Subspace Identification of SISO Hammerstein Systems: Application to Stretch Reflex Identification

Jalaleddini, Kian; Kearney, Robert E.

doi:10.1109/tbme.2013.2264216

Cited by 55 publications

(25 citation statements)

References 21 publications

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“…The large variability in the polynomial nonlinearity at large velocities is likely related to the amplitude distribution of the velocity signal, which despite having velocities distributed over the entire sets of values, is highly concentrated around zero (Jalaleddini and Kearney, 2013). Finally, the reflex natural frequency was accurately estimated, and the reflex damping was slightly underestimated.…”

Section: Discussionmentioning

confidence: 99%

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Estimation of Time-Varying, Intrinsic and Reflex Dynamic Joint Stiffness during Movement. Application to the Ankle Joint

Guarín

Kearney

2017

Front. Comput. Neurosci.

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Dynamic joint stiffness determines the relation between joint position and torque, and plays a vital role in the control of posture and movement. Dynamic joint stiffness can be quantified during quasi-stationary conditions using disturbance experiments, where small position perturbations are applied to the joint and the torque response is recorded. Dynamic joint stiffness is composed of intrinsic and reflex mechanisms that act and change together, so that nonlinear, mathematical models and specialized system identification techniques are necessary to estimate their relative contributions to overall joint stiffness. Quasi-stationary experiments have demonstrated that dynamic joint stiffness is heavily modulated by joint position and voluntary torque. Consequently, during movement, when joint position and torque change rapidly, dynamic joint stiffness will be Time-Varying (TV). This paper introduces a new method to quantify the TV intrinsic and reflex components of dynamic joint stiffness during movement. The algorithm combines ensemble and deterministic approaches for estimation of TV systems; and uses a TV, parallel-cascade, nonlinear system identification technique to separate overall dynamic joint stiffness into intrinsic and reflex components from position and torque records. Simulation studies of a stiffness model, whose parameters varied with time as is expected during walking, demonstrated that the new algorithm accurately tracked the changes in dynamic joint stiffness using as little as 40 gait cycles. The method was also used to estimate the intrinsic and reflex dynamic ankle stiffness from an experiment with a healthy subject during which ankle movements were imposed while the subject maintained a constant muscle contraction. The method identified TV stiffness model parameters that predicted the measured torque very well, accounting for more than 95% of its variance. Moreover, both intrinsic and reflex dynamic stiffness were heavily modulated through the movement in a manner that could not be predicted from quasi-stationary experiments. The new method provides the tool needed to explore the role of dynamic stiffness in the control of movement.

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Section: Discussionmentioning

confidence: 99%

“…PRALDS signals have velocities distributed over the entire range of possible values and so it provides a rich set of values with which to estimate the reflex static-nonlinearity (Jalaleddini and Kearney, 2013). …”

Section: Simulation Studymentioning

confidence: 99%

Estimation of Time-Varying, Intrinsic and Reflex Dynamic Joint Stiffness during Movement. Application to the Ankle Joint

Guarín

Kearney

2017

Front. Comput. Neurosci.

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“…This algorithm provides unbiased estimates of EMG-Torque dynamics in experimental conditions where the feedback is significant as discussed in Golkar and Kearney (2015). This method uses past inputs and outputs as instrumental variables in a manner similar to the subspace Hammerstein identification approach described by Jalaleddini and Kearney (2013). …”

Section: Experimental Studymentioning

confidence: 99%

Linear Parameter Varying Identification of Dynamic Joint Stiffness during Time-Varying Voluntary Contractions

Golkar

Tehrani

Kearney

2017

Front. Comput. Neurosci.

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Dynamic joint stiffness is a dynamic, nonlinear relationship between the position of a joint and the torque acting about it, which can be used to describe the biomechanics of the joint and associated limb(s). This paper models and quantifies changes in ankle dynamic stiffness and its individual elements, intrinsic and reflex stiffness, in healthy human subjects during isometric, time-varying (TV) contractions of the ankle plantarflexor muscles. A subspace, linear parameter varying, parallel-cascade (LPV-PC) algorithm was used to identify the model from measured input position perturbations and output torque data using voluntary torque as the LPV scheduling variable (SV). Monte-Carlo simulations demonstrated that the algorithm is accurate, precise, and robust to colored measurement noise. The algorithm was then used to examine stiffness changes associated with TV isometric contractions. The SV was estimated from the Soleus EMG using a Hammerstein model of EMG-torque dynamics identified from unperturbed trials. The LPV-PC algorithm identified (i) a non-parametric LPV impulse response function (LPV IRF) for intrinsic stiffness and (ii) a LPV-Hammerstein model for reflex stiffness consisting of a LPV static nonlinearity followed by a time-invariant state-space model of reflex dynamics. The results demonstrated that: (a) intrinsic stiffness, in particular ankle elasticity, increased significantly and monotonically with activation level; (b) the gain of the reflex pathway increased from rest to around 10–20% of subject's MVC and then declined; and (c) the reflex dynamics were second order. These findings suggest that in healthy human ankle, reflex stiffness contributes most at low muscle contraction levels, whereas, intrinsic contributions monotonically increase with activation level.

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“…Hence the term 'plant inversion.' System identification has been an extensive field since the middle of last century [95,60], and continues to make progress as sensors, algorithms and processing power increase [96,97,98,99].…”

Section: Sensory Differencesmentioning

confidence: 99%

On neuromechanical approaches for the study of biological and robotic grasp and manipulation

Valero-Cuevas

Santello

2017

J NeuroEngineering Rehabil

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Biological and robotic grasp and manipulation are undeniably similar at the level of mechanical task performance. However, their underlying fundamental biological vs. engineering mechanisms are, by definition, dramatically different and can even be antithetical. Even our approach to each is diametrically opposite: inductive science for the study of biological systems vs. engineering synthesis for the design and construction of robotic systems. The past 20 years have seen several conceptual advances in both fields and the quest to unify them. Chief among them is the reluctant recognition that their underlying fundamental mechanisms may actually share limited common ground, while exhibiting many fundamental differences. This recognition is particularly liberating because it allows us to resolve and move beyond multiple paradoxes and contradictions that arose from the initial reasonable assumption of a large common ground. Here, we begin by introducing the perspective of neuromechanics, which emphasizes that real-world behavior emerges from the intimate interactions among the physical structure of the system, the mechanical requirements of a task, the feasible neural control actions to produce it, and the ability of the neuromuscular system to adapt through interactions with the environment. This allows us to articulate a succinct overview of a few salient conceptual paradoxes and contradictions regarding under-determined vs. over-determined mechanics, under- vs. over-actuated control, prescribed vs. emergent function, learning vs. implementation vs. adaptation, prescriptive vs. descriptive synergies, and optimal vs. habitual performance. We conclude by presenting open questions and suggesting directions for future research. We hope this frank and open-minded assessment of the state-of-the-art will encourage and guide these communities to continue to interact and make progress in these important areas at the interface of neuromechanics, neuroscience, rehabilitation and robotics.

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Subspace Identification of SISO Hammerstein Systems: Application to Stretch Reflex Identification

Cited by 55 publications

References 21 publications

Estimation of Time-Varying, Intrinsic and Reflex Dynamic Joint Stiffness during Movement. Application to the Ankle Joint

Estimation of Time-Varying, Intrinsic and Reflex Dynamic Joint Stiffness during Movement. Application to the Ankle Joint

Linear Parameter Varying Identification of Dynamic Joint Stiffness during Time-Varying Voluntary Contractions

On neuromechanical approaches for the study of biological and robotic grasp and manipulation

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