Torque-sensorless control of a high-ratio, backdrivable Wolfrom-gearbox for safe human-centered robotics

Abstract

Safe physical human–robot interaction (pHRI) with compact, high-ratio actuators remains challenging in the absence of dedicated torque sensing. While high transmission ratios enable lightweight and efficient actuation, they are widely believed to degrade the ability to detect external disturbances through motor-side measurements — yet this limitation has not been rigorously quantified. We introduce a torque-sensorless control framework for a high-ratio, backdrivable Wolfrom gearbox (222:1), combining a double-inertia analytical model with a higher-order sliding-mode disturbance observer (HOSM-DOB). The analytical model yields a closed-form expression for disturbance-detection bandwidth as a function of gear ratio and motor inertia. The HOSM-DOB estimates external torques in real time using only motor-side measurements and is integrated into an impedance controller with active inertia shaping to reduce effective reflected inertia and mitigate impact forces. Experimental validation on a single-degree-of-freedom testbed, including controlled collisions measured with a Pilz Robot Measurement System (PRMS), demonstrates torque estimation errors below 10% for soft contacts. The HOSM-DOB outperforms a classical disturbance observer by 35% in detecting high-frequency impacts. Compliance with ISO/TS 15066 safety limits is confirmed up to a maximum motor speed of 7000 rpm, comparable to existing collaborative robot platforms. The bandwidth analysis reveals a fundamental trade-off between gear ratio, motor inertia, and sensing performance, demonstrating that classical inertia-matching principles do not maximize impact detectability. The results establish that high-ratio, backdrivable actuators — when combined with observer-based control — can achieve both high torque density and safe interaction, providing a viable alternative to direct-drive and harmonic-drive solutions in human-centered robotics.