Measuring Multi-Joint Stiffness during Single Movements: Numerical Validation of a Novel Time-Frequency Approach

Abstract

This study presents and validates a Time-Frequency technique for measuring 2-dimensional multijoint arm stiffness throughout a single planar movement as well as during static posture. It is proposed as an alternative to current regressive methods which require numerous repetitions to obtain average stiffness on a small segment of the hand trajectory. The method is based on the analysis of the reassigned spectrogram of the arm's response to impulsive perturbations and can estimate arm stiffness on a trial-by-trial basis. Analytic and empirical methods are first derived and tested through modal analysis on synthetic data. The technique's accuracy and robustness are assessed by modeling the estimation of stiffness time profiles changing at different rates and affected by different noise levels. Our method obtains results comparable with two well-known regressive techniques. We also test how the technique can identify the viscoelastic component of non-linear and higher than second order systems with a non-parametrical approach. The technique proposed here is very impervious to noise and can be used easily for both postural and movement tasks. Estimations of stiffness profiles are possible with only one perturbation, making our method a useful tool for estimating limb stiffness during motor learning and adaptation tasks, and for understanding the modulation of stiffness in individuals with neurodegenerative diseases.

Analytical Study of Perceptual and Motor Transparency in Bilateral Teleoperation

“…In our framework, the optimal parameters of the teleoperation channel as well as overall system stability depend on the impedance of the operator. Therefore, techniques for estimating the impedance of the operator during posture maintenance [57], [61] and movement [62], [63] can be used for adjustment of channel parameters. Recent attempts to incorporate the impedance of the user in teleoperation control showed promising results.…”

Arm Stiffness During Assisted Movement After Stroke: The Influence of Visual Feedback and Training

“…We modeled the upper limb as a planar double pendulum with two degrees of freedom [29], [31], [49] (1) where is the Cartesian space trajectory in response to a perturbation and , , and are the matrices of arm inertia, damping, and stiffness, respectively.…”

“…We adopted an innovative method that is capable of characterizing the impedance of the limb with a drastic reduction in movement repetitions [49]. The method is based on a time-frequency analysis and characterizes the mechanical properties of the limb by monitoring the variation of the limb's resonant frequencies in response to a single mechanical perturbation.…”

“…The assistive force, modulated based on performance, was switched off as soon as a subject reached the current target. Thus, the protocol implicitly included a steplike force perturbation at the end of each movement, as required by the new time-frequency technique for stiffness estimation [49]. We had three specific goals for this study: 1) to obtain a reliable means of measuring the mechanical proprieties of the upper limb during robotic therapy; 2) to assess the effects of robot assisted training and visual feedback on arm stiffness and viscosity; 3) to determine if the stiffness measure and its relation to training and visual feedback depend on arm position, speed and level of assistance.…”

Inter-Joint Coordination Deficits Revealed in the Decomposition of Endpoint Jerk During Goal-Directed Arm Movement After Stroke

“…Specifically, planar movements were modeled using the minimum jerk (MJ) time profile 3,48 and the sigmoidal (SG) time profile. 49 Limb segment parameters for each subject were estimated using each of the following estimation methods: Hanavan (HV); 50 Dempster (DE); 51 Chandler (CH); 52 Clauser (CL); 53 McConville (MC); 54 Zatsiorsky and Seluyanov (Z1); 55 Zatsiorsky (Z2); 56 and de Leva (DL). 57 A detailed comparison between the eight inertial parameter estimation methods can be found in.…”