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A Compact PCB-Integrated Inductive Six-Axis Force/Torque Sensor
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DOI：10.1109/JSEN.2026.3683368.png)
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Abstract
En 中文
This article presents a compact six-axis force/torque (F/T) sensor based on inductive displacement measurement with full PCB integration of sensing and electronics. A flexure structure and conductive target plate are co-designed with multilayer planar and vertical coils so that each wrench component produces a distinct inductive response. Finite-element analysis yields a 6 × 6 stiffness matrix that guides the flexure geometry, resulting in a sensor with 85-mm diameter, 36-mm height, and ranges of ±890 N $(F_{x}, F_{y})$ , ±1435 N $(F_{z})$ , ±27 ${\mathrm {N}} \cdot {\mathrm {m}} (T_{x}, T_{y}$ ), and ±45 ${\mathrm {N}} \cdot {\mathrm {m}} (T_{z})$ . The coil array is interfaced to an inductance-to-digital converter (LDC) and a microcontroller on the same PCB, providing real-time F/T estimates via a controller area network flexible data-rate (CAN-FD) interface at up to 4 kHz without external data-acquisition hardware. The nonlinear mapping between the six-channel inductance readings and the applied wrench is identified experimentally. Several candidate models are compared, including linear, polynomial, sigmoid, Gaussian, and rational functions; a constrained rational model achieves the lowest fitting error (root mean square error (RMSE) 0.0009, linearity error 0.11%) with only five parameters and is adopted for calibration. Static experiments against a commercial six-axis F/T sensor show maximum full-scale errors of 0.64% in force and 0.75% in torque, with low cross-axis coupling and up to 55 351 quantization levels. Drop-impact tests demonstrate reliable dynamic tracking of the reference sensor over 1–200 Hz, with a mean coherence of 0.963. Under BLDC motor/inverter and Wi-Fi/RF interference, the normalized noise increase remains below 4% and 15.1%, respectively, indicating that the proposed inductive platform maintains stable performance for embedded robotic joint and end-effector sensing.
Keywords:
Calibration
force/torque (F/T) sensors
inductive sensors
robotic sensors
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