## 1 Introduction
One of the main challenges in applications using a MA and unknown static nodes is how to design the path the MA will follow. Generally, such a design is aimed at: (i) finding UNNs in the ROI with as few errors as possible when the MA uses the path designed; (ii) finding all nodes in the ROI if possible; and (iii) spending as little energy as possible. In the literature, many studies have been conducted in different scenarios to achieve these and similar objectives. These studies generally addressed essential evaluation criteria such as localization accuracy and did not address realistic channel parameters. In most of these studies, obstacle-free scenarios in the ROI were considered, and obstacle-presence scenarios were not considered. In this paper, a mobile path planning model based on nested regular hexagons (NHex) is introduced for MANAL in WSNs. The proposed model has been designed to consider the criteria for increasing the accuracy and localization ratio  
Figure 1: Mobile anchor node assisted localization [7]. of localized nodes for an obstacle-presence scenario. Additionally, realistic wireless channel features are used to evaluate the performance of different mobility models. In summary, we make the following contributions to a path planning model for MANAL in WSNs:  
1. In this study, a new model called NHexCurves is proposed. The proposed model's different localization performances are compared with the other five models in the regular obstacle environment used in the Z-curve [9] study. This comparison was made on a reliable wireless channel to obtain realistic and fair results. 2. To the best of our knowledge, no study in the literature addresses HILBERT, LMAT, H-curve, and M-curves models with different evaluation criteria in obstacle-presence environments and compares them in these scenarios. In other words, none of the models discussed in this study, except Z-curve, have been performance evaluated in environments with regular obstacles. However, in the Z-curve study, the authors only showed the performance results of their own path planning schemes in the obstacle-presence scenario and did not compare them with the performance of other schemes. 3. Using two localization algorithms, one is range-based, and one is range-free, the variation of the performance of different path models with varying algorithms of localization is examined. 4. In this study, the same localization method was used in the same localization scenario for all path planning models whose localization performance was examined. For example, this is not the case in [10]. The remainder of this paper is organized as follows: in Section 2, mobility and path planning models are classified from general to specific, and then related studies are introduced. Additionally, some localization algorithms used to evaluate path planning models are examined in this section. In Section 3, the network model and its adjustments are given, and the assumptions used in this study are noted. In Section 4, the path planning model proposed in this study and its ideas are introduced. Performance evaluations of the proposed model and some path planning models in the literature in a realistic channel for the obstacle-presence scenario are given in Section 5. Section 6 summarizes results and future work.