## 3 Cooperative Algorithms for Mobile Sensors
### Area Coverage Performance and Algorithm Limitations
In this case, when each vehicle communicates its foreseen location at its next communication step, the asymmetric configuration becomes unstable and the group alternates between a configuration where \(V_{1}\) and \(V_{4}\) are further away than \(V_{2}\) and \(V_{3}\) and another one in which \(V_{1}\) and \(V_{4}\) are closer than \(V_{2}\) and \(V_{3}\) to the asset. Finally, as a more complex scenario, ten vehicles are simulated. Figure 8 shows the agent path and the final formation obtained, with the HVA placed at the center of the vehicles detection area. The agent locations around the asset depend on their initial positions and, as the number of vehicles increases, it becomes more complicated to characterize the final distribution of agents. A theoretical analysis of such a problem is however beyond the scope of the paper. As shown through simulations the proposed method is able to solve the general area coverage problem, reducing the overlap of sonar detection sonars and ensuring that each agent maintains at least one other vehicle in its communication range. The approach, which is suited to be implemented on underwater vehicles, requires little communication among the vehicles. Furthermore, with limited modifications on the type of information transmitted but without introducing additional data exchange or algorithmic complexity, it instigates additional and more complex team behaviors (e.g., patrolling). The resulting behavior of the team of AUVs is strongly dependent on the parameters of the interest functions associated with each rule of the algorithm. The slope of the functions, in fact, determines the strength of each rule and their relative weight, at each time step. A steep asset attraction function (\(h_{A}\)) implies an increase in the attractive field of the HVA while a modification in the shape of the cooperation function relates to the detection sonar overlap. For instance, a more gentle slope for \(h_{C}(. )\)produces, on one hand, an increase in the sonars overlap, reducing the total area coverage, but, on the other hand, it increases the total detection level, as it can be computed using, for example, the approach proposed in [17]. The selection of the specific parameters is hence a design tradeoff and depends on the specific application. The flexibility of the proposed algorithm, based on the selection of appropriate interest functions to obtain desired global behaviors, represents, at the same time, its main limitation. It may in fact be difficult to tune the function parameters to achieve the desired mission goal and in the cases treated here the choice was based on empirical rules. Further investigations are ongoing to analytically guarantee the optimality of the selection. While different approaches exist in literature on the area coverage problem by means of a network of cooperating sensors/agents (see for example [18] and [19]), they are, however, designed for reliable radio-based networks and for isotropic propagation media, often assuming unlimited communication ranges. Even in the cases where communication constraints are explicitly considered [20], they are typically assumed as indirected and homogeneous. On the contrary, the approach proposed in this work has been devised from the beginning to be able to tackle communication and detection variations, and specifically tailored to the characteristics of the underwater channel. The cooperation interest function \(h_{C}\) is, in fact, computed on the basis of the detection and communication performance encountered as the mission proceeds, and it may be made dependent on the direction, allowing for the inclusion of detection and communication directivity. Figure 6: Area coverage performance with three vehicles. The optimal locations for the agents to obtain the total coverage of a circle of radius \(R_{M}\) are the vertices of the inscribed triangle. A circular motion is stimulated when each vehicle communicates its foreseen location at its next communication step.