Compact Optical Single-axis Joint Torque Sensor Using Redundant Photo-Reflectors and Quadratic-Programming Calibration

Abstract

This study proposes a non-contact photo-reflector-based joint torque sensor for precise joint-level torque control and safe physical interaction. Current-sensor-based torque estimation in many collaborative robots suffers from poor low-torque accuracy due to gearbox stiction/friction and current-torque nonlinearity, especially near static conditions. The proposed sensor optically measures micro-deformation of an elastic structure and employs a redundant array of photo-reflectors arranged in four directions to improve sensitivity and signal-to-noise ratio. We further present a quadratic-programming-based calibration method that exploits redundancy to suppress noise and enhance resolution compared to least-squares calibration. The sensor is implemented in a compact form factor (96 mm diameter, 12 mm thickness). Experiments demonstrate a maximum error of 0.083%FS and an RMS error of 0.0266 Nm for z-axis torque measurement. Calibration tests show that the proposed calibration achieves a 3 sigma resolution of 0.0224 Nm at 1 kHz without filtering, corresponding to a 2.14 times improvement over the least-squares baseline. Temperature chamber characterization and rational fitting based compensation mitigate zero drift induced by MCU self heating and motor heat. Motor-level validation via torque control and admittance control confirms improved low torque tracking and disturbance robustness relative to current-sensor-based control.

Figures (13)

• Figure 1: Configuration and operating principle of the proposed sensor. When an external torque is applied, the reflective surface rotates, altering the amount of light reflected toward the photo-reflector; this change in reflected intensity causes the output voltage to increase or decrease accordingly.
• Figure 2: Assembly of the printed circuit board (PCB) and the elastic structure, and parameters of the elastic beam.
• Figure 3: Schematic illustration of the elastic structure. Here, $\Delta r_t$ denotes the bending angle induced by $T_z$, and $F_A$ represents the force applied due to $T_z$.
• Figure 4: Assembly overview: (a) photograph of the assembled PCB and elastic structure; (b) PCB layout showing the sensor location; (c) FEA of the elastic structure.
• Figure 5: Calibration setup: (a) photograph of the calibration setup using the ATI MINI85, the proposed sensor, and a lever arm; (b) schematic diagram of the communication interfaces and experimental devices used for the calibration setup.