*4.3. Experimental Results in a Static Environment*

In Section 4.3, the proposed algorithm is compared with the A\* algorithm. Because the A\* algorithm always finds the shortest path, it can see how quickly the proposed algorithm can find the shortest path. The proposed algorithm and the A\* algorithm were tested by four robots to find a path with an arbitrary numbers of obstacles in random initial positions. The test was repeated 100 times on the generated map, which is changed 5000 times to obtain the route visited by the robot and the shortest path for each robot to reach the target point. In the first case, the search area and the time to reach the target point of the proposed algorithm is smaller than the A\* algorithm, but the actual travel distance of the robot is increased, as shown in Figures 8 and 9. Figures 8 and 9 depict the results of the A\* algorithm and the proposed algorithm, respectively. The average search range of A\* algorithm is 222 node visitation. The shortest paths of robots 1 to 4 were 35, 38, 43, and 28 steps, respectively, and the proposed algorithm, where each robot path are 41, 39, 44, and 31 steps, had 137 visited nodes.

**Figure 8.** The simulation result of A\* algorithm for the first situation.

**Figure 9.** The simulation result of proposed algorithm for the first situation.

As shown in Figures 10 and 11, which are the result of the A\* algorithm and the proposed algorithm, respectively for the second case, the search range of the proposed algorithm is similar to that of the A\* algorithm. The average search range of A\* algorithm is 80 node visitation. The shortest paths of robots 1 to 4 were 33, 29, 28, and 21 steps, and the proposed algorithm had 65 visited nodes, where each robot pathare 34, 36, 32, and 25 steps, respectively.

**Figure 10.** The simulation result of A\* algorithm for the second situation.

**Figure 11.** The simulation result of proposed algorithm for the second situation.

In the third case without obstacles in environment, as shown in Figures 12 and 13, the search range of two algorithms is the same, and the movement path of the robot is similar. The average search range of the A\* algorithm was 66 node visitation. The shortest paths of robots 1 to 4 were 33, 29, 28, 21, and 66 steps; the proposed algorithm had 66 visited nodes, and each robot path was 34, 31, 28, and 22 steps, respectively.

**Figure 12.** The simulation result of A\* algorithm result for the third situation.

**Figure 13.** The simulation result of proposed algorithm for the third situation.

In the fourth case, the search range of both algorithms is similar, and the movement path of the robot is the same. Figures 14 and 15 show the results of the A\* algorithm and the proposed algorithm, respectively. In the average search range of A\* algorithm, robot visited 121 nodes, and the shortest paths of robots 1 to 4 were 40, 38, 36, and 23 steps respectively. And the proposed algorithm had 100 visited nodes, and the shortest path of each robot is 40, 39, 36, and 23 steps, respectively.

**Figure 14.** The simulation result of A\* algorithm for the fourth situation.

**Figure 15.** The simulation result of proposed algorithm for the fourth situation.

Table 1 shows the search range of the proposed algorithm and A\* algorithm for each situation. The search range is one of the most important factors on effective robot navigation to the target point. As shown in Table 1, the proposed algorithm has a smaller search range than the A\* algorithm.

**Table 1.** The average search range of A\* and the proposed algorithm.


Table 2 shows the generated path for each robot according to the situation for both proposed and A\* algorithm. The proposed algorithm results in no less number of steps than A\* in an average generation. In general, A\* algorithm is not always searching for the optimal path because it always searches the optimal path in a static environment. However, the proposed algorithm generates the path faster than A\*.


**Table 2.** The robot average generation path of A\* and the proposed algorithm.

Table 3 shows the frequency of occurrence of each situation when a total of 5000 experiments were conducted. Although the search area is small, the situation 1 where the robot generation path is long shows about 58% of occurrence, and the situation 2 where the search area and travel distance are similar is about 34%. According to the simulation result, the search range of the proposed method is always smaller and the robot generation path is the same or similar to the robot path generated by the A\* algorithm with a probability of about 34.76%.

**Table 3.** Frequency of occurrence by situation.

