## 2 Literature Review  
Considering 2D environments, there are many studies on distributed controllers to make all robots rendezvous, considering the case where a robot measures the relative position of its nearby robot [7; 30; 31; 32]. In [33], circumcenter-based consensus algorithms were introduced to achieve distributed rendezvous of multiple robots. However, how to handle faulty robots was not discussed in [33]. Considering 2D environments, [34] introduced rendezvous controllers that are tolerant to faulty robots. However, this method needs a controllable sensing range, which may not be feasible in practice. The authors of [35] considered the optimal consensus problem of asynchronous sampling single-integrator and double-integrator multi-robot systems utilizing distributed model predictive control algorithms. Event-driven rendezvous strategies [36; 37; 38] for multi-agent systems were motivated by the use of embedded microprocessors with limited resources that will gather information and actuate the individual agent controller updates. Considering event-triggered rendezvous controls, [38] proved that if the communication graph is connected, consensus is achieved exponentially. The authors of [37] showed that with appropriate control gains in event-triggering conditions, subsystems employing discrete-time signals from neighbors achieve the state consensus. The authors of [36] studied the rendezvous problem of multi-robot systems by parallel event-triggered connectivity-preserving controls. The event-triggered control laws in [36] can assure the system convergence, and can maintain the connectivity of the time-varying and position-dependent communication network. However, [36; 37; 38] considered 2D environments without obstacles. In cluttered underwater environments, obstacles can block the communication link between robots, resulting in the loss of a robot. Our study handles practical scenarios where multiple underwater robots are deployed in cluttered environments (e.g., [29]). In obstacle-rich environments, the communication (interaction) link between robots may be blocked owing to obstacles. In such scenarios, it is important to assure that the communication link is preserved while every robot maneuvers. As far as we know, the proposed distributed rendezvous control is unique in overcoming communication link failure or invisible robots. As far as we know, other studies on distributed rendezvous controls [7; 30; 31; 32; 36; 37; 38] assumed that a robot can measure the relative position of its neighbor robot using local sensors, such as laser. However, no physical sensors were clearly described for this local interaction. In other words, other rendezvous controls in [7; 30; 31; 32; 36; 37; 38] were designed, while the specific sensors that were used for the controls were not considered. However, considering specific sensors is crucial, since robots move based on local sensing measurements. Considering 2D environments, [39] addressed rendezvous algorithