Soft pneumatic actuators are strong and compliant but their force-displacement relationship is hysteretic — the same position corresponds to different forces depending on the loading history. This makes closed-loop control difficult. External force sensors add bulk and fragility to systems valued precisely for their softness.

The solution embeds a conductive nickel wire inside the actuator's fiber reinforcement and measures its inductance. As the actuator deforms, the wire geometry changes, and the inductance shifts. The obvious approach — mapping inductance to displacement — inherits the hysteresis problem. Inductance-length curves show strong hysteresis, making position estimation unreliable.

But inductance-force curves at constant pressure are nearly hysteresis-free.

This is the structural insight. The hysteresis in force-displacement arises from internal friction and viscoelastic effects that depend on deformation history. But the inductance responds primarily to the geometric configuration of the wire, which at a given pressure correlates deterministically with force regardless of how the actuator reached that state. The path-dependent variable (displacement) and the path-independent variable (force at constant pressure) share the same sensor but reveal different physics.

A nonlinear hybrid observer — an Extended Kalman Filter combined with constrained optimization — resolves the remaining ambiguities where the inductance-force mapping is locally non-injective. The result is force estimation accuracy comparable to external load cells, achieved with a wire that weighs almost nothing and bends with the actuator.

The bypass is not eliminating hysteresis. It is choosing to measure a quantity that the hysteresis does not contaminate.