# Real-Time Path Planning for Strategic Missions
## 5 Results and Discussion
### A Brief Comparative Analysis  
Considering that a comparative analysis can be made on the quality of a path planning strategy, this subsection demonstrates that the proposed strategy works in a similar (and often better) way than the proposals in [11; 12; 13; 14]. Thus, the purpose of the following simulations is two-fold: validate the proposed strategy and compare it with others as well in a static environment.  
Figures 3-5 show the comparison with five works, which aims to navigate in a structured or dynamic environment. Before starting the comparison, it is worth mentioning the following considerations: this paper performs (a) an implementation of the LPA* algorithm, (b) a Manhattan navigation system is used to describe robot navigation, (c) the entire environment and any change on it are considered known (or can be detected and reported to the planner) and (d) all simulations are performed with similar/identical environment characteristics (size, discretization, position of the objects and so on). When analyzing the figures, the routes resulted from our strategy correspond to the black lines, whereas the routes resulting from the algorithms under comparison are those in gray.  
Figure 2: (**a**) Map and graph used in the experiment and (**b**) its characteristics. It is noteworthy that when the state cost is \(\infty\), the node or state is not opened.  
Figure 3 shows that the DPNA-GA has a strong influence of the obstacles on the path construction. In the same scenario, the LPA* responds similarly, but its computed route is closer to the obstacles, as shown in the figure. In this last case, notice that the agent does not perform unnecessary maneuvers to avoid the obstacles and, despite having its movements limited by Manhattan navigation, its route is still secure enough. Therefore, the LPA* algorithm is more efficient once the agent travels a shorter path and, consequently, spends less energy to reach the goal.  
Figure 4a highlights that the firefly algorithm [12] performs a local optimization, which consequently makes the robot perform more movements than necessary to achieve the objective. In contrast, LPA* found the path that requires less movements to avoid the obstacle. In other words, the agent goes directly towards the target, overcoming the obstacle. Following, Figure 4b illustrates that the Matrix-Binary Codes based Genetic Algorithm (MGA) algorithm [13] is more efficient than the previous one, although still performing a reactive maneuver, i.e., the agent only avoids the obstacle after detecting it. In turn, as a result of a deliberative strategy, LPA* returns the path represented in black line, once it has the knowledge of the map previously.  
Figure 4: Comparison with the (**a**) firefly algorithm by [PERSON] in [12] and (**b**) Matrix-Binary Codes based Genetic Algorithm (MGA) controller by [PERSON] in [13].  
Figure 3: Comparison with Dynamic Planning Navigation Algorithm optimized with genetic algorithm (DPNA-GA) controller by [PERSON] in [11].  
Figure 5a shows the comparison with the ACOIC algorithm [14]. Notice that the traveled paths are almost identical, because both of them use the Manhattan description and work in a deliberative way. Finally, a similar behavior can be observed in Figure 5b, where the difference between the routes occurs because the IGA algorithm [17] uses 8-neighborhoods instead of 4-, as LPA* does.