cs.ROMar 19, 2026

Inductance-Based Force Self-Sensing in Fiber-Reinforced Pneumatic Twisted-and-Coiled Actuators

Authors: Yunsong Zhang, Tianlin Li, Mingyang Yang, Feitian Zhang

Organizations: Robotics and Control Laboratory, School of Advanced Manufacturing and Robotics, and the State Key Laboratory of Turbulence and Complex Systems, Peking University, Beijing 100871, China

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Abstract

Fiber-reinforced pneumatic twisted-and-coiled actuators (FR-PTCAs) offer high power density and compliance but their strong hysteresis and lack of intrinsic proprioception limit effective closed-loop control. This paper presents a self-sensing FR-PTCA integrated with a conductive nickel wire that enables intrinsic force estimation and indirect displacement inference via inductance feedback. Experimental characterization reveals that the inductance of the actuator exhibits a deterministic, low-hysteresis inductance-force relationship at constant pressures, in contrast to the strongly hysteretic inductance-length behavior. Leveraging this property, this paper develops a parametric self-sensing model and a nonlinear hybrid observer that integrates an Extended Kalman Filter (EKF) with constrained optimization to resolve the ambiguity in the inductance-force mapping and estimate actuator states. Experimental results demonstrate that the proposed approach achieves force estimation accuracy comparable to that of external load cells and maintains robust performance under varying load conditions.

Figures & tables

Fig. 1: Conceptual overview of the proposed inductive self-sensing framework for FR-PTCAs. A helically wrapped conductive nickel wire enables intrinsic inductive sensing without external rigid sensors. While the inductance-length relationship exhibits strong hysteresis, the inductance-force mapping remains deterministic and low-hysteresis at constant pressures. Leveraging this property, a nonlinear hybrid observer processes inductance measurements to enable real-time estimation of actuator force and internal states.
Fig. 2: Fabrication process of the self-sensing FR-PTCA. Schematics of the fabrication platform and its stages: (a) precursor preparation and drawing, (b) conductive fiber wrapping, (c) twisting, (d) coiling.
Fig. 3: Experimental setup for the FR-PTCA. (a) Isometric Platform. (b) Isotonic Platform.
Fig. 4: Experimental characterization of the FR-PTCA. (a) Force-length relationship at constant pressures. (b) Force-pressure relationship at fixed lengths.
Fig. 5: Experimental characterization of the FR-PTCA inductance response. (a) Inductance versus output force at varying internal pressures. (b) Inductance versus internal pressure under isometric conditions for different lengths. (c) Inductance versus actuator length under isobaric conditions.
Fig. 6: Validation of the proposed data-driven self-sensing model. (a) Experimental versus estimated inductance-force relationship. (b) Model prediction of inductance versus length, illustrating indirect hysteresis compensation. (c) Fitting results of inductance versus pressure. (d) Three-dimensional visualization of the inductance-pressure-force mapping, demonstrating the generalization capability of the model across the workspace.
Fig. 7: Experimental validation of the force and displacement estimation. (a) Measured versus estimated force over time. (b) Measured versus estimated actuator length. (c) Instantaneous force estimation error. (d) Instantaneous displacement estimation error.
Fig. 8: Block diagram of the proposed control framework.
Fig. 9: Experimental results of closed-loop force control. (a),(c) Sinusoidal force tracking at 0.2 Hz and 0.05 Hz, respectively. (b),(d) Triangular force tracking at 0.2 Hz and 0.05 Hz, respectively.
TrajectoryMethodRMSEMAEImp. (%)
  (N / mm)(N / mm)(RMSE)
Force Tracking (Unit: N)
Sine (0.2 Hz)Open-Loop0.12350.0995-
Sensor FB0.07210.064941.6%
Self-Sensing0.07130.062442.3%
Triangle (0.2 Hz)Open-Loop0.11110.0899-
TABLE I: Comparison of trajectory tracking errors for different control methods
Fig. 10: Experimental results of closed-loop displacement control. (a),(b) Displacement tracking for sinusoidal trajectories at 0.2 Hz and 0.05 Hz, respectively. (c),(d) Corresponding tracking errors for the 0.2 Hz and 0.05 Hz trajectories.
Fig. 11: Experimental results of the load perturbation analysis. (a),(b) Comparison between the self-sensed force and the actual force measured by the load cell under step-change loading conditions. (c),(d) Corresponding trends trends between the measured inductance and applied force. (e) Experimental setup with randomly placed weights of varying mass.
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