Limit Cycles to Enhance Human Performance Based on Phase Oscillators

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Thomas G. Sugar ◽  
Andrew Bates ◽  
Matthew Holgate ◽  
Jason Kerestes ◽  
Marc Mignolet ◽  
...  

Wearable robots including exoskeletons, powered prosthetics, and powered orthotics must add energy to the person at an appropriate time to enhance, augment, or supplement human performance. This “energy pumping” at resonance can reduce the metabolic cost of performing cyclic tasks. Many human tasks such as walking, running, and hopping are repeating or cyclic tasks where assistance is needed at a repeating rate at the correct time. By utilizing resonant energy pumping, a tiny amount of energy is added at an appropriate time that results in an amplified response. However, when the system dynamics is varying or uncertain, resonant boundaries are not clearly defined. We have developed a method to add energy at resonance so the system attains the limit cycle based on a phase oscillator. The oscillator is robust to disturbances and initial conditions and allows our robots to enhance running, reduce metabolic cost, and increase hop height. These methods are general and can be used in other areas such as energy harvesting.

Author(s):  
Sangram Redkar

<span>Wearable robots including exoskeletons, powered prosthetics, and powered orthotics must add energy to the person at an appropriate time to enhance, augment, or supplement human performance. Adding energy while not being in sync with the user can dramatically hurt performance. Many human tasks such as walking, running, and hopping are repeating or cyclic tasks and a robot can add energy in sync with the repeating pattern for assistance. A method has been developed to add energy at the appropriate time to the repeating limit cycle based on a phase oscillator. The phase oscillator eliminates time from the forcing function which is based purely on the motion of the user. This approach has been simulated, implemented and tested in a robotic backpack which facilitates carrying heavy loads. The device oscillates the load of the backpack, based on the motion of the user, in order to add energy at the correct time and thus reduce the amount of energy required for walking with a heavy load. Models were developed in Working Model 2-D, a dynamics simulation software, in conjunction with MATLAB to verify theory and test control methods. The control system developed is robust and has successfully operated on different users, each with their own different and distinct gait. The results of experimental testing validated the corresponding models.</span>


Author(s):  
Jason Kerestes ◽  
Thomas G. Sugar ◽  
Matthew Holgate

We are developing methods to add a bounded amount of energy to assist body motion. Energy is added based on the phase angle of the limb to create a “phase oscillator.” The energy is added assisting motion creating an oscillatory behavior. An anti-phase angle can be used to subtract energy from body motion as well. Using a “phase oscillator” controller, a powered hip exoskeleton assisted a runner and demonstrated a reduction in metabolic cost.


Author(s):  
Hui Wu ◽  
Dongwook Kim

The synchronization in large populations of interacting oscillators has been observed abundantly in nature, emergining in fields such as physical, biological and chemical system. For this reason, many scientists are seeking to understand the underlying mechansim of the generation of synchronous patterns in oscillatory system. The synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model. The Kuramoto model can be used to understand the emergence of synchronization in nextworks of coupled, nonlinear oscillators. In particular, this model presents a phase transition from incoherence to synchronization. In this paper, we investigated the distribution of order parameter γ which describes the strength of synchrony of these oscillators. The larger the order parameter γ is, the more extent the oscillators are synchronized together. This order parameter γ is a critical parameter in the Kuramoto model. Kuramoto gave a initial estimate equation for the value of the order parameter by giving the value of the coupling constant. But our numerical results show that the distribution of the order parameter is slightly different from Kuramoto’s estimation. We gave an estimation for the distribution of order parameter for different values of initial conditions. We discussed how the numerical result will be distributed around Kuramoto’s analytical equation.


2008 ◽  
Vol 2008 ◽  
pp. 1-8
Author(s):  
L. H. A. Monteiro ◽  
I. Gonzalez ◽  
J. R. C. Piqueira

Oscillator networks have been developed in order to perform specific tasks related to image processing. Here we analytically investigate the existence of synchronism in a pair of phase oscillators that are short-range dynamically coupled. Then, we use these analytical results to design a network able of detecting border of black-and-white figures. Each unit composing this network is a pair of such phase oscillators and is assigned to a pixel in the image. The couplings among the units forming the network are also dynamical. Border detection emerges from the network activity.


