# Pipe Routing with Topology Control for Decentralized and Autonomous UAV Networks +
## 5 Topology Control
### Topology Control Scheme  
In Figure 5, the node \(N^{\prime}\) (shown in yellow) on the route has a low node degree, below a user-selected threshold \(Th\), due to pipe thinning. This low degree reduces the probability of finding an alternate route in the pipe region from the target UAV to the BS. In this section,  
Figure 5: Illustration of pipe thinning problem, where the node \(N^{\prime}\) has no one-hop neighbors except the upstream and downstream nodes on the current route.  
we propose a topology control scheme that uses pheromone-based mobility control to solve the pipe thinning problem.  
Since all UAVs in the network follow the BS-CAP mobility model (which is a repel pheromone-based mobility scheme), their mobility is influenced by the pheromone values of cells [7]. The digital pheromone information is propagated to the neighbors using the Hello messages. In our updated approach, nodes on the current route apply a pheromone mask to nullify the nearby repel pheromone if their node degree is below _Th_. As a result, neighboring nodes that are not part of the current route are induced to move into the region; see Figure 6 for an illustration.  
Consider a node \(N^{\prime}\) located in cell \((x,y)\), with repel pheromone map \(P_{M}\) (see Section 3). If a pheromone mask is applied by node \(N^{\prime}\), its resulting pheromone map \(P^{\prime}_{M}\) becomes  
\[P^{\prime}_{M}=P_{M}\odot A \tag{8}\]  
where \(A\) is the pheromone mask and \(\odot\) represents an element-wise product. \(A\) is a rectangular region of dimension \(2L\times L\) centered on the cell \((x,y)\) of node \(N^{\prime}\), and oriented perpendicular to the vector connecting the upstream and downstream nodes of \(N^{\prime}\) (see Figure 6). The size \(L\) is the signal transmission range of the UAV, i.e., the maximum one-hop distance between the UAVs. The pheromone values of cells in A are set to zero. The mask update can be equivalently viewed as depositing an attract pheromone value in each cell equivalent to its current repel pheromone value, resulting in a net pheromone value of zero. This helps cells in the \(2L\times L\) region to attract UAVs relative to cells outside the masked region, whose repel pheromone values are generally positive.  
The nodes arriving in the newly masked region provide potential alternate links and improve the robustness of the pipe region around the current route node(s). The pheromone mask is then retracted by the node(s) on the current route once its number of one-hop neighbors exceeds _Th_. The topology control algorithm is described in Algorithm 1. We use the threshold _Th_ = 2 in our simulations. Although higher _Th_ attracts more nodes to the one-hop regions of the current route, doing so does not necessarily improve routing performance and can degrade the network area coverage at low node densities.  
Figure 6: Applying a pheromone mask to attract UAVs.  
```
1// For a current route
2 foreach node \(N^{\prime}\) in the current route; except BSdo
3 Get \(d_{N^{\prime}}\) = one-hop node degree excluding upstream and downstream nodes;
4 // Node degree threshold, \(Th=2\)
5 if\(d_{N^{\prime}}\leq Th\)then
6 // Pipe node density low in region
7 Apply pheromone mask, \(P^{\prime}_{M}=P_{M}\odot A\) from (8);
8
9 else
10 // Pipe node density not low in region
11 Remove pheromone mask, \(P^{\prime}_{M}=P_{M}\);
12
13 end if
14
15 end for
```  
**Algorithm 1**Topology Control