## 4 Pilot Study Results of Locomotion Interface Device with 2-Dimensional Running
### Running Performance of High-Level Controller  
The proposed high-level controller should be able to compensate the position error regardless of the user's intended gait speed and changes in direction during running. Therefore, the pilot study of omnidirectional locomotion was carried out with one user (Sex: man, Age: 33) to verify acceleration performance of the proposed ODT with the designed controller. For this purpose, we asked the user to change direction by step turning, while running as fast as possible on the active surface of the ODT. In this study, we aimed to determine whether or not the ODT allows the user to perform omnidirectional locomotion while remaining unaffected by the acceleration limitations of the proposed system. Before starting the test, the user is briefed on how the system works, and the use was allowed to walk or run in the system for 10 min freely to familiarize how the system works. In the pilot test, the user completed three laps, generating a circular path in the VR environment. The running velocity was displayed on a 360\({}^{\circ}\) screen at 0\({}^{\circ}\) and 180\({}^{\circ}\) orientations in a spherical display surrounding the proposed ODT. As shown in Figure 15a, the user achieved a gait speed of 1.8-2.8 m/s. The angular velocity filtered using a low-pass filter with a cut-off frequency of 1 Hz is shown in Figure 15b. The average angular velocity was 0.23 rad/s. Figure 15c shows the active surface speed of the ODT controlled by the low-level controller according to commands given by the high-level controller. As shown in Figure 15d, although the user performed rapid changes in direction during running, the maximum acceleration of the active surface was less than 1.1 m/s\({}^{2}\). Thus, the proposed locomotion interface device can handle about 2.7 times the maximum acceleration achieved when a user changes direction while running at 1.8-2.8 m/s. Figure 14: System configuration and gain parameters of the high-level controller used to evaluate running performance. the beginning and end of running period due to the angular speed being zero. However, during omnidirectional running, \(r\) ranges from 6.1-35.7 m. As indicated by the solid red lines in Figure 15f, the local maximum radii of 29.3 m and 35.7 m occurred at 35 s and 69 s; when the user's angular speed reached the local minimum values. The local minimum radii (dashed red lines) occurred at 21 s, 38 s, and 50 s when the user's angular velocity was near its local maximum values. It should be noted that according to Equation (11), the acceleration value of the proposed ODT is proportional to the product of the user's velocity and angular velocity. However, based on Equation (13), \(r_{c}\) is proportional to the user's speed and is inversely proportional to the angular velocity of the user. Contrary to the Virtual Walking Machine [9], which aims to allow omnidirectional walking using two parallel robots, the proposed locomotion interface device does not have mechanical constraints with respect to the radius of curvature for omnidirectional locomotion. In addition, it allows for directional changes by the user, even during running, and has a sufficient acceleration capacity. Therefore, this study shows that the acceleration performance of the developed ODT is sufficient to handle high-speed (i.e., running) omnidirectional locomotion. We also observed the position errors. The position errors are calculated by curve-fitting using the least squares method, as shown in Figure 16. The center of the ellipse is located within less than 0.05 m of the reference position, and the length of the long and short axis of the ellipse was about 0.36 m and 0.27 m, respectively. These magnitudes of position error did not affect to the user's running, and the subject could successfully accomplish the omnidirectional running. Therefore, it can be concluded that the developed locomotion interface device with the proposed ODT can stay within the acceptable range of position error when the speed and orientation are changed dynamically.