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Research Papers

Online Estimation Algorithm for a Biaxial Ankle Kinematic Model With Configuration Dependent Joint Axes

[+] Author and Article Information
Y. H. Tsoi

Department of Mechanical Engineering, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand

S. Q. Xie

Department of Mechanical Engineering, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealands.xie@auckland.ac.nz

J Biomech Eng 133(2), 021005 (Jan 24, 2011) (11 pages) doi:10.1115/1.4003315 History: Received April 06, 2010; Revised December 09, 2010; Posted December 22, 2010; Published January 24, 2011; Online January 24, 2011

The kinematics of the human ankle is commonly modeled as a biaxial hinge joint model. However, significant variations in axis orientations have been found between different individuals and also between different foot configurations. For ankle rehabilitation robots, information regarding the ankle kinematic parameters can be used to estimate the ankle and subtalar joint displacements. This can in turn be used as auxiliary variables in adaptive control schemes to allow modification of the robot stiffness and damping parameters to reduce the forces applied at stiffer foot configurations. Due to the large variations observed in the ankle kinematic parameters, an online identification algorithm is required to provide estimates of the model parameters. An online parameter estimation routine based on the recursive least-squares (RLS) algorithm was therefore developed in this research. An extension of the conventional biaxial ankle kinematic model, which allows variation in axis orientations with different foot configurations had also been developed and utilized in the estimation algorithm. Simulation results showed that use of the extended model in the online algorithm is effective in capturing the foot orientation of a biaxial ankle model with variable joint axis orientations. Experimental results had also shown that a modified RLS algorithm that penalizes a deviation of model parameters from their nominal values can be used to obtain more realistic parameter estimates while maintaining a level of estimation accuracy comparable to that of the conventional RLS routine.

FIGURES IN THIS ARTICLE
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Copyright © 2011 by American Society of Mechanical Engineers
Topics: Algorithms , Errors
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References

Figures

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Figure 1

The superposition of indicative ankle, subtalar, foot, and global coordinate frames on a three dimensional surface model of the foot-ankle structure. Thick dotted lines represent the axes about which rotations occur.

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Figure 2

A computer aided design model of the ankle rehabilitation robot used to gather the experimental data (reproduced from Ref. 24)

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Figure 3

Bar graphs showing the estimation errors relating to the simulation study in Euler angles in terms of maximum absolute errors and root mean square errors

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Figure 4

Time histories of the estimated axis tilt angles (solid lines) as obtained by algorithm 1 over the duration of the simulation. Actual trajectories of the axis tilt angles over the simulation are also shown (dotted lines).

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Figure 5

The trajectories of the axis tilt angles as determined by the final parameter estimates of algorithm 2 (thin solid lines) and algorithm 3 (thick solid lines). Actual trajectories of the axis tilt angles over the simulation are also shown (thick dashed lines). Note that these parameters are shown for the first half of the simulation for clarity, and a similar trend is observed in the remaining half.

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Figure 6

The errors in estimation of the ankle and subtalar joint angles using parameters obtained from the identification trials. Data relating to algorithms 1–3 are respectively given by the thin solid lines, the thick solid lines, and the thick dashed lines.

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Figure 7

Bar graphs showing the estimation errors obtained from the experimental data in Euler angles in terms of maximum absolute errors and root mean square errors

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Figure 8

The measured and estimated ZXY Euler angles of the robot/foot orientation using the RLS algorithm (algorithm 3). Thick lines represent the measured quantities, while thin lines represent the estimated values.

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Figure 9

The measured and estimated ZXY Euler angles of the robot/foot orientation using the modified RLS algorithm (algorithm 4). Thick lines represent the measured quantities, while thin lines represent the estimated values.

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Figure 10

The estimated ankle (black) and subtalar (gray) joint displacements obtained using algorithms 3 and 4

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