Inherently integrated microfiber-based flexible proprioceptive sensor for feedback-controlled soft actuators

Soft robots benefit from compliant actuation (pneumatic, hydraulic, electrical, magnetic, thermal, ionic) that enables large deformations, simple designs, low weight, and safety. Reliable operation in dynamic environments requires sensory feedback to monitor actuator states in real-time. Prior approaches add heterogeneous sensors (resistive, capacitive, magnetic, inductive, optical) onto or into pneumatic actuators, but this increases structural complexity and wiring/soldering, raises manufacturing costs, and introduces mechanical mismatch and poor interfacial stability. The research question is whether a pneumatic fiber-reinforced actuator can provide inherent proprioception using only its essential components, thereby simplifying construction while enabling accurate feedback control. The study proposes and validates a design where two conductive microfibers serve simultaneously as radial expansion limiting fibers and as electrodes of a capacitive bending sensor, delivering real-time proprioception without additional sensing components. Analytical and finite element models are developed to link pressure, bending, and capacitance, and the approach is demonstrated in closed-loop control and soft robotic applications (gripper and prosthetic hand).

Embedded or attached heterogeneous sensors have been integrated into soft pneumatic actuators for self-sensing, including resistive, capacitive, magnetic, inductive, and optical strain sensors. Examples include optical waveguide curvature sensors embedded in bidirectional bending actuators (Chen et al.) and feedback control using commercial flex-bend sensors (Gerboni et al.). While effective for monitoring deformation, these integrations often require intricate wiring and numerous rigid solder joints, increasing system complexity, manufacturing effort and cost, and risking interfacial failure due to mechanical mismatch between soft bodies and rigid sensor elements. Consequently, there is a need for soft actuators with inherent sensing that avoids heterogeneous components, thereby improving robustness, manufacturability, and suitability for real-world deployment.

Design: A fiber-reinforced pneumatic soft actuator comprises an elastomeric chamber, an axial strain-limiting fiber along the chamber, and helically wound radial expansion limiting fibers. Two of the radial limiting fibers are replaced by parallel conductive microfibers (radius ~100 μm) wound helically (clockwise or counterclockwise), forming a distributed capacitive bending sensor using the two conductive fibers as electrodes. Bending under pressure arises from radial confinement by helical fibers and asymmetric longitudinal stretch due to the axial strain-limiting fiber. The sensor’s capacitance decreases with bending because fiber spacing increases asymmetrically on the convex side while remaining nearly constant on the concave side. Modeling and simulation: Finite element method simulations predict bending angle versus internal pressure and distal tip trajectory. An analytical model balances pressure-induced and elastomer restoring bending moments to derive pressure–bending relationships, and a geometric formulation provides tip trajectories. A second analytical model derives capacitance C(θ) of the helical microfiber capacitor as a function of bending angle by integrating contributions of each helical turn, accounting for fiber radius, outer radius, pitch, permittivity, and azimuthal angle. Both models use measurable parameters without fitting. Fabrication: Elastomeric chambers (Dragon Skin 10 medium) are molded using 3D-printed PLA molds with helical ribs and a sacrificial steel rod; ends are capped, and an inlet tube is added. An axial Kevlar (para-aramid) fiber is laid in a longitudinal groove. Four helical radial fibers are wound: two normal Kevlar fibers in one direction and two conductive stainless-steel microfibers (Adafruit ADA-640) in the opposite direction. The assembly is encapsulated in a thin silicone layer to secure fibers. Variants include different chamber diameters (10, 14, 18 mm) and helical pitches (2–4 mm), and reconfiguration of the axial fiber (removed for extension, helically laid for twisting-extension, or regionally varied for multi-motion actuators). Characterization: Internal pressure is supplied via a pressure controller and compressor; bending angle is measured from camera images. Capacitance between conductive microfibers is measured with an LCR meter at 300 Hz. Isometric and isotonic tip forces are measured with a force gauge. Durability is evaluated over 10,000 pressure cycles. Response and recovery times are defined to 63.2% of steady-state deformation. Environmental robustness is assessed near non-conductive and conductive objects. A local field sensing configuration uses multiple microfiber electrode pairs to sense different regions in a multi-motion actuator. Control: A Two-Degree-Of-Freedom (TDOF) controller combines a disturbance observer, PID, and feedforward using a nominal actuator model. System identification (sampling 12.5 Hz, 0.01–5 Hz frequency response) provides the transfer function. The controller regulates internal pressure to maintain bending under external loads. Applications: A soft gripper with three proprioceptive actuators on a robotic arm performs pick-and-place with real-time sensing and closed-loop control against external loading. A soft prosthetic hand with five proprioceptive actuators demonstrates gesture expression/recognition and object grasping; capacitance signatures are used for simple real-time object classification.

