# A Glider-Assisted Link Disruption Restoration Mechanism in Underwater Acoustic Sensor Networks
## 4 The GALO Algorithm
### The GALO Algorithm
Volume \(A_{1}\) is the glider's trajectory coverage volume and volume \(A_{2}\) is the zone defined by the C1 and C2 constraints. That is, the range indicated by the volume \(A_{1}\) is expressed by Equation (12), and the range indicated by the volume \(A_{2}\) is expressed by Equation (13): \[ \begin{array}{l}\mathit{trail}(x)=0\end{array} \] (12) \[ \begin{array}{l}\mathit{trail}(\mathit{x})=0\end{array} \] (13) \[ \begin{array}{l}\mathit{s.t.}\\ \mathit{C1.}\ \ \ \ \ TL_{ag}<TL_{th1}\\ \mathrm{C2.}\ \ \ \ TL_{gb}<TL_{th2}\end{array} \] The original problem of Equation (5) is thus transformed into a new problem for solving the suboptimal solution, as shown in Equation (14). The solution obtained to achieve the shortest distance between the two regions is the sub-optimal solution of the original problem. It is the position for the glider to restore the link: \[\min\{d(A_{1},A_{2})\}\] (14)  
Based on the above calculation, the glider can arrive the optimal or sub-optimal position to restore the link disruption as a relay node. However, if the data packet needs a long time to be transmitted or the link needs a long time to be restored, there may be a link disruption between the node and the glider due to currents. Thence designing a method to withstand currents is necessary when the glider prepares restoring the disrupted link. We consider that the glider has two kinds of movement (sawtooth and spiral movement). It achieves a sawtooth profile through the buoyancy adjusting unit and the attitude adjusting unit. The spiral movement is achieved by combining the sawtooth movement with the roll adjustment unit. When the glider arrives at the calculated position, it transforms its movement mode into a spiral movement. That is because it can move within a relatively small volume in a spiral movement. In additions, the maximum total speed, vertical speed and horizontal speed of the glider are 2.05 m/s, 1.88 m/s and 1.93 m/s, respectively. As an important performance parameter of counteracting currents, the greater horizontal speed indicates a stronger anti-flow ability [10; 11], and higher reliability in the harsh environment. In addition, the communication between node and glider with a specific trajectory has been studied [9]. Therefore, the conversion of movement model can complete the communication between node and glider without disruption. In this networking process, the cluster head node can calculate the probability of the link disruption in this cluster. In general, the probability of link disruption can be calculated as \(F_{ab}=Pr(log_{2}(1+|H_{ab}|^{2}SNR_{ab})<R_{A})=Pr(|H_{ab}|<\frac{2^{R_{A}}- 1}{5\text{N}R_{ab}})\)[25]. However, for a link with higher probability of disruption than \(F_{ab}\), it indicates that the environment of the acoustic channel here is rather harsh. In this case, in order to improve the restoration efficiency, we add the calculated position of the link to the periodic path of the glider until the environment there is improved. In our network model, we assume that the deployment of original sensor nodes has satisfied the coverage and connectivity conditions. Therefore, the probability of link disruption will not be high and that glider can complete its tasks of monitoring and restoring the link.