Animals coordinate their movements through distributed neural circuits, but soft robots still typically depend on external, centralized electronics for control. Building soft robots that operate without centralized electronic controllers while remaining responsive to their environment remains a frontier challenge in soft robotics. In this work we introduce a soft-robot control architecture inspired by leaky integrate-and-fire models of biological neural circuits. The Pneumatic neuron (Pneu-ron) is a soft actuator that unifies energy conversion, logic, and actuation in one component. Each module combines a low-boiling-point fluid (LBF), a heater, and a mechanical switch into a self-excitable unit. Boiling the LBF inflates the module and triggers excitation and inhibition of adjacent modules in a process we call "inflate-and-fire". When interconnected into excitatory-inhibitory rings, Pneu-rons generate stable, sequential oscillations whose frequency emerges from the material dynamics and environmental conditions. By harnessing the inflation of Pneu-rons for actuation these networks can drive oscillatory locomotion of soft robots. Pneu-ron networks sustain oscillation under mechanical load and thermal variations, adapting through material physics rather than computation. Dynamical modeling of these networks reveals a dimensionless bifurcation diagram that dictates the network's oscillatory behavior. Encoding logic and actuation into material-level modules presents a new avenue for adaptive, electronics controller-free, soft robots.

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