We introduce a soft robot actuator composed of a pre-stressed elastomer film embedded with shape memory alloy (SMA) and a liquid metal (LM) curvature sensor. SMA-based actuators are commonly used as electrically-powered limbs to enable walking, crawling, and swimming of soft robots. However, they are susceptible to overheating and long-term degradation if they are electrically stimulated before they have time to mechanically recover from their previous activation cycle. Here, we address this by

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... embedding the soft actuator with a capacitive LM sensor capable of measuring bending curvature. The soft sensor is thin and elastic and can track curvature changes without significantly altering the natural mechanical properties of the soft actuator. We show that the sensor can be incorporated into a closed-loop "bang-bang" controller to ensure that the actuator fully relaxes to its natural curvature before the next activation cycle. In this way, the activation frequency of the actuator can be dynamically adapted for continuous, cyclic actuation. Moreover, in the special case of slower, low power actuation, we can use the embedded curvature sensor as feedback for achieving partial actuation and limiting the amount of curvature change.