Soft robots have applications in safe human-robot interactions, manipulation of fragile objects, and locomotion in challenging and unstructured environments. In this paper, we present a computational method for augmenting soft robots with proprioceptive sensing capabilities. Our method automatically computes a minimal stretch-receptive sensor network to user-provided soft robotic designs, which is optimized to perform well under a set of user-specified deformation-force pairs. The sensorized robots are able to reconstruct their full deformation state, under interaction forces. We cast our sensor design as a sub-selection problem, selecting a minimal set of sensors from a large set of fabricable ones which minimizes the error when sensing specified deformation-force pairs. Unique to our approach is the use of an analytical gradient of our reconstruction performance measure with respect to selection variables. We demonstrate our technique on a bending bar and gripper example, illustrating more complex designs with a simulated tentacle.
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