# A Mobile Gait Training System Providing an Active Interaction
## 2 Proposed System
### Augmentng Part  
The augmenting part is responsible for augmenting the virtual content on the floor, providing interaction with the trainee, and updating it in real time according to the training distance. That is, it takes roles in matching a coordinate system, generating a virtual object on foot coordinates (called virtual guide), and updating it based on training distance. In this system, the content augmented on the floor is displayed in a size of 150 cm \(\times\) 250 cm. In order to provide interaction within the content to the trainee, the trainee's feet coordinates must be generated as objects inside the content. The above function operates according to the procedure shown in Figure 5.  
Figure 4: A procedure for driving of the moving part: (**a**) foot coordinates reception; (**b**) calculation of distance between trainee; (**c**) maintenance distance based on calculated distance; (**d**) calculation of training distance based on robot’s travel distance.  
First, in step (a), both feet coordinates are received from the sensing part, and the system matches the coordinates from the sensing part and the augmenting part to use the trainee's both feet coordinates for content. Coordinate matching between the sensing part and the augmenting part is performed using a checkboard. The checkboard is projected according to the size of the projected content. Calculate the number of the projected checkboard squares (\(C_{x}\)) of the horizontal length and the number of checkboard squares (\(C_{y}\)) of the vertical length. During this process, the projected checkboard quadrilateral is a square and has a length of A in the content. Using this, the proportional expression is as shown in Equation (1).  
\[150 cm=C_{x}\times A,\ \ 250 cm=C_{y}\times A \tag{1}\]  
In step (b), a virtual object for tracking the position of the trainee's feet in real time is generated using Equation (1). Through the above process, virtual feet objects centered on each foot coordinates of the trainee are generated to interact with objects inside the content. In addition, for real-time content updates based on the trainee's gait distance, the trainee's gait distance must be calculated from the coordinates of the robot which are transmitted to the augmenting part.  
The above function operates according to the procedure shown in Figure 6. First, in step (a), the travel distance of the robot is received from the moving part, and the gait distance of the trainee is calculated accordingly. After this step, in order to reflect the trainee's gait distance in the content, the system matches the coordinates between the moving part and the augmenting part. As described previously, a checkboard is used for coordinate matching. Project the checkboard as the size of the projected content, and move the robot forward by \(R_{y}\). The proportional equation is obtained by counting the number of checkboard squares that the robot passed. In step (b), the content is updated in real time according to the travel distance of the trainee by moving the position of the virtual camera inside the content using Equation (2).  
\[R_{y}=C_{y}\times A \tag{2}\]  
Figure 5: A procedure for virtual object based on foot coordinates: (**a**) foot coordinates reception; (**b**) generation of virtual object based on foot coordinates.  
Figure 6: A procedure for updating content based by the distance between trainee: (**a**) calculation of training distance based on robot’s travel distance; (**b**) content updates based on training distance.  
Through the above process, virtual feet objects centered, respectively on the trainee's two-foot coordinates can be created to interact with the objects inside the content, and the content can be updated according to the trainee's travel distance.