## 6 Results  
In this study, the performances of two navigation systems (fuzzy logic and potential field navigation systems, both utilizing the fuzzy positioning system) were evaluated with the developed robot navigation simulator. Figure 13a-d show the simulation results, paths of the robot, and avoidance of obstacles until the robot reaches the targets in various environments. In the results, the robot in each moving step is symbolized by square shapes, wherein the blue and red colors represent the moving path of the robot using fuzzy logic and potential field navigation, respectively. In the moving path, the denser parts of overlapped square shapes indicate that the moving velocity is lesser than that of the other parts. Figure 12: Parameters influencing simulation of robot motion. Figure 13a shows the robot's path to the target after it avoided round and square-shaped obstacles; the navigation is shown to be successful without any collisions occurring with the obstacles. As shown in Figure 13b, the robot navigated through a passageway to reach the target, and Figure 13c shows the path from one room to another. Figure 13d shows the performance of the navigation system in an environment with scattered obstacles. The robot reached the final target after three other targets without any collisions. Table 4 summarizes the simulation results of the study in terms of path length, navigation time, and robot velocity. For the fuzzy navigation system, the velocity of the robot varies depending on the value of the coupling constant K in Equations (6) and (7). In this study, the value of K was set such that it minimized the errors between the simulation results and the performance of the actual robot, the latter being subject to a function of  
Figure 13: Simulation results of autonomous fuzzy navigation system with fuzzy positioning—(\(\square\): navigation path using fuzzy logic navigation system, \(\square\): navigation path using potential field navigation system): (**a**) navigation path to reach target after avoiding obstacles; (**b**) navigation path in narrow pathway; (**c**) navigation path to reach to the target in a room; (**d**) navigation path to reach multiple targets. hardware specifications. Ultimately, the values of K and r were set to 1 rad/s and 3 cm, respectively. For the potential field navigation system wherein the linear approximation method was used to calculate moving distance in each step, the linear function was set such that it produced distance values in the range from 3-4 cm corresponding to the minimum distance value in the simulation environment, and these results indicate that the potential field navigation system shows a higher moving velocity than the fuzzy logic navigation system. For an obstacle, the behavioral rules for following the edge of the obstacles in the fuzzy logic navigation system were activated in the fuzzy rule evaluation stage; the robot with fuzzy logic navigation follows the edge of obstacles, which results in a higher path length (Figure 13a), whereas the robot with potential field navigation moves toward the middle of the pathway because the repulsive potential is minimized here, resulting in a shorter path length (Figure 13b-d). Thus, the moving paths of the two navigation techniques are different. Among all results, the fuzzy logic navigation system showed a smoother moving path than the potential field navigation system, as shown in Figure 12. The 81 behavior rules as well as the 4 input and 2 output membership functions in the fuzzy logic navigation system interact well; further, the fuzzy logic navigation system produced smoother moving paths than the potential field navigation system, wherein the steering angle is calculated according to the repulsive and attractive potential data. A faster navigation velocity was observed in simulation 4 than in other simulations while simulation 4 also exhibited longer navigation time and distance.