Stochastic Estimation of Human Ankle Mechanical Impedance in Lateral/Medial Rotation

2014 ◽  
Author(s):  
Evandro M. Ficanha ◽  
Mohammad Rastgaar
Keyword(s):  
Degrees Of Freedom ◽  
Muscle Activation ◽  
Transfer Functions ◽  
Linear Time ◽  
Mechanical Impedance ◽  
Linear Time Invariant ◽  
Ankle Impedance ◽  
Human Ankle ◽  
Medial Rotation ◽  
The Difference

This article compares stochastic estimates of human ankle mechanical impedance when ankle muscles were fully relaxed and co-contracting antagonistically. We employed Anklebot, a rehabilitation robot for the ankle to provide torque perturbations. Surface electromyography (EMG) was used to monitor muscle activation levels and these EMG signals were displayed to subjects who attempted to maintain them constant. Time histories of ankle torques and angles in the lateral/medial (LM) directions were recorded. The results also compared with the ankle impedance in inversion-eversion (IE) and dorsiflexion-plantarflexion (DP). Linear time-invariant transfer functions between the measured torques and angles were estimated for the Anklebot alone and when a human subject wore it; the difference between these functions provided an estimate of ankle mechanical impedance. High coherence was observed over a frequency range up to 30 Hz. The main effect of muscle activation was to increase the magnitude of ankle mechanical impedance in all degrees of freedom of ankle.

scholarly journals Stochastic Estimation of the Multi-Variable Mechanical Impedance of the Human Ankle With Active Muscles

2010 ◽  
Author(s):  
Mohammad A. Rastgaar ◽  
Patrick Ho ◽  
Hyunglae Lee ◽  
Hermano Igo Krebs ◽  
Neville Hogan
Keyword(s):  
Muscle Activation ◽  
Transfer Functions ◽  
Linear Time ◽  
Plantar Flexion ◽  
Mechanical Impedance ◽  
Linear Time Invariant ◽  
Ankle Muscles ◽  
Human Ankle ◽  
Time Histories ◽  
The Difference

This article compares stochastic estimates of multi-variable human ankle mechanical impedance when ankle muscles were fully relaxed, actively generating ankle torque or co-contracting antagonistically. We employed Anklebot, a rehabilitation robot for the ankle, to provide torque perturbations. Muscle activation levels were monitored electromyographically and these EMG signals were displayed to subjects who attempted to maintain them constant. Time histories of ankle torques and angles in the Dorsi-Plantar flexion (DP) and Inversion-Eversion (IE) directions were recorded. Linear time-invariant transfer functions between the measured torques and angles were estimated for the Anklebot alone and when it was worn by a human subject, the difference between these functions providing an estimate of ankle mechanical impedance. High coherence was observed over a frequency range up to 30 Hz. The main effect of muscle activation was to increase the magnitude of ankle mechanical impedance in both DP and IE directions.

scholarly journals Stochastic Estimation of Multi-Variable Human Ankle Mechanical Impedance

2009 ◽  
Author(s):  
Mohammad A. Rastgaar ◽  
Patrick Ho ◽  
Hyunglae Lee ◽  
Hermano Igo Krebs ◽  
Neville Hogan
Keyword(s):  
Transfer Functions ◽  
Linear Time ◽  
Plantar Flexion ◽  
Mechanical Impedance ◽  
Linear Time Invariant ◽  
Human Ankle ◽  
Time Histories ◽  
The Difference ◽  
Time Invariant ◽  
Impedance Functions

This article presents preliminary stochastic estimates of the multi-variable human ankle mechanical impedance. We employed Anklebot, a rehabilitation robot for the ankle, to provide torque perturbations. Time histories of the torques in Dorsi-Plantar flexion (DP) and Inversion-Eversion (IE) directions and the associated angles of the ankle were recorded. Linear time-invariant transfer functions between the measured torques and angles were estimated for the Anklebot and when the Anklebot was worn by a human subject. The difference between these impedance functions provided an estimate of the mechanical impedance of the ankle. High coherence was observed over a frequency range up to 30 Hz, indicating that this procedure yielded an accurate measure of ankle mechanical impedance in DP and IE directions.

scholarly journals Interpretation of the Directional Properties of Voluntarily Modulated Human Ankle Mechanical Impedance

2010 ◽  
Author(s):  
Patrick Ho ◽  
Hyunglae Lee ◽  
Mohammad A. Rastgaar ◽  
Hermano Igo Krebs ◽  
Neville Hogan
Keyword(s):  
Muscle Activation ◽  
Mechanical Impedance ◽  
In Vivo Studies ◽  
General Representation ◽  
Quantitative Characterization ◽  
Ankle Impedance ◽  
Human Ankle ◽  
Electromyographic Recording

This article presents the results of two in-vivo studies providing measurements of human static ankle mechanical impedance. Accurate measurements of ankle impedance when muscles were voluntarily activated were obtained using a therapeutic robot, Anklebot, and an electromyographic recording system. Important features of ankle impedance, and their variation with muscle activity, are discussed, including magnitude, symmetry and directions of minimum and maximum impedance. Voluntary muscle activation has a significant impact on ankle impedance, increasing it by up to a factor of three in our experiments. Furthermore, significant asymmetries and deviations from a linear two-spring model are present in many subjects, indicating that ankle impedance has a complex and individually idiosyncratic structure. We propose the use of Fourier series as a general representation, providing both insight and a precise quantitative characterization of human static ankle impedance.