2003 ◽  
Vol 13 (05) ◽  
pp. 1183-1195 ◽  
Author(s):  
YU HUANG

The linear wave equation on an interval with a van der Pol nonlinear boundary condition at one end and an energy-pumping condition at the other end is a useful model for studying chaotic behavior in distributed parameter system. In this paper, we study the dynamics of the Riemann invariants (u, v) of the wave equation by means of the total variations of the snapshots on the spatial interval. Our main contributions here are the classification of the growth of total variations of the snapshots of u and v in long-time horizon, namely, there are three cases when a certain parameter enters a different regime: the growth (i) remains bounded; (ii) is unbounded (but nonexponential); (iii) is exponential, for a large class of initial conditions with finite total variations. In particular, case (iii) corresponds to the onset of chaos. The results here sharpen those in an earlier work [Chen et al., 2001].


2020 ◽  
Author(s):  
Marleny Arones ◽  
Mohammad Shourijeh ◽  
Carolynn Patten ◽  
Benjamin J. Fregly

AbstractAssessment of metabolic energy cost as a metric for human performance has expanded across various fields within the scientific, clinical, and engineering communities. As an alternative to measuring metabolic cost experimentally, musculoskeletal models incorporating metabolic cost models have been developed. However, to utilize these models for practical applications, the accuracy of their metabolic cost predictions requires improvement. Previous studies have reported the benefits of using personalized musculoskeletal models for various applications, yet no study has evaluated how model personalization affects metabolic cost estimation. This study investigated the effect of musculoskeletal model personalization on estimates of metabolic cost of transport (CoT) during post-stroke walking using three commonly used metabolic cost models. We analyzed data previously collected from two male stroke survivors with right-sided hemiparesis. The three metabolic cost models were implemented within three musculoskeletal modeling approaches involving different levels of personalization. The first approach used a scaled generic OpenSim model and found muscle activations via static optimization (SOGen). The second approach used a personalized EMG-driven musculoskeletal model with personalized functional axes but found muscle activations via static optimization (SOCal). The third approach used the same personalized EMG-driven model but calculated muscle activations directly from EMG data (EMGCal). For each approach, the muscle activation estimates were used to calculate each subject’s cost of transport (CoT) at different gait speeds using three metabolic cost models (Umberger 2003, Umberger 2010, and Bhargava 2004). The calculated CoT values were compared with published CoT trends as a function of stance time, double support time, step positions, walking speed, and severity of motor impairment (i.e., Fugl-Meyer score). Overall, U10-SOCal, U10-EMGCal, U03-SOCal, and U03-EMGCal were able to produce slopes between CoT and the different measures of walking asymmetry that were statistically similar to those found in the literature. Although model personalization seemed to improve CoT estimates, further tuning of parameters associated with the different metabolic cost models in future studies may allow for realistic CoT predictions. An improvement in CoT predictions may allow researchers to predict human performance, surgical, and rehabilitation outcomes reliably using computational simulations.


1994 ◽  
Vol 116 (3) ◽  
pp. 379-385 ◽  
Author(s):  
C. D. Rahn ◽  
C. D. Mote

One position sensor, a bilinear observer, and quadratic, observer-based feedback to a parametric actuator asymptotically stabilize n-modes of a flexible system. Using a perturbation approach, the transient and forced response of a controlled mode are approximated. The decay rate and resonance amplitude are related to the control gains, initial conditions, and forcing amplitude. A forced spillover instability is discovered that can destabilize uncontrolled modes with insufficient damping. A control bound is determined, based on the damping coefficients and frequencies of the modes, that prevents this instability. Experiments on a tension-controlled, pinned-pinned beam demonstrate that parametric control provides substantially faster transient decay and constrained response at resonance.


Author(s):  
Juan De La Fuente ◽  
Susheelkumar C. Subramanian ◽  
Prudhvi Tej Chinimilli ◽  
Sangram Redkar ◽  
Thomas Sugar

Abstract This paper presents the design of a phase-based robust oscillator for wearable robots that assists the human performing periodic or repetitive tasks. The robustness of the phase oscillator controller is evaluated by finding bounds for perturbations that guaranteed the stability of the output. Then, the Lyapunov redesign method is applied to construct a robust controller using a bounding function which can handle the uncertainties such as noise and perturbations in the overall human-robot system. The robust controller produces a bounded control signal to modify the amplitude and frequency of the resulting second-order oscillator to modulate the stiffness and damping properties. In this paper, the focus is put on the wearable robot that assists human hip joint while performing periodic activities such as walking. The proposed approach is verified through a simple pendulum experiment. The results show that a better limit cycle can be obtained with Lyapunov redesigned phase oscillator which controls the radial spread of the steady state. Finally, the potential of the proposed approach for hip assistance in a healthy subject wearing HeSa (Hip Exoskeleton for Superior Assistance) during periodic activities are discussed.


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