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Research Papers

Modeling and Optimal Control of an Energy-Storing Prosthetic Knee

[+] Author and Article Information
Antonie J. van den Bogert1

 Orchard Kinetics, Cleveland, OHbogert@orchardkinetics.com

Sergey Samorezov, William A. Smith

 Department of Biomedical Engineering, Cleveland Clinic, Cleveland, OH

Brian L. Davis

 Austen BioInnovation Institute, Akron, OH

1

Corresponding author.

J Biomech Eng 134(5), 051007 (Jun 05, 2012) (8 pages) doi:10.1115/1.4006680 History: Received June 21, 2011; Revised March 26, 2012; Posted May 01, 2012; Published June 05, 2012; Online June 05, 2012

Advanced prosthetic knees for transfemoral amputees are currently based on controlled damper mechanisms. Such devices require little energy to operate, but can only produce negative or zero joint power, while normal knee joint function requires alternative phases of positive and negative work. The inability to generate positive work may limit the user’s functional capabilities, may cause undesirable adaptive behavior, and may contribute to excessive metabolic energy cost for locomotion. In order to overcome these problems, we present a novel concept for an energy-storing prosthetic knee, consisting of a rotary hydraulic actuator, two valves, and a spring-loaded hydraulic accumulator. In this paper, performance of the proposed device will be assessed by computational modeling and by simulation of functional activities. A computational model of the hydraulic system was developed, with methods to obtain optimal valve control patterns for any given activity. The objective function for optimal control was based on tracking of joint angles, tracking of joint moments, and the energy cost of operating the valves. Optimal control solutions were obtained, based on data collected from three subjects during walking, running, and a sit-stand-sit cycle. Optimal control simulations showed that the proposed device allows near-normal knee function during all three activities, provided that the accumulator stiffness was tuned to each activity. When the energy storage mechanism was turned off in the simulations, the system functioned as a controlled damper device and optimal control results were similar to literature data on human performance with such devices. When the accumulator stiffness was tuned to walking, simulated performance for the other activities was sub-optimal but still better than with a controlled damper. We conclude that the energy-storing knee concept is valid for the three activities studied, that modeling and optimal control can assist the design process, and that further studies using human subjects are justified.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic representation of the proposed hydraulic system, showing the double-vane rotary actuator on the left, two valves, and accumulators. Pressures P, flow rates v, valve controls u, and knee flexion angle ϕ are indicated. The stator and hydraulic components will be attached to the shank, and the rotor will be attached to the socket for the residual femur. The low-pressure accumulator absorbs volume change without pressure change, and the spring-loaded high-pressure accumulator is responsible for energy storage.

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Figure 2

Qualitative representation of hypothesized control profiles for the proposed hydraulic system

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Figure 3

Optimal control solutions for normal walk (subject 1). Top row: full optimization which found an optimal accumulator stiffness of 4.15 MPa cm−3 . Middle row: optimization in which accumulator stiffness was fixed at 5.0 MPa cm−3 . Bottom row: optimization in which valve 1 was kept closed. Valves are open when control signal is one, and closed when control signal is zero.

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Figure 4

Optimal control solutions for slow run (subject 1). Top row: full optimization which found an optimal accumulator stiffness of 7.64 MPa cm−3 . Middle row: optimization in which accumulator stiffness was fixed at 5.0 MPa cm−3 . Bottom row: optimization in which valve 1 was kept closed.

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Figure 5

Optimal control solutions for the sit-stand-sit cycle (subject 1). Top row: full optimization which found an optimal accumulator stiffness of 1.71 MPa cm−3 . Middle row: optimization in which accumulator stiffness was fixed at 5.0 MPa cm−3 . Bottom row: optimization in which valve 1 was kept closed.

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