to generate propulsion. The robots navigate through narrow spaces, through grassy plants, and push objects weighing over 16x their body weight. Such robots can allow distributed environmental monitoring as well as continuous measurement of plant and water parameters for aqua-farming.