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Locomotion is enabled by a pair of soft, millimeter-thin, undulating pectoral fins, in which traveling waves are electrically excited to generate propulsion. The actuators, robot design, and power supply are codesigned to enable high-performance locomotion in a scaled-down system. A single soft electrohydraulic actuator per side generates the traveling wave. A compact and lightweight power supply enables untethered operation, made possible by decreasing the operating voltage of the electrohydraulic actuators to below 500 volts and their power consumption to 35 milliwatts. By an experimental study and by modeling, we determined optimum dimensions and operating conditions across designs and size scales. The robots navigate through narrow spaces and through grassy plants and push objects weighing more than 16 times their body weight. 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