Perception in soft robotics is crucial to allow a safe interaction to effectively explore the environment. Despite the inherent capabilities of soft materials, embedding reliable sensing in soft actuators or robots could introduce constraints in the overall design (e.g., loss of deformability, undesired trajectories, etc.) or reduce their compliant characteristics. Consequently, an adequate stiffness for both sensor and actuator becomes a crucial design parameter. In particular, for sensing the deformation related to actuation motion, sensing and actuating strategies must work in full mechanical synergy. In this view, an inductive sensing solution is presented, exploiting open-cell foam and a copper (Cu) wire in an Inductive Foam Sensor (IFS). Due to entangled air cells high deformability is enabled upon vacuum pressure, and proprioceptive information is provided. The IFS is then successfully integrated into the earlier developed Ultralight Hybrid Pneumatic Artificial Muscle (UH-PAM), which encases an elastomeric bellow skin and plastic rings. Such sensorized UH-PAM (SUH-PAM) is capable of a high contraction ratio (54% upon −80 kPa), while the inductive sensing shows a high sensitivity of 0.01031/1% and a hysteresis of 5.35%, with an average error of 1.85%, respectively. In order to implement a robust feedback control system, an adaptable proportional sliding mode control is presented. As a result, the SUH-PAM motion can be controlled to the mm-scale, with an RMSE of 0.925 mm, and high robustness against disturbances is demonstrated.