Optimal Control and Forward Dynamics of Human Periodic Motions Using Fourier Series for Muscle Excitation Patterns

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
Mohammad Sharif Shourijeh ◽  
John McPhee
Keyword(s):  
Optimal Control ◽  
Fourier Series ◽  
Dynamic Optimization ◽  
Muscle Activation ◽  
Metabolic Energy ◽  
Forward Dynamics ◽  
Objective Functions ◽  
Periodic Motions ◽  
Dynamic Simulations ◽  
Time Integral

Forward dynamic simulations of a periodic forearm motion were developed in order to explore the efficiency of using a Fourier-series-based parameterization function for muscle excitations within dynamic optimization. The specific objectives of this study were to develop such a simulation and validate the predictions. Several time-integral objective functions, including muscle activation effort and metabolic energy, were used to see the effects of each on the optimal results. For validation, the motion and muscle electromyograms (EMGs) of three adult subjects were captured, where each trial was replicated twice. Fourier-series pattern parameterization was found to be an efficient choice for the muscle excitations in simulating human musculoskeletal dynamics.

Bifurcation Trees of Periodic Motions to Chaos in a Parametric, Quadratic Nonlinear Oscillator

2014 ◽  
Vol 24 (05) ◽  
pp. 1450075 ◽  
Author(s):  
Albert C. J. Luo ◽  
Bo Yu
Keyword(s):  
Fourier Series ◽  
Nonlinear Systems ◽  
Analytical Solutions ◽  
Nonlinear Oscillator ◽  
Series Solution ◽  
Parametric Oscillator ◽  
Periodic Motions ◽  
Parametric Oscillators ◽  
Harmonic Term ◽  
Nonlinear Behaviors

In this paper, bifurcation trees of periodic motions to chaos in a parametric oscillator with quadratic nonlinearity are investigated analytically as one of the simplest parametric oscillators. The analytical solutions of periodic motions in such a parametric oscillator are determined through the finite Fourier series, and the corresponding stability and bifurcation analyses for periodic motions are completed. Nonlinear behaviors of such periodic motions are characterized through frequency–amplitude curves of each harmonic term in the finite Fourier series solution. From bifurcation analysis of the analytical solutions, the bifurcation trees of periodic motion to chaos are obtained analytically, and numerical illustrations of periodic motions are presented through phase trajectories and analytical spectrum. This investigation shows period-1 motions exist in parametric nonlinear systems and the corresponding bifurcation trees to chaos exist as well.

Initial phase of maximal voluntary and electrically stimulated knee extension torque development at different knee angles

2004 ◽  
Vol 97 (5) ◽  
pp. 1693-1701 ◽  
Author(s):  
C. J. de Ruiter ◽  
R. D. Kooistra ◽  
M. I. Paalman ◽  
A. de Haan
Keyword(s):  
Muscle Activation ◽  
Knee Extensor ◽  
Surface Emg ◽  
Knee Extension ◽  
Voluntary Contraction ◽  
Voluntary Activation ◽  
Knee Angle ◽  
Time Integral ◽  
Voluntary Contractions ◽  
Torque Development

We investigated the capacity for torque development and muscle activation at the onset of fast voluntary isometric knee extensions at 30, 60, and 90° knee angle. Experiments were performed in subjects ( n = 7) who had high levels (>90%) of activation at the plateau of maximal voluntary contractions. During maximal electrical nerve stimulation (8 pulses at 300 Hz), the maximal rate of torque development (MRTD) and torque time integral over the first 40 ms (TTI40) changed in proportion with torque at the different knee angles (highest values at 60°). At each knee angle, voluntary MRTD and stimulated MRTD were similar ( P < 0.05), but time to voluntary MRTD was significantly longer. Voluntary TTI40 was independent ( P > 0.05) of knee angle and on average (all subjects and angles) only 40% of stimulated TTI40. However, among subjects, the averaged (across knee angles) values ranged from 10.3 ± 3.1 to 83.3 ± 3.2% and were positively related ( r2 = 0.75, P < 0.05) to the knee-extensor surface EMG at the start of torque development. It was concluded that, although all subjects had high levels of voluntary activation at the plateau of maximal voluntary contraction, among subjects and independent of knee angle, the capacity for fast muscle activation varied substantially. Moreover, in all subjects, torque developed considerably faster during maximal electrical stimulation than during maximal voluntary effort. At different knee angles, stimulated MRTD and TTI40 changed in proportion with stimulated torque, but voluntary MRTD and TTI40 changed less than maximal voluntary torque.

Estimation of Muscle Forces About the Ankle During Gait in Healthy and Neurologically Impaired Subjects

2011 ◽  
pp. 320-347
Author(s):  
Daniel N. Bassett ◽  
Joseph D. Gardinier ◽  
Kurt T. Manal ◽  
Thomas S. Buchanan
Keyword(s):  
Muscle Activation ◽  
Inverse Dynamics ◽  
Biomechanical Model ◽  
Forward Dynamics ◽  
Muscle Forces ◽  
Dynamics Model ◽  
Joint Moments ◽  
Neurologically Impaired ◽  
Model Predictions ◽  
Contraction Dynamics

This chapter describes a biomechanical model of the forces about the ankle joint applicable to both unimpaired and neurologically impaired subjects. EMGs and joint kinematics are used as inputs and muscle forces are the outputs. A hybrid modeling approach that uses both forward and inverse dynamics is employed and physiological parameters for the model are tuned for each subject using optimization procedures. The forward dynamics part of the model takes muscle activation and uses Hill-type models of muscle contraction dynamics to estimate muscle forces and the corresponding joint moments. Inverse dynamics is used to calibrate the forward dynamics model predictions of joint moments. In this chapter we will describe how to implement an EMG-driven hybrid forward and inverse dynamics model of the ankle that can be used in healthy and neurologically impaired people.

Period Motions and Stability in a Nonlinear Spring Pendulum

2018 ◽  
Author(s):  
Albert C. J. Luo ◽  
Yaoguang Yuan
Keyword(s):  
Fourier Series ◽  
Excitation Frequency ◽  
Analytic Method ◽  
Analytical Prediction ◽  
Discrete Fourier Series ◽  
Periodic Motions ◽  
Harmonic Frequency ◽  
Pendulum System ◽  
Nonlinear Spring ◽  
The Stability

In this paper, period-1 motions varying with excitation frequency in a periodically forced, nonlinear spring pendulum system are predicted by a semi-analytic method. The harmonic frequency-amplitude for periodical motions are analyzed from the finite discrete Fourier series. The stability of the periodical solutions are shown on the bifurcation trees as well. From the analytical prediction, numerical illustrations of periodic motions are given, the comparison of numerical solution and analytical solution are given.

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