• Inherent sensing and actuation: Two parallel conductive microfibers serve as both radial expansion limiting fibers and electrodes of a capacitive bending sensor, eliminating heterogeneous sensing components and rigid soldering.
• Actuation performance: Bending up to ~240° (experimentally demonstrated up to ~250°) with good agreement between experiments, FEM, and analytical models for bending angle vs pressure and distal tip trajectory.
• Forces: Isometric (fixed-angle) and isotonic (fixed-pressure) tip force characterizations show stable, nearly linear trends across tested angles and pressures; larger chamber diameters yield higher tip forces at a given pressure.
• Proprioceptive sensing: Capacitive response decreases monotonically with bending; analytical C(θ) model matches experiments. Reported sensitivity up to 1.2 pF rad⁻¹. Sensor exhibits negligible hysteresis across pressure cycles and flow rates, with stable response over 10,000 cycles at 90 kPa.
• Dynamics: Mechanical response time ~71 ms and recovery time ~38 ms (to 63.2% of steady-state deformation) at 50 kPa. Sensor response and recovery times ~71 ms and ~82 ms to a pressure step.
• Robustness: Actuator and sensor maintain function after significant mechanical impact (e.g., car run-over). Environmental tests show baseline capacitance shifts near conductive objects (steel, aluminum, human hand) but reproducible relative changes; negligible effect near non-conductive objects (paper, PP, glass).
• Parametric effects: Increasing chamber diameter (10 → 18 mm) increases bending range, tip force, and sensor sensitivity; helical pitch (2–4 mm) has negligible effect on main performance. Removing or helically arranging the axial fiber enables extension and twisting-extension motions; a multimotion actuator integrates extension, twisting-extension, and bending with local proprioceptive sensing in each region.
• Closed-loop control under load: With TDOF control, a single actuator maintained ~43.5° bending at 36 kPa under external loads up to 120 g by adjusting internal pressure; without TDOF, bending collapsed above ~60 g. In a three-finger gripper, closed-loop control sustained payloads up to ~155 g versus ~35 g open-loop (≈3.3× improvement).
• Prosthetic hand and classification: Five-finger prosthetic hand expresses gestures (rock–paper–scissors) with distinct capacitance signatures per finger, enabling gesture recognition. Simple real-time classification of four objects (balloon, marker pen, apple, ball) achieved ~91.25% accuracy over 100 trials.
• Cost and manufacturability: Built entirely from commercially available materials; estimated cost per actuator (including sensing) ~USD 0.92; simplified wiring with no rigid soldering improves practicality and reliability.

The study addresses the challenge of reliable, real-time feedback in soft pneumatic actuators without adding heterogeneous sensors. By co-opting conductive microfibers already needed for fiber reinforcement as capacitive electrodes, the actuator achieves integrated proprioception while reducing system complexity, wiring, and interfacial mismatch. Analytical and FEM models accurately predict mechanical bending and capacitive behavior using only measurable parameters, enabling model-based design and control. The negligible hysteresis and high durability underpin stable sensing-actuation coupling, supporting closed-loop operation. The TDOF controller leverages the proprioceptive signal to maintain target bending under external disturbances, and application demonstrations (gripper, prosthetic hand) show real-time sensing, robust manipulation, and preliminary object classification. Together, the results validate inherent proprioception as a practical, low-cost pathway to intelligent, feedback-controlled soft actuators suitable for real-world human–robot interaction.

The work introduces a microfiber-based capacitive proprioceptive sensor inherently integrated into a fiber-reinforced pneumatic actuator by using two conductive microfibers as both reinforcement and electrodes. The actuators deliver large bending, fast response, negligible hysteresis, long-cycle durability, and accurate, model-predictable sensing. The approach simplifies fabrication and wiring, enhances interfacial stability, reduces cost, and enables robust closed-loop control and practical use in soft grippers and prosthetic hands. Future research directions include: (1) increasing output force via higher-modulus elastomers; (2) systematic exploration of structural/material parameters (fiber diameter, wall thickness, chamber modulus) to further optimize performance and refine analytical models; (3) improving adhesion between microfibers and elastomer to prevent fiber drift; and (4) advancing control and classification algorithms (e.g., machine learning) to enhance manipulation and object recognition.

• Baseline capacitance is sensitive to nearby conductive objects, which can shift absolute readings; although relative changes remain reproducible, shielding or compensation may be needed in certain environments.
• Output force can be limited by elastomer mechanical properties; stronger materials may be required for heavier-load applications.
• Potential drift of microfibers within the elastomer matrix could affect long-term stability; improved microfiber–elastomer adhesion is suggested.
• Detailed parameter dependence (fiber diameter, wall thickness, material modulus) on actuation and sensing requires further study to optimize performance and update models.