Local frame alignment between an inertial measurement unit (IMU) system and an optical motion capture system (MCS) is necessary to combine the two systems for motion analysis and to validate the accuracy of IMU-based motion data by using references obtained through the MCS. In this study, we propose a new quaternion-based local frame alignment method where equations of angular velocity transformation are used to determine the frame alignment orientation in the form of quaternion. The performance of the proposed method was compared with those of three other methods by using data with different angular velocities, noises, and alignment orientations. Furthermore, the effects of the following three factors on the estimation performance were investigated for the first time: (i) transformation concept, i.e., angular velocity transformation vs. angle transformation; (ii) orientation representations, i.e., quaternion vs. direction cosine matrix (DCM); and (iii) applied solvers, i.e., nonlinear least squares method vs. least squares method through pseudoinverse. Within our limited test data, we obtained the following results: (i) the methods using angular velocity transformation were better than the method using angle transformation; (ii) the quaternion is more suitable than the DCM; and (iii) the applied solvers were not critical in general. The proposed method performed the best among the four methods. We surmise that the fewer number of components and constraints of the quaternion in the proposed method compared to the number of components and constraints of the DCM-based methods may result in better accuracy. Owing to the high accuracy and easy setup, the proposed method can be effectively used for local frame alignment between an IMU and a motion capture system.

A treadmill was used to perform continuous walking tests in a limited space that can be covered by marker-based optical motion capture systems. Most treadmill-based gait data are analyzed based on gait cycle percentage. However, achieving continuous walking motion trajectories over time without time normalization is often required, even if tests are performed under treadmill walking conditions. This study presents a treadmill-to-overground mapping method of optical marker trajectories for treadmill-based continuous gait analysis, by adopting a simple concept of virtual origin. The position vector from the backward moving virtual origin to a targeted marker within a limited walking volume is the same as the position vector from the fixed origin to the forward moving marker over the ground. With the proposed method, it is possible (i) to observe the change in physical quantity visually during the treadmill walking, and (ii) to obtain overground-mapped gait data for evaluating the accuracy of the inertial-measurement-unit-based trajectory estimation. The accuracy of the proposed method was verified from various treadmill walking tests, which showed that the total travel displacement error rate was 0.32% on average.

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