Magnetically Self-Sealed MR Haptic Actuator With PWM-Based Excitation and High-Fidelity Torque Control

Dong Qiang; Tian Yuan; Song Yang; Kequan Xia; Thomas Reddyhoff; Yikun Zhang; Cheng Cheng; Min Yu

cs.ROAug 20, 2026

Magnetically Self-Sealed MR Haptic Actuator With PWM-Based Excitation and High-Fidelity Torque Control

Authors: Dong Qiang, Tian Yuan, Song Yang, Kequan Xia, Thomas Reddyhoff, Yikun Zhang, Cheng Cheng, Min Yu

Organizations: Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, U.K. · School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China

Abstract

Accurate and stable torque rendering is essential for safe and perceptive human--machine interaction. Magnetorheological fluid (MRF)-based actuators offer a compact and rapidly controllable solution for haptic feedback, but their practical implementation requires reliable fluid sealing, low-hysteresis excitation, accurate torque control, and stable long-duration operation. This article presents an integrated MRF haptic system featuring a compact magnetically self-sealed rotary actuator, low-hysteresis PWM operation, high-fidelity model-based torque rendering, and stable performance during long-time operation. Magnetostatic simulation guides the arrangement of magnetic and nonmagnetic materials to focus flux in the multidisk torque and permanent-magnet sealing regions, enabling a maximum 600 N $\cdot$ mm/A output. Experiments show that higher PWM frequencies reduce hysteresis and improve repeatability. At 10 kHz, the response is represented by a nonlinear model that varies with the direction and speed of torque change. The real-time controller combines feedforward, hysteresis compensation, PI feedback, and sliding-mode correction. Compared with PID, it reduces square-wave overshoot, undershoot, and steady-state RMSE by 77.4%, 61.9%, and 68.3%, respectively. It tracks sinusoidal and biomechanics-model-based references, and a 1.5-h test shows only a 2.5 $^\circ$ C rise near the coil with no clear tracking loss. This high-fidelity torque rendering will fundamentally transform human--robot collaboration by making interactions safer, more efficient, and more intuitive.

Figures & tables

Fig. 1: Representative application example of the proposed MRF rotary haptic actuator in robot-assisted surgery. The operator manipulates the user-side haptic interface to generate motion commands for the surgical robot, which reproduces the commanded motion in the task environment and performs tool–tissue interaction. The resulting interaction force/torque signal is transmitted back to the user-side interface and rendered by the MRF actuator as controllable resistive torque, thereby providing the operator with real-time haptic feedback during manipulation.

Fig. 2: MRF haptic actuator architecture and operating principle of the proposed magnetically self-sealed MRF haptic actuator. (a) Overall sectional view of the integrated rotary actuator. (b) Exploded view of the prototype assembly. (c) Enlarged sealing region, where the permanent magnet forms a dedicated sealing flux path and the flux-focusing teeth locally enhance the magnetic field for MRF sealing. (d) Enlarged working region enabling efficient field-dependent modulation of the magnetorheological effect for controllable torque generation. (e) Torque-feedback mechanism of the rotary haptic interface. (f) PWM-controlled MRF shear mechanism, in which the drive current excites the coil, the resulting magnetic field induces particle-chain structures across the shear gap, and the resistance of these structures to relative disk motion produces a continuously adjustable resistive torque. The sealing and working regions are designed as magnetically decoupled functional zones, so that the sealing field stabilizes the MRF distribution without significantly disturbing the controllable torque-generation region.

Symbol	Parameter	Value
$N_{c}$	Coil turns	1000
$D_{s}$	Main shaft diameter	6 mm
$D_{j}$	Actuator outer diameter	68.4 mm
$H_{j}$	Actuator height	19.8 mm
$g_{w}$	MRF working gap	0.2 mm
$g_{s}$	Seal gap	0.1 mm

TABLE I: Key design parameters of the proposed MRF haptic actuator

Fig. 3: Magnetostatic field distribution of the proposed MRF haptic actuator under a coil current of 500 mA. The magnetic flux is concentrated primarily in the disk-based working region and the peripheral sealing regions, supporting controllable torque generation and magnetically assisted fluid sealing, respectively.

Fig. 4: (a) Experimental setup for open-loop characterisation and closed-loop torque-rendering experiments. (b) Signal flow for characterisation and control of the proposed MRF haptic actuator. The test rig integrates motor-driven rotary excitation, torque and encoder measurements, PWM-based power driving, and FPGA–RT real-time implementation.

