## 4 The Rotational Orbit Based Inter Node Adjustment (ROBINA)  
The ROBINA takes the available number of nodes and its neighboring intermediate forwarding node around the sinks for reliable data transmission. Firstly, the sensor, relay, and gateway nodes are nominated and randomly deployed without the ROBINA, as shown in Figure 2. All these nodes are deployed as anchored positions, and take data information towards the sinks. In order to avoid a collision, it is assumed that one node can carry and transfer the data one packet at a time [23; 24; 25; 26]. Due to the increased traffic volume, the empty void nodes form void regions. At that location, the internode adjusts and transmits a beacon message requesting an alternate. An alternate path based on rotational orbits is established around the SNNs. Its radius must include both the node's void dead area and the set of neighboring nodes. It consists of multiple nodes that ensure the recovery of data with higher priority. The following mathematical expression is used to adjust internodes around SNNs in Equation (1). \[A\ (AdjNi)=\frac{E\ (Ni)}{\big{(}\ SNN_{range}*N+f(Ni)} \tag{1}\]  
where _f_(_Ni_) = {1 1 0} (=0 for a dead state, or =1 for an alive state)  
From Equation (1): the \(A\) (_AdjNi_) is the selected area for the proposed scheme in the network that firstly calculates the _E_(_Ni_) energy of the node and the range of (\(SNN_{range}\)) where _f_(_Ni_) = {1 1 0} (=0 for a dead state, or =1 for an alive state). In the equation described above, we take a scenario in which node _'i'_ sends data to node _'j'_ with energy _'E'_; first, it explores the _'N'_ towards the _'Sn'_, then, for all nodes that wait for Packet ACKnowledg (\(P_{\text{ACK}}\)), takes the time (t) in such a way that \(N_{ij}\) = {\(n_{i}\in n_{j}\ ^{\sim}\ E_{ji}\): \(\forall\ AdjNi*\ SNNs+Dn\)}, for orbit pathTp = \(\sum_{n=i}^{j}(Nij*SNNs)\), then PACK in total time for path establishment counts the set of neighboring nodes with sink [27] as mentioned in Equation (2) with Selection Operation (\(Sel_{op}\)). \[Sel_{op}=\frac{Ns-Dn}{Sn} \tag{2}\]  
The following equation ensures that the \(P_{\text{ACK}}\) from Node _'i'_ to _'j'_ with _'E'_ is as expected in Equation (3), where \(P_{\text{ACK}}\) is discussed in detail. \[P_{\text{ACK}}\ (N)=\prod_{j=0}^{d=1}\forall\ SNNs\ (Dn)\subseteq Sn \tag{3}\]  
Additionally, in the following section with Algorithm 1, the procedure of (I\({}_{\text{AFN}}\)) for forwarding the Beacon Message (BM) is discussed. In Algorithm 2, the detailed description of data delivery using a path adjustment mechanism is discussed. The PA-ROBINA works with internode adjustment as I\({}_{\text{AFN}}\); while setting the internodes between the void nodes, the path will automatically adjust at that region and rescue the dead nodes. For the adjustment of the region of the path, the range of _SNNs_ plays a role in determining which path is closer to sonobuoys so that it is easier for the path-based nodes like internodes to send the acknowledgment of the nodes that are not alive [28; 29; 30; 31; 32; 33]. Moreover, the working of ROBINA for the adjustment of internode and its PA-ROBINA for setting the rotational shortest path are described in Algorithms 1 and 2,  
Figure 2: Nodes are randomly deployed in the IoUTs scenario without applying the ROBINA algorithm (especially when the path is not established). respectively. In Figure 3, the overall working of ROBINA is explained with its acoustic scenario. Usually, the scenario Underwater consists of relay nodes, sensor nodes, and gateway nodes. The relay nodes are considered as the immediate medium to pass the communication from source to destination. Gateways are present to receive data packets from relay nodes, which arepassed through the desired destination. The whole scenario is followed by an intentionally rotating path (from left to right) that is orbital in shape. The increasing trend of every orbit shape presents the refeclection of the rotating path where needed.