*1.2. Connectivity-Based Proposals*

Despite its well-known inefficiencies, there exist some few approaches without any connection requirements where robots meet each other by chance. Nevertheless, this section only surveys the proposals that depend on connectivity in one way or another.

In [21] a behaviour-based approach is presented. The architecture is designed to guide the exploration constraining the fleet to keep within the communication range, establishing a mobile network. The well-known disk model and a graph structure are used to model the network connectivity and identify possible disconnections. Frontier cells are evaluated regarding costs (computed utilising a flooding algorithm) and information utility (based on the ideas proposed in [3]). Behaviours are selected according to the network topology conditions.

In [22] a centralised communicative exploration algorithm is proposed. Communicative exploration implies that the team of robots have to maintain connections between each other at all times. The target selection is based on a utility function that weights the benefits of exploring new regions versus the goal of keeping connected. While connectivity is valued using the classic *disc* model, the costs of the shortest paths are computed from the Manhattan distance notion. Due to spatial and movement restrictions, specific behaviours are defined to deal with deadlocks. Also following a centralised approach, [23] presents four fully reactive exploration strategies. They consist in translating the distance to tasks and disconnection situations into artificial forces that pull and push the robot to reach new positions smoothly, avoiding them to lose connectivity. The radio signal quality is modelled considering both the communication range and the distance attenuation effect. Deadlocks are avoided by assigning tasks to a cluster of robots. This allocation guarantees that robots belonging to the same cluster do not exert conflicting forces upon each other towards different directions.

In [24], the authors propose a decentralised version of the strategy proposed in [22] based on message exchanging and a graph structure where the group always tries to keep a biconnected network efficiently. Communication model is based on the classic *disc* model. In consequence, robot mobility is restricted by the communication range. Using the same graph theory, in [25] the experimental validation of a distributed algorithm that preserves connectivity is also discussed. Nevertheless, a different coordination mechanism—supported by a market-based negotiation algorithm—is adopted. Unfortunately, only results on connectivity maintenance are shown, lacking exploration metrics reports.

The proposal of [26] aims to maintain and repair the underlying wireless mesh network while the coverage task is being performed, all at once. The system works in a fully asynchronous and distributed way. Differently from previous works, the authors propose a network disconnection detection by checking the real state of connections without assumptions on communication range or propagation model. On the contrary, all nodes require knowledge about the area to be covered and on global positions.

In [15] the robots can disconnect as long as they regain connectivity periodically following a distributed but synchronous strategy. Authors address coordination implicitly through localisation data exchanging. Robots are forced to wait for others before making a decision. The system works as an optimisation method where each variable is optimised at a time in a round-robin while the others remain unchangeable. In [27] the authors describe a heterogeneous multi-robot system for exploration tasks. They consider several explorer robots and conceive a particular robot playing the role of relay dispenser. This agent is in charge of place relays when and where it is necessary to support the video/audio streaming generated by explorers.

In [28] the problem of exploration and mapping is addressed by using a *Decentralised POMDP*. This technique takes advantage of local interaction and coordination from the interaction-oriented resolution of decentralised decision makers. *Distributed value functions (DVS)* are used by decoupling the multi-agent problem into a set of individual agent problems. In order to address full local observability, limited information sharing, and communication breaks, an extension of the *DVS* methodology is proposed and applied in multi-robot exploration so that each robot computes locally a strategy that minimises the interaction between fleet members and maximises the coverage achieved by the team, even in communication constrained environments. A decision step consists in building the model, computing the policy from the *DVS* and producing a trajectory.

Rendezvous-based techniques have also been used to deal with limited communication ranges. In [16] robots are enabled to move out of the communication range but forced to rejoin the group frequently. After moving out the communication range robots have to return to a pre-arranged meeting point to exchange the information gathered during the disconnection period in order to avoid exploration overlaps.

The proposal presented in [29] describes a *Particle Swarm Optimisation* based approach to achieving fault-tolerance in preventing communication network splits. The principal objective is to keep the fleet *k*-connected. Considering that the application domain defines the fault-tolerance level required to the system, a MANET connectivity algorithm is extended with the concept of *k*-fault-tolerance.

A multi-robot system for crisis management is described in [30]. The system is composed of mobile sensors (ground robots—UGV) and mobile relays (aerial vehicles—UAV). However, some robots may change roles dynamically during the mission (e.g., UAVs equipped with both wireless routers and cameras). The problem is modelled and solved using constrained-based local search on a communication model based on graph theory.

In [31] a fully distributed approach for multi-robot sweep exploration is introduced. The proposal aims to guarantee full coverage using a minimum number of messages and to maintain connectivity at all times, even under severe restrictions on the communication type, range, and quality. The algorithm proposed uses communication not only to exchange information but to direct the robot movements. Communication intensity is used in order to disperse the fleet while beacons are used to mark locations of interest.

In [32] a multi-robot exploration algorithm based on multiple behaviours is proposed. Quad-rotors are asked to explore and map an indoor zone with unreliable communication and limited battery life. Robots are enabled to change roles both dynamically according to intrinsic and extrinsic factors (e.g., boundaries/distances and battery level) and hierarchically in order to explore and avoid collision among each other. The remaining battery level is considered in order to avoid losing gathered information. Quad-rotors are also able to leave the network, but after a fixed period they search for regaining connectivity. Relay robots are designated to forward information from/to the more distant robots improving communication between team members. Although no optimal relay placement is computed, the existence of relays is crucial in the proposed scheme.

In [33,34] the relay node dynamic re-positioning problem is tackled. The proposed solution relies on optimisation procedures and evolutionary algorithms to find the best relay locations and how the robots should move to these points. The authors follow a centralised multi-stage approach where one node is in charge of computing the best assignment regarding both connectivity and throughput.

In [35], the problem of how to connect one or more remote units to a base station investing a limited number of intermediate relay robots in constrained communication environments is investigated. The authors study the complexity of the optimal relay placement problem and propose methodologies to create chains or trees of relays as required by different static scenarios. By contrast, in changing environments static solutions cannot be successfully applied because the location optimality does not hold over time.

In [36] the exploration problem is addressed ensuring a time-varying connected topology in *3D* cluttered environments but following a decentralised control strategy which enables simultaneous multi-task exploration.

Another centralised but asynchronous strategy is followed in [19,37] in order to address the problem of multi-robot exploration under recurrent connectivity. In these works, the authors leverage a variant of the Steiner tree problem that appears as a particular case of different known graph optimisation problems. Robot placement is treated as an optimisation problem through Integer Linear Programming. Exact and approximated algorithms are compared on particular scenarios.