Fig. 5: Open-loop characterization of the proposed MRF haptic actuator. (a) PWM-frequency-dependent torque–input hysteresis loops and extracted hysteresis metrics. (b) Hysteresis dependence on input frequency under the selected 10 kHz PWM regime. (c) Hysteresis dependence on operating range under the selected 10 kHz PWM regime. (d) Feature extraction and control-oriented model construction under the selected 10 kHz PWM regime.

Fig. 6: System architecture of the proposed MRF rotary haptic actuator for torque rendering in robot-assisted surgery. The operator commands the surgical robot through the user-side interface, while the resulting tool–tissue interaction force/torque is converted into a torque reference and tracked by the hierarchical controller. The MRF actuator renders the corresponding resistive torque to the operator, thereby closing the real-time haptic feedback loop.

Parameter	Value	Note
$T_{s}$	$1.0\times 10^{-3}~\mathrm{s}$	Real-time sampling period
$T_{f,ref}$	$2.0\times 10^{-3}~\mathrm{s}$	Reference-torque filter
$T_{f,meas}$	$2.0\times 10^{-3}~\mathrm{s}$	Measured-torque filter
$\eta_{ff}$	$0.66$	Feedforward scaling
$\eta_{hys}$	$1.60$	Hysteresis-compensation scaling
$T_{min}$	$8.25~\mathrm{N\,mm}$	Lower backbone bound

TABLE II: Implementation Parameters of the Proposed HHC Controller

Fig. 7: Closed-loop comparison of PID, FF–PI, and the proposed controller under representative torque-rendering tasks. (a) Large-amplitude square-wave response. (b) Repeated square-wave response. (c) Sinusoidal response. (d) Biomechanics-inspired interaction torque profile constructed from typical needle–tissue interaction phases [ 20 , 21 , 22 ] .

Reference input	Metric	PID	FF–PI	Proposed HHC	Reduction vs. PID	Reduction vs. FF–PI
Square-wave references †	RMSE [N mm]	34.69	32.54	31.32	9.7%	3.7%
	Avg. response time [s]	0.102	0.082	0.080	21.9%	2.5%
	Avg. overshoot [N mm]	22.35	19.75	5.05	77.4%	74.4%
	Avg. undershoot [N mm]	19.53	21.30	7.43	61.9%	65.1%
	Steady-state RMSE [N mm]	6.39	4.68	2.02	68.3%	56.8%
Sinusoidal reference	Trajectory RMSE [N mm]	14.43	16.59	15.95	-10.5%	3.9%

TABLE III: Quantitative Closed-Loop Tracking Performance of Different Controllers

Fig. 8: Long-duration closed-loop stability test of the proposed MRF haptic actuator. (a) Torque tracking response and temperature variation during continuous operation. (b) Enlarged view of the selected tracking segment. (c) Thermocouple placement on the housing and top side for temperature monitoring.

Fig. 9: Haptic feedback validation based on in vivo validated biomechanical model of brain drug injection. (a) Schematic of localized brain drug injection and local pressure generation during injection. (b) Signal flow from biomechanical pressure modelling to MRF haptic torque rendering. (c) Closed-loop tracking results under three representative flow rate ( $Q_{i}$ ) and tissue permeability ( $\kappa_{i}$ ) conditions, with the corresponding tracking errors shown below.

Haptic Feedback

Haptic feedback conveys touch, force, motion, or material properties through devices that let people and robots perceive and respond to interaction.

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HapticWorld: an Interactive World Simulator with Real-time Torque Feedback

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Haptic Feedback World Models for Robotics Contact-Rich Robotic Manipulation Robotic Data Collection World Models

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Contact-rich manipulation depends on force sensing that is hard to infer from visual signals alone, both for collecting demonstrations and for training policies. Force-annotated data, however, remains hard to obtain at scale: real-robot collection ties every demonstration to physical hardware, physics simulators report contact forces that deviate systematically from real measurements, and learned world simulators, though scalable and realistic, are vision-only, so operators feel nothing during data collection and the data carries no force/torque (F/T) labels. We present HapticWorld, an interactive world simulator that predicts joint torque together with observations and renders it back to the operator in real time, closing the haptic loop between a human and a learned world model. Across three contact-rich tasks, torque feedback raises data collection throughput by 1.6 times on average. Policies trained on HapticWorld-generated demonstrations succeed in 54/60 real-world trials, approaching the 56/60 upper bound of real-world data, and far exceeding the 19/60 success rate of the vision-only baseline. Moreover, the success rates measured inside HapticWorld closely match real-world evaluation, demonstrating that HapticWorld can serve as a stand-alone F/T-conditioned policy evaluation platform.

Abstract

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