# Pipe Routing with Topology Control for Decentralized and Autonomous UAV Networks +
## 3 Overview of Pheromone-Based UAV Mobility Model  
Pheromone mobility models use digital repel pheromones to promote exploration and fast coverage of an area, without prior information [3; 7]. A digital pheromone mimics natural pheromones with deposition, evaporation, and diffusion characteristics stored in a virtual map divided into grid cells called a digital pheromone map. We assume that UAVs move in a two-dimensional space (that is, at constant altitude) to search a given area. Although the UAV's positions and trajectories are continuous-valued, to represent the pheromone map, we divide the area into a grid of \(C\times C\) cells, each identified by its \((x,y)\) coordinates. Each UAV moves toward cells with the minimum repel pheromone value and deposits a repel pheromone of magnitude '1' in cells scanned along its trajectory. After a deposit in the cell \((x,y)\), the repel pheromone diffuses to the surrounding cells at a constant rate \(\psi\in[0,1]\). The pheromone of each cell also evaporates at a constant rate \(\lambda\in[0,1]\), allowing UAVs to revisit cells after a time interval as the target locations may change over time [7]. The pheromone value \(p_{(x,y)}\) in a cell \((x,y)\) at time \(t\) is described as [3; 7],  
\[p_{(x,y)}(t) = (1-\lambda)\cdot\left[(1-\psi)\cdot p_{(x,y)}(t-1)+\partial p_{(x, y)}(t-1,t)+\partial d_{(x,y)}(t-1,t)\right] \tag{1}\]where \((1-\psi)\cdot p_{(x,y)}(t-1)\) is the pheromone value remaining in cell \((x,y)\) after diffusion to the surrounding cells, \(\partial p_{(x,y)}(t-1,t)\) is the new pheromone value deposited in the update interval \((t-1,t)\), and \(\partial d_{(x,y)}(t-1,t)\) is the additional pheromone diffused to the current cell from its eight surrounding cells in the update interval \((t-1,t)\), which is described as [3; 7],  
\[\partial d_{(x,y)}(t-1,t)=\frac{\psi}{8}\cdot\sum_{a=-1}^{1}\sum_{b=-1}^{1}p_{ (x+a,y+b)}(t-1) \tag{2}\]  
Each UAV maintains a digital pheromone map \(P_{M}\) containing the pheromone values of the cells, where \(P_{M}\in[0,1]^{C\times C}\). In a decentralized UAV network, each UAV exchanges its local digital pheromone information (its \(5\times 5\) surrounding neighborhood cells) with its one-hop neighbors by using the periodic 'hello' messages [7]. Pheromone mobility models efficiently cover areas by distancing UAVs from each other and previously visited cells. However, they may weaken the node degree and BS connectivity (Node degree is the number of one-hop neighbors that determines the local connectivity of a UAV and BS connectivity is defined as the existence of a path to the BS) due to a UAV's limited transmission range, particularly at low UAV density. Note that a strong node degree is essential in decentralized networks for reliable communication and coordination among UAVs. Likewise, strong BS connectivity is crucial for effective information transmission from UAVs to the BS. Thus, we consider a decentralized, connectivity-aware, pheromone-based UAV mobility model such as the BS-CAP model [7] in our experiments to provide fast area coverage, strong node degree, and base station connectivity. In BS-CAP, UAVs also move and deposit repel pheromones on digital pheromone maps (\(P_{M}\)). The trajectory of a UAV (controlled by its next-waypoint cell) is decided on the basis of the repel pheromone in cells and the node degree at a set of candidate waypoints while ensuring that the next-waypoint maintains a route to the BS. The coverage and connectivity trade-off is controlled by adjusting the weight given to the UAVs' node degree at the waypoints. In the sequel, we also modify the BS-CAP model to provide topology control in the pipe and increase the density of UAVs around a route (see Sections 4 and 5). Another connectivity-aware UAV mobility model used in our experiments is the ConCov model [29], which uses a modified flocking behavior to provide trade-offs between coverage and BS connectivity.