This work presents a low-complexity modular sensor grid architecture to provide a smart skin to non-convex shapes, such as a robot body and legs. To configure a sensing skin shaped by arbitrary cuts and rapid changes in designs, we use a wavefront planning approach to generate a minimum-depth spanning tree of an arbitrary topology of contiguous, regularly arranged modular sensing units on a flexible substrate wired network. A Finite State Machine protocol for extracting this topology and sensor information is shown that is robust to destructive sensor loss, device failure, and transmission noise. The architecture is designed to require as little state complexity at each node as possible to minimize the area and cost of such a network implemented in printable semiconductor technology. Simulation data show recovery from network failures and extension of the architecture to larger networks with arbitrary geometry, and a sample synthesis of the verified architecture logic is shown to have a very low state and combinational logic complexity. A proof-of-concept implementation of the architecture using microcontrollers and optical proximity sensors on a flexible substrate show integration with a Scaled Composite Manufacturing process used for Biomimetic Millirobots.