## 3 Results and Discussion
### Verification of the Experiments in the Complicated Environment  
Figure 12 depicts the operating state of the experiment of one subject--wheelchair trajectory, time history of gaze direction \(\varphi_{g}\), direction of movement \(\varphi_{out}\), and speed \(\varphi_{out}\)--when the subject performed a right turn on the front and back passages. Figures 13 and 14 demonstrate gaze detection results, state of the experiment, result obtained from integration of MF based on environmental recognition and fuzzy set theory when the subject performed a right turn on the front and back passage. Figure 15 shows the details of Figure 13(d-3,e-3,d-4). Figure 16 shows the details of Figure 14(d-3,e-3,d-4,e-4). Video S1-1 and S2-1 shows the state of the experiment, S1-2 and S2-2 shows the environmental recognition, S1-3 and S2-3 shows the MF when the subject performed a right turn on the front and back passage.  
Figure 12: Results obtained when subjects executed a right turn on the front (**1**) and back (**2**) passage (**a**) wheelchair trajectory; (**b**) gaze direction \(\varphi_{g}\); (**c**) direction of movement \(\varphi_{out}\); (**d**) Speed \(\varphi_{out}\).  
We confirmed that the gaze and passage were able to be detected at each time in the real environment. In the section A in Figure 13a, the subject is gazing at the passage in front, and as a result the direction of movement changes to the right direction, and he turned right at the front passage. Figure 13a,b show that the subject is gazing near the direction \(\varphi_{p5}\) which is the front passage, but because the wall is approaching, the output direction \(\varphi_{out}\) is determined to the left of the direction \(\varphi_{p5}\). Figure 13c,d show that the subject is gazing near the direction \(\varphi_{p4}\) which is the front passage, and there is no wall in that direction, so the output direction \(\varphi_{out}\) is determined near the direction \(\varphi_{p4}\).  
In the section B in Figure 13b, the subject is gazing at the back passage, and as a result the direction of movement goes in a straight line and he did not turn right at the front passage. Figure 15a,b show that the subject is gazing near the direction \(\varphi_{p3}\) which is the back passage, but because the wall is approaching, the output direction \(\varphi_{out}\) is determined to the left of the direction \(\varphi_{p3}\). In section C, the subject is gazing at the back passage, and as a result the direction of movement changes to the right direction, and he turned right at the back passage. Figure 15c,d show that the subject is gazing near the direction \(\varphi_{p1}\) which is the back passage, and there is no wall in that direction, so the output direction \(\varphi_{out}\) is determined near the direction \(\varphi_{p1}\).  
These results confirm the ability of a passenger to operate the wheelchair by merely gazing towards the direction in which he or she wishes to move in an unknown environment.  
Figure 13: Results obtained when the subject executed a right turn on the front passage: (**1**) 0.9 s; (**2**) 5.5 s; (**3**) 7.1 s; (**4**) 9.6 s; (**5**) 13.2 s; (**a**) World camera image; (**b**) RGB camera image; (**c**) Real environment; (**d**) Integration of MF \(\mu_{mix}\); (**e**) LRF + data.  
Figure 14: Results obtained when the subject executed a right turn on the back passage: (**1**) 2.8 s; (**2**) 5.8 s; (**3**) 11.4 s; (**4**) 17.1 s; (**5**) 21.4 s; (**a**) World camera image; (**b**) RGB camera image; (**c**) Real environment; (**d**) Integration of MF \(\mu_{mix}\); (**e**) LRF data.  
Figure 15: Details of Figure 13: (**a**) Detail of (d-3); (**b**) Detail of (e-3); (**c**) Detail of (d-4); (**d**) Detail of (e-4).  
Simultaneously, the effectiveness of the proposed system during operation in a complex environment is also confirmed. Furthermore, it was confirmed by multiple subjects.