Document Type

Journal Article

Publication Title

Applied Sciences (Switzerland)








School of Science


Australian Academy of Science, grant 121080864383 / Further funding information available at:


Yepes, J. C., Rúa, S., Osorio, M., Pérez, V. Z., Moreno, J. A., Al-Jumaily, A., & Betancur, M. J. (2022). Human-robot interaction torque estimation methods for a lower limb rehabilitation robotic system with uncertainties. Applied Sciences, 12(11).


Lower limb rehabilitation robot (LLRR) users, to successfully conduct isotonic exercises, require real-time feedback on the torque they exert on the robot to meet the goal of the treatment. Still, direct torque measuring is expensive, and indirect encoder-based estimation strategies, such as inverse dynamics (ID) and Nonlinear Disturbance Observers (NDO), are sensitive to Body Segment Inertial Parameters (BSIPs) uncertainties. We envision a way to minimize such parametric uncertainties. This paper proposes two human–robot interaction torque estimation methods: the Identified ID-based method (IID) and the Identified NDO-based method (INDO). Evaluating in simulation the proposal to apply, in each rehabilitation session, a sequential two-phase method: (1) An initial calibration phase will use an online parameter estimation to reduce sensitivity to BSIPs uncertainties. (2) The torque estimation phase uses the estimated parameters to obtain a better result. We conducted simulations under signal-to-noise ratio (SNR) = 40 dB and 20% BSIPs uncertainties. In addition, we compared the effectiveness with two of the best methods reported in the literature via simulation. Both proposed methods obtained the best Coefficient of Correlation, Mean Absolute Error, and Root Mean Squared Error compared to the benchmarks. Moreover, the IID and INDO fulfilled more than 72.2% and 88.9% of the requirements, respectively. In contrast, both methods reported in the literature only accomplish 27.8% and 33.3% of the requirements when using simulations under noise and BSIPs uncertainties. Therefore, this paper extends two methods reported in the literature and copes with BSIPs uncertainties without using additional sensors.



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Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.