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# A Universal Ankle–Foot Prosthesis Emulator for Human Locomotion Experiments

[+] Author and Article Information
Joshua M. Caputo

Experimental Biomechatronics Laboratory,
Department of Mechanical Engineering,
Carnegie Mellon University,
Pittsburgh, PA 15213
e-mail: jmcaputo@andrew.cmu.edu

Steven H. Collins

Experimental Biomechatronics Laboratory,
Department of Mechanical
Engineering & Robotics Institute,
Carnegie Mellon University,
Pittsburgh, PA 15213
e-mail: stevecollins@cmu.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received February 22, 2013; final manuscript received December 4, 2013; accepted manuscript posted December 12, 2013; published online February 13, 2014. Assoc. Editor: Kenneth Fischer.

J Biomech Eng 136(3), 035002 (Feb 13, 2014) (10 pages) Paper No: BIO-13-1098; doi: 10.1115/1.4026225 History: Received February 22, 2013; Revised December 04, 2013; Accepted December 12, 2013

## Abstract

Robotic prostheses have the potential to significantly improve mobility for people with lower-limb amputation. Humans exhibit complex responses to mechanical interactions with these devices, however, and computational models are not yet able to predict such responses meaningfully. Experiments therefore play a critical role in development, but have been limited by the use of product-like prototypes, each requiring years of development and specialized for a narrow range of functions. Here we describe a robotic ankle–foot prosthesis system that enables rapid exploration of a wide range of dynamical behaviors in experiments with human subjects. This emulator comprises powerful off-board motor and control hardware, a flexible Bowden cable tether, and a lightweight instrumented prosthesis, resulting in a combination of low mass worn by the human (0.96 kg) and high mechatronic performance compared to prior platforms. Benchtop tests demonstrated closed-loop torque bandwidth of 17 Hz, peak torque of 175 $Nm$, and peak power of 1.0 kW. Tests with an anthropomorphic pendulum “leg” demonstrated low interference from the tether, less than 1 $Nm$ about the hip. This combination of low worn mass, high bandwidth, high torque, and unrestricted movement makes the platform exceptionally versatile. To demonstrate suitability for human experiments, we performed preliminary tests in which a subject with unilateral transtibial amputation walked on a treadmill at 1.25 $ms-1$ while the prosthesis behaved in various ways. These tests revealed low torque tracking error (RMS error of 2.8 $Nm$) and the capacity to systematically vary work production or absorption across a broad range (from −5 to 21 J per step). These results support the use of robotic emulators during early stage assessment of proposed device functionalities and for scientific study of fundamental aspects of human–robot interaction. The design of simple, alternate end-effectors would enable studies at other joints or with additional degrees of freedom.

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## Figures

Fig. 1

Mechatronic design of the universal prosthesis emulator. (a) The system comprises three elements: (1) powerful off-board motor and control hardware, (2) a flexible tether transmitting mechanical power and sensor signals, and (3) a lightweight instrumented end-effector. This division of components was chosen to maximize responsiveness and minimize end-effector mass during treadmill walking. (b) Free-body diagram of the end-effector. Internal Bowden cable transmission forces pull the synthetic rope upwards while equally and oppositely pushing the aluminum frame downwards. Rope tension is transmitted through the pulley, sprocket, chain, and leaf spring, giving rise to a ground reaction force at the toe. The effect is equivalent to an ankle plantarflexion torque, resulting in a reaction force and moment at the interface with the human user. (c) Photograph of the instrumented prosthesis. A pulley–sprocket component magnifies transmission forces and allows direct measurement of spring deflection. A tensioning spring keeps the chain engaged. A limit switch protects against excessive plantarflexion. A universal adapter attaches to the socket or prosthesis simulator worn by the user. A dorsiflexion spring comprised of rubber bands retracts the toe, e.g., during leg swing. Fiberglass leaf springs provide series elasticity for ankle torque measurement and control. A separate leaf spring directly connected to the frame (not the toe) comprises the heel.

Fig. 2

Results of benchtop tests of mechatronic performance with the experimental prosthesis emulator. (a) Torque measurement accuracy. We performed tests in which we applied known torques by suspending weights from the toe in a range of known configurations, and found RMS measurement error of 3.3 N m. (b) Closed-loop torque step response. We fixed the base and toe of the prosthesis and applied 175 N m step changes in desired torque. Across 10 trials, we measured average 90% rise times of 0.062 s. (c) Bode plot of frequency response under closed-loop torque control. We fixed the base and toe of the prosthesis and applied chirps in desired torque from 56.5 to 133 N m, then smoothed the resulting curves and averaged over 10 trials. We calculated an average −3 dB bandwidth of 17 Hz.

Fig. 3

Impedance control law used during walking trials. Desired torque is a piecewise linear function of ankle position, with separate dorsiflexion (negative velocity) and plantarflexion (positive velocity) phases. Default curve parameters were selected to roughly match the torque–angle relationship observed for the biological ankle during normal walking. Plantarflexion segments were manipulated across conditions to alter the net positive ankle joint work over the step cycle.

Fig. 4

Tracking of impedance control law during walking. (a) Measured torque–angle relationship as one subject with unilateral transtibial amputation walked at 1.25 ms-1 for 1 min (52 strides). Each step resulted in a similar amount of net joint work, 7.88 ± 1.28 J, visible here as work-loop area. (b) Joint torque over the stance period during 1 min of walking, normalized to % stance. Average stance duration was 0.58 ± 0.02 s. The average RMS torque error was 2.8 Nm. Note that time–trajectory error appears smaller than error in angle–torque space, while the latter is more meaningful in terms of work production or absorption.

Fig. 5

Modulating the impedance control law parameters resulted in a variety of work loops during walking, demonstrating system versatility. We measured average net work per step as one subject with unilateral transtibial amputation walked at 1.25 ms-1 for 1 min (52 strides) with plantarflexion curve parameters set to five different values (a)–(e). Top: Average net joint work produced (positive) or absorbed (negative) during each step, mean ± st. dev. Bottom: Average impedance relationship for each condition, computed as the time-averaged ankle torque by time-averaged joint angle. We measured energy absorption of −5 J in condition (a), similar to the damping effects of conventional dynamic–elastic response prostheses. In condition (c), 8 J of work was produced per step, similar to the contribution of ankle plantarflexor muscles during human walking. We measured energy production of 21 J in condition (e), which would constitute a very large input from a robotic prosthesis.

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