## 2 Related Work
### Mobile Anchor--Static Node
MA cannot provide sufficient information to UNNs located at ROI boundaries to estimate their location using the HILBERT path planning model. This will increase localization error and reduce the number of localized nodes. The HILBERT path planning model is shown in Figure 4a. [PERSON] et al. [29] presented a path planning scheme called LMAT based on trilateration for MAs. In this scheme, the distance between the two locations in which the MA broadcasts location information is defined as the resolution. MA continues its trajectory by forming symmetrical equilateral triangles and broadcasts location information to UNNs at each vertex of these equilateral triangles. This process ensures that the collinearity problem is solved successfully. High localization accuracy and high localization ratio are achieved with LMAT. However, the length of the path traveled by the MA is long. The LMAT path planning model is shown in Figure 4b. [PERSON] et al. [9] proposed a MA path planning scheme called Z-curve. The MA's path is \"Z\"-shape. In this study, the authors divided the ROI into squares for three levels and connected the \"Z\" shapes at each level. As with most mobile path planning models in WSNs, providing three non-collinear points to UNNs in the Z-curve model is one of the main objectives. Additionally, the Z-curve performance is evaluated in the presence of obstacles, and the Z-curve obstacle-handling trajectory is proposed to reduce the obstacle problem in localization. The Z-curve model is shown in Figure 4c. [PERSON] et al. [11] presented a MA path planning scheme called H-curve. This scheme is called H-curve because of the multi-curved \"H\"-shaped paths in the design. The path was designed to solve the collinearity problem, shorten the distance traveled by MA, and cover each UNN with at least three different MA. This study's critical point is to create a distance difference \(d_{m}/2\) between two rows, \(d_{m}\) MA's step interval. Thus, the two rows do not overlap, the number of points decreases, and ultimately a triangle-like communication form is created. Weighted Centroid Localization (WCL) and Weight-Compensated Weighted Centroid Localization (WCWCL) methods were used as localization estimation methods. The H-curve path planning model is shown in Figure 4d. Figure 4: Different mobile path planning models in obstacle-free field. [PERSON] et al. [10] devised a different path planning scheme that follows MA's trajectory \"M\" shape. Therefore, they called the proposed scheme \"M-curves\". In this study, two successive rows are patterned with the letters M and W. There is a \(d_{m}\)-long space between the letters M or W in each row. A \(d_{m}/2\) distance difference is created between two rows. Thus, a triangle-like communication form was obtained, similar to the H-curve, and a solution was found to the collinearity problem. The authors used the \"Centroid Method\" as the localization estimation method and aimed to increase the performance of the proposed method by adding the \"Dolphin Swarm Algorithm (DSA)\". The M-curves path planning model is shown in Figure 4e. Some static path planning schemes proposed in the literature have been designed and tested in obstacle-presence scenarios. For example, in [30], [PERSON] et al. presented obstacle-avoiding localization algorithms based on the path planning scheme called V-curve. The main curve of the V-curve path planning mechanism is the combination of SCAN and Z-curve. In this study, the presence of static and dynamic obstacles in the sensing field was examined. If a repulsive force is applied to the MA by the obstacle, it will use the backtracking technique until it reaches the previous node \(Sj\) successfully visited. After a delay, it moves back into the V-Curve path. If the problem recurs, it will follow along an edge of the \(Sj\) node. In [31], [PERSON] et al. proposed a new path planning algorithm called SLMAT, combining LMAT and SCAN algorithms to enable a trade-off between location accuracy and energy consumption.