Instrumented Walkway for Estimation of the Ankle Impedance in Dorsiflexion-Plantarflexion and Inversion-Eversion During Standing and Walking

2015 ◽  
Author(s):  
Evandro M. Ficanha ◽  
Guilherme Ribeiro ◽  
Mohammad Rastgaar Aagaah
Keyword(s):  
Degrees Of Freedom ◽  
Force Plate ◽  
Mechanical Impedance ◽  
Standing Position ◽  
Camera System ◽  
Ankle Impedance ◽  
System A ◽  
Human Ankle ◽  
Applied Forces ◽  
And Inversion

This paper describes in detail the fabrication of an instrumented walkway for estimation of the ankle mechanical impedance in both dorsiflexion-plantarflexion (DP) and in inversion-eversion (IE) directions during walking in arbitrary directions and standing. The platform consists of two linear actuators, each capable of generating ±351.3 N peak force that are mechanically coupled to a force plate using Bowden cables. The applied forces cause the force plate to rotate in two degrees of freedom (DOF) and transfer torques to the human ankle to generate DP and IE rotations. The relative rotational motion of the foot with respect to the shin is recorded using a motion capture camera system while the forces applied to the foot are measured with the force plate, from which the torques applied to the ankle are calculated. The analytical methods required for the estimation of the ankle torques, rotations, and impedances are presented. To validate the system, a mockup with known stiffness was used, and it was shown that the developed system was capable of properly estimating the stiffness of the mockup in two DOF with less than 5% error. Also, a preliminary experiment with a human subject in standing position was performed, and the estimated quasi-static impedance of the ankle was estimated at 319 Nm/rad in DP and 119 Nm/rad in IE.

Estimation of the 2-DOF Time-Varying Impedance of the Human Ankle

2017 ◽  
Author(s):  
Evandro Ficanha ◽  
Guilherme Aramizo Ribeiro ◽  
Lauren Knop ◽  
Mohammad Rastgaar Aagaah
Keyword(s):  
Degrees Of Freedom ◽  
Muscle Activation ◽  
Stance Phase ◽  
Impedance Control ◽  
The Body ◽  
Time Varying ◽  
Ankle Impedance ◽  
Impedance Modulation ◽  
Human Ankle ◽  
Vibrating Platform

The human ankle plays a major role in locomotion as it the first major joint to transfer the ground reaction torques to the rest of the body while providing power for locomotion and stability. One of the main causes of the ankle impedance modulation is muscle activation [1, 2], which can tune the ankle’s stiffness and damping during the stance phase of gait. The ankle’s time-varying impedance is also task dependent, meaning that different activities such as walking at different speeds, turning, and climbing/descending stairs would impose different profiles of time-varying impedance modulation. The impedance control is commonly used in the control of powered ankle-foot prostheses; however, the information on time-varying impedance of the ankle during the stance phase is limited in the literature. The only previous study during the stance phase, to the best of the authors knowledge, reported the human ankle impedance at four points of the stance phase in dorsiflexion-plantarflexion (DP) [1] during walking. To expand previous work and estimate the impedance in inversion-eversion (IE), a vibrating platform was fabricated (Fig. 1) [3]. The platform allows the ankle impedance to be estimated at 250 Hz in both DP and IE, including combined rotations in both degrees of freedom (DOF) simultaneously. The results can be used in a 2-DOF powered ankle-foot prosthesis developed by the authors, which is capable of mimicking the ankle kinetics and kinematics in the frontal and sagittal planes [4]. The vibrating platform can also be used to tune the prosthesis to assure it properly mimics the human ankle dynamics. This paper describes the results of the preliminary experiments using the vibrating platform on 4 male subjects. For the first time, the time-varying impedance of the human ankle in both DP and IE during walking in a straight line are reported.

scholarly journals Quantitative Characterization of Steady-State Ankle Impedance With Muscle Activation

2010 ◽  
Author(s):  
Hyunglae Lee ◽  
Patrick Ho ◽  
Mohammad A. Rastgaar ◽  
Hermano Igo Krebs ◽  
Neville Hogan
Keyword(s):  
Steady State ◽  
Vector Field ◽  
Degrees Of Freedom ◽  
Muscle Activation ◽  
Human Subjects ◽  
Mechanical Impedance ◽  
Field Analysis ◽  
Lower Extremity Function ◽  
Ankle Impedance

Characterization of multi-variable ankle mechanical impedance is crucial to understanding how the ankle supports lower-extremity function during interaction with the environment. This paper reports quantification of steady-state ankle impedance when muscles were active. Vector field approximation of repetitive measurements of the torque-angle relation in two degrees of freedom (inversion/eversion and dorsiflexion/plantarflexion) enabled assessment of spring-like and non-spring-like components. Experimental results of eight human subjects showed direction-dependent ankle impedance with greater magnitude than when muscles were relaxed. In addition, vector field analysis demonstrated a non-spring-like behavior when muscles were active, although this phenomenon was subtle in the unimpaired young subjects we studied.

Complementary Sensitivity Design of PID Controllers for Arbitrary-Order Transfer Functions With Time Delay

2008 ◽  
Author(s):  
Tooran Emami ◽  
John M. Watkins
Keyword(s):  
Time Delay ◽  
Transfer Functions ◽  
Linear Time ◽  
Order System ◽  
Pid Controllers ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Plant Transfer ◽  
Time Invariant

A graphical technique for finding all proportional integral derivative (PID) controllers that stabilize a given single-input-single-output (SISO) linear time-invariant (LTI) system of any order system with time delay has been solved. In this paper a method is introduced that finds all PID controllers that also satisfy an H∞ complementary sensitivity constraint. This problem can be solved by finding all PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. A key advantage of this procedure is the fact that it does not require the plant transfer function, only its frequency response.

Optimal Nonlinear Estimation of Linear Stochastic Systems: The Multivariable Extension

1996 ◽  
Vol 118 (2) ◽  
pp. 350-353 ◽  
Author(s):  
M. A. Hopkins ◽  
H. F. VanLandingham
Keyword(s):  
Stochastic Systems ◽  
Transfer Functions ◽  
Mimo Systems ◽  
Linear Time ◽  
Nonlinear Method ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Time Invariant ◽  
Time Systems

This paper extends to multi-input multi-output (MIMO) systems a nonlinear method of simultaneous parameter and state estimation that appeared in the ASME JDSM&C (September, 1994), for single-input single-output (SISO) systems. The method is called pseudo-linear identification (PLID), and applies to stochastic linear time-invariant discrete-time systems. No assumptions are required about pole or zero locations; nor about relative degree, except that the system transfer functions must be strictly proper. In the earlier paper, proofs of optimality and convergence were given. Extensions of those proofs to the MIMO case are also given here.

Zeno-free adaptive event-triggered control design

2018 ◽  
Vol 41 (8) ◽  
pp. 2328-2337 ◽  
Author(s):  
Hassan Adloo ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Degrees Of Freedom ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Performance Criterion ◽  
Linear Time Invariant ◽  
Event Triggering ◽  
Linear Time Invariant Systems ◽  
System States ◽  
Time Invariant ◽  
Event Triggered

This paper presents a new general framework for adaptive event-triggered control strategy to extend average inter-event interval, while maintaining the performance of the system. The proposed event-triggering mechanism is acquired from input to state stability conditions, which is defined in terms of system states as well as an adaptation parameter. Under the Lipschitz assumption, a positive lower bound on sampling durations is also established that is essential to restrain the Zeno behavior. Applying the proposed method to linear time-invariant systems, leads to sufficient conditions to guarantee asymptotic stability in the form of matrix inequalities. Moreover, it is shown that there exist more degrees of freedom to improve the performance criterion from theoretical aspects. Finally, in order to show capability of the proposed method and its better performance compared with some recent works, numerical simulations are presented.

Parameter Uncertainty Modeling Using the Multidimensional Principal Curves

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
M. Sepasi ◽  
F. Sassani ◽  
R. Nagamune
Keyword(s):  
Transfer Functions ◽  
Linear Time ◽  
Optimization Technique ◽  
Parametric Uncertainty ◽  
Uncertainty Modeling ◽  
Principal Component ◽  
Linear Matrix ◽  
Linear Time Invariant ◽  
Uncertain Variables ◽  
Uncertainty Model

This paper proposes a technique to model uncertainties associated with linear time-invariant systems. It is assumed that the uncertainties are only due to parametric variations caused by independent uncertain variables. By assuming that a set of a finite number of rational transfer functions of a fixed order is given, as well as the number of independent uncertain variables that affect the parametric uncertainties, the proposed technique seeks an optimal parametric uncertainty model as a function of uncertain variables that explains the set of transfer functions. Finding such an optimal parametric uncertainty model is formulated as a noncovex optimization problem, which is then solved by a combination of a linear matrix inequality and a nonlinear optimization technique. To find an initial condition for solving this nonconvex problem, the nonlinear principal component analysis based on the multidimensional principal curve is employed. The effectiveness of the proposed technique is verified through both illustrative and practical examples.

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