State space navigation using geometrically symmetric inflatables

Soft robots rely on continuous control to achieve complex functionality. Their autonomous behavior is currently limited by a lack of embodied computation and the ability to store information of past events. Inflatable soft actuators typically relax once pressure is removed and, thus, do not exhibit state-space behavior when combined. As a result, rather than embodying memory and logic, inflatable soft robots implement these functions in software. Prior work has shown that mechanical instabilities can endow soft structures with discrete states, yet accessing all possible combinations of states in coupled systems remains challenging and often requires precise geometric tuning of structures. Here we demonstrate that geometric symmetry can be exploited to create truly bistable inflatable actuators with snap-up and snap-down pressures that are equal in magnitude and opposite in sign, enabling permanent memory and fully accessible state spaces using a single pressure input. By gluing two identical conical shell actuators back to back, we obtain nearly point-symmetric pressure-volume characteristics, whose absolute snapping pressures scale directly with material stiffness. As a result, nested pressure-volume curves, where actuators with higher snap-up pressures also have lower snap-down pressures, are achieved simply by varying the shear modulus of the material while keeping the geometry constant. We validate this principle through numerical simulations and experiments and show that three serially connected nested actuators can reliably access all eight global states and function as a pneumatic 1-to-3 demultiplexer. More broadly, this symmetry-based design strategy enables scalable mechanical memory and logic in soft robotic systems, reducing control complexity and opening pathways toward fully embodied pneumatic computation.