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7 November 2026

27 Pages

Methods for Estimating Human Joint and Endpoint Stiffness

,
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Research Unit of Advanced Robotics and Human-Centred Technologies, Università Campus Bio-Medico di Roma, 00128 Rome, Italy
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Sensors2026, 26(21), 7052;https://doi.org/10.3390/s26217052 
(registering DOI)
This article belongs to the Section Wearables

Abstract

Mechanical stiffness is the displacement-dependent component of mechanical impedance. In joint coordinates, it describes the local mapping from small angular displacements to changes in joint torque; when using Cartesian coordinates, endpoint stiffness describes the corresponding mapping from small spatial displacements to changes in endpoint force. Both quantities are relevant to neuromechanical assessment and to applications in rehabilitation and physical human–robot interaction. However, selecting an estimation method remains difficult because stiffness is not estimated and validated consistently across studies. This review provides an application-oriented synthesis of methods for estimating human joint and endpoint stiffness. Following study inclusion, methods were classified along a mutually exclusive primary axis as either perturbation-response identification, in which stiffness is derived from the mechanical response to a deliberately imposed perturbation used for identification, or non-perturbative inference, in which stiffness is inferred from measurements acquired without such an identification perturbation. Experimental conditions and sensing or modeling choices were retained as orthogonal descriptors rather than additional methodological classes. Because standardized head-to-head comparisons against common reference measurements remain scarce, the available evidence does not support a universal ranking of estimation accuracy. The proposed benchmarking framework and decision tree, therefore, match method selection to application requirements rather than prescribing a globally superior approach. The synthesis further shows that reproducible use requires a precise definition of what is estimated and under which conditions, together with sufficient methodological detail to replicate the estimation and validation procedures.

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