Transversely curved composite shells of liquid crystal elastomer and polyethylene terephthalate with innervated electrodes present millisecond‐scale actuation with ≈200 mW electrical power inputs at low voltages (≈1 V). The molecular orientation is aligned to direct the thermomechanical work‐content to evert the native curvature. When powered, the curved structure initially remains latent and builds up strain energy. Thereafter, the work content is released in an ms‐scale impulse. The thin‐film actuators are powered against opposing loads to perform up to 10−5 J of work. High speed imaging reveals tip velocities of several 100 mm s−1 with powers approaching 10−4 J s−1. The design eschews bistability. After snap‐through, when the power is off, the actuator spontaneously resets to its native state. The actuation profiles are functions of the geometry and the electrical pulse patterns. The latency of actuation is reduced by powering the actuators with pulses that trigger snap‐through, allow its reset to the native state, but prevent its cooling to the ambient before subsequent actuation cycles. The actuation is harnessed in sub‐gram scale robots, including water‐strider mimicking configurations and steerable robots that can navigate on compliant (sand) and hard (slippery) surfaces. A viable template for impulsive actuation using frugal electrical power emerges.