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Research Papers

Tracking the Motion of Hidden Segments Using Kinematic Constraints and Kalman Filtering

[+] Author and Article Information
Kjartan Halvorsen

Biomechanics and Motor Control, The Swedish School of Sport and Health Sciences, Box 5626, 11486 Stockholm, Swedenkjartan.halvorsen@gih.se

Christopher Johnston1

Department of Anatomy, Physiology and Biochemistry, Faculty of Veterinary Medicine and Animal Sciences, Swedish University of Agricultural Sciences, Uppsala, Sweden

Willem Back

Department of Equine Sciences, Faculty of Veterinary Medicine, Utrecht University, Utrecht, The Netherlands

Virgil Stokes, Håkan Lanshammar

Department of Information Technology, Uppsala University, Uppsala, Sweden

1

Also at Equine Hospital Strömsholm, Kolbäck, Sweden.

J Biomech Eng 130(1), 011012 (Feb 11, 2008) (9 pages) doi:10.1115/1.2838035 History: Received October 02, 2006; Revised May 21, 2007; Published February 11, 2008

Motion capture for biomechanical applications involves in almost all cases sensors or markers that are applied to the skin of the body segments of interest. This paper deals with the problem of estimating the movement of connected skeletal segments from 3D position data of markers attached to the skin. The use of kinematic constraints has been shown previously to reduce the error in estimated segment movement that are due to skin and muscles moving with respect to the underlying segment. A kinematic constraint reduces the number of degrees of freedom between two articulating segments. Moreover, kinematic constraints can help reveal the movement of some segments when the 3D marker data otherwise are insufficient. Important cases include the human ankle complex and the phalangeal segments of the horse, where the movement of small segments is almost completely hidden from external observation by joint capsules and ligaments. This paper discusses the use of an extended Kalman filter for tracking a system of connected segments. The system is modeled using rigid segments connected by simplified joint models. The position and orientation of the mechanism are specified by a set of generalized coordinates corresponding to the mechanism’s degrees of motion. The generalized coordinates together with their first time derivatives can be used as the state vector of a state space model governing the kinematics of the mechanism. The data collected are marker trajectories from skin-mounted markers, and the state vector is related to the position of the markers through a nonlinear function. The Jacobian of this function is derived. The practical use of the method is demonstrated on a model of the distal part of the limb of the horse. Monte Carlo simulations of marker data for a two-segment system connected by a joint with three degrees of freedom indicate that the proposed method gives significant improvement over a method, which does not make use of the joint constraint, but the method requires that the model is a good approximation of the true mechanism. Applying the method to data on the movement of the four distal-most segments of the horse’s limb shows good between trial consistency and small differences between measured marker positions and marker positions predicted by the model.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

A simple mechanism with 9DOF consisting of two rigid bodies connected by a spherical joint with 3DOF

Grahic Jump Location
Figure 2

The axes of rotation of the four-segment model of the distal limb of the horse, and the placement of the markers. The limb is in reference position.

Grahic Jump Location
Figure 3

MSE plotted against amplitude of the systematic error. The solid line corresponds to the results from the EKF; the dashed line to results without kinematic constraints.

Grahic Jump Location
Figure 4

MSE plotted against error in joint center position. The solid line corresponds to the results from the EKF; the dashed line to results without kinematic constraints.

Grahic Jump Location
Figure 5

MSE in the three parameters, plotted against the value of the second parameter. Results based on 100 repetitions.

Grahic Jump Location
Figure 6

Joint angles (in degrees) from eight trials under similar conditions for a single horse. One hundred frames of data (240Hz sampling rate) are plotted starting 20 frames prior to the hoof strike event, which is indicated by dotted lines.

Grahic Jump Location
Figure 7

Measured data and model output for the three coordinates of a marker on the hoof. The time unit is frame number (240Hz sampling rate). The solid line corresponds to the model output; the dashed line to the measured marker trajectory. Note that data are missing between frames 25 and 30 (marker not seen).

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