# Sensorimotor Control Using Adaptive Neuro-Fuzzy Inference for Human-Like Arm Movement
## 5 Results and Discussion  
### Measurements  
The initial assessment of the subjects' performance is conducted through the offline image processing methodology. The distribution of the radii of the drawings obtained from the image processing indicates the drawing procedure's correctness. Verifying that the subject radii exhibit a bell-shaped histogram consistently distributed in line with statistical expectations is crucial. Therefore, the image processing results are essential in validating the experimental procedures. After the participants complete the drawing task, we employ the image processing procedure to identify the circles' initial, way, and center points. Figure 8 depicts a sample result of the implemented method on the test sheet. The green-colored text designates the initial point, the yellow-colored text indicates the way point, and the center of rotation, shown in red, represents the midline point location. Subsequently, the extracted data for the radii of the circle-like drawings are calculated. The results for the sample test are illustrated in Figure 9. The green, yellow, and red lines in Figure 9 signify the circle-like drawing's starting, way, and final points, respectively. The next step involves determining the angles of each segment based on the online measurement method. Figure 10 shows a sample recording of the resulting Euler angles from the joint movements during the circle-drawing task. After collecting each joint angle from the subjects, the next step is calculating the force difference using Equation (15) for the ANFIS architecture. The performance of the ANFIS's force variation is then compared to a scenario where a single constant \(\vartheta\) parameter is not trained through the ANFIS. In our study, we conducted a comparison between the performance outcomes associated with two distinct approaches to determining the internal force parameter within the musculoskeletal arm model. The first approach utilizes the ANFIS to determine the internal force parameter \(\vartheta\). The second approach relies on a single, static internal force parameter that was predetermined and remained unchanged throughout the control process. Figure 8: The detected initial, center, and way points of a sample drawing are respectively highlighted with green, red, and yellow colors. Figure 9: The image processing results of radius calculation. The start, via, and final points of the drawing are each represented by lines in green, yellow, and red colors, respectively. The comparison results in Figure 11 highlight the performance differences between the two approaches. As Figure 11 shows, the result demonstrates an improvement in more human-like muscle force generation with the ANFIS approach. The variance in muscle force difference when using the constant parameter is 2.692, whereas the ANFIS method shows a variance of only 0.454. When the variance approaches zero, it indicates that the model provides an accurate and precise approximation. A smaller variance signifies that the predicted values are closely clustered around the mean, having a more reliable and consistent model fit. Therefore, a lower variance in the force difference, as achieved by the ANFIS method, implies a superior and more precise approximation of the human-like muscle force compared to the constant parameter model. For a more detailed examination of the force difference, an enlarged view between 0.4 and 0.8 seconds of Figure 11 is presented in Figure 12.  
Moreover, the peak in Figure 11 at approximately 0.2 s is likely associated with the movement initiation in human circle drawing due to biomechanical factors and the motor control involved in such tasks. When the person begins a drawing motion, especially a circular one, there is a need to overcome inertia and start the movement from a static position. The initial burst of force may be required to set the hand in motion, mainly if resistance or the drawing surface offers some friction.