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Research Papers

Ground Reaction Force Estimation in Prosthetic Legs With Nonlinear Kalman Filtering Methods

[+] Author and Article Information
Seyed Fakoorian

Department of Electrical Engineering
and Computer Science,
Cleveland State University,
Cleveland, OH 44115
e-mail: s.fakoorian@csuohio.edu

Vahid Azimi

School of Electrical and Computer Engineering,
Georgia Institute of Technology,
Atlanta, GA 30313

Mahmoud Moosavi

Department of Electrical Engineering
and Computer Science,
Cleveland State University,
Cleveland, OH 44115

Hanz Richter

Department of Mechanical Engineering,
Cleveland State University,
Cleveland, OH 44115
e-mail: h.richter@csuohio.edu

Dan Simon

Department of Electrical Engineering
and Computer Science,
Cleveland State University,
Cleveland, OH 44115
e-mail: d.j.simon@csuohio.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 6, 2016; final manuscript received March 10, 2017; published online July 20, 2017. Assoc. Editor: Dumitru I. Caruntu.

J. Dyn. Sys., Meas., Control 139(11), 111004 (Jul 20, 2017) (11 pages) Paper No: DS-16-1583; doi: 10.1115/1.4036546 History: Received December 06, 2016; Revised March 10, 2017

A method to estimate ground reaction forces (GRFs) in a robot/prosthesis system is presented. The system includes a robot that emulates human hip and thigh motion, along with a powered (active) transfemoral prosthetic leg. We design a continuous-time extended Kalman filter (EKF) and a continuous-time unscented Kalman filter (UKF) to estimate not only the states of the robot/prosthesis system but also the GRFs that act on the foot. It is proven using stochastic Lyapunov functions that the estimation error of the EKF is exponentially bounded if the initial estimation errors and the disturbances are sufficiently small. The performance of the estimators in normal walk, fast walk, and slow walk is studied, when we use four sensors (hip displacement, thigh, knee, and ankle angles), three sensors (thigh, knee, and ankle angles), and two sensors (knee and ankle angles). Simulation results show that when using four sensors, the average root-mean-square (RMS) estimation error of the EKF is 0.0020 rad for the joint angles and 11.85 N for the GRFs. The respective numbers for the UKF are 0.0016 rad and 7.98 N, which are 20% and 33% lower than those of the EKF.

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Figures

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Fig. 1

The robotic model of the hip robot/prosthesis system. It is desired to eliminate the load cells on the foot and instead estimate forces with an EKF.

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Fig. 2

State estimation of joint displacements of the robot with the use of EKF and four measurements during normal gait speed. Note that the initial estimate quickly converges to the true state. (a) The estimate of the hip displacement, (b) the estimate of the thigh angle, (c) the estimate of the knee angle, and (d) the estimate of the ankle angle.

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Fig. 3

State estimation of the robot velocities with the use of EKF and four measurements during normal gait speed

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Fig. 4

Horizontal and vertical GRFs estimations with the use of EKF and four measurements during normal gait speed

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Fig. 6

The simulation results show the divergence of the estimation error with small initial error and large noise terms. The sixth state is used here for illustration purposes, but similar results hold for all of the other states as well. (a) The estimate of x6(t) and (b) the estimation error ξ6(t).

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Fig. 7

The simulation results show the divergence of the estimation error with large initial error and small noise terms. The sixth state is used here for illustration purposes, but similar results hold for all of the other states as well. (a) The estimate of x6(t) and (b) the estimation error ξ6(t).

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Fig. 5

The simulation results show the boundedness of the estimation error with small initial error and small noise terms. The sixth state is used here for illustration purposes, but similar results hold for all of the other states as well. (a) The estimate of x6(t) and (b) the estimation error ξ6(t).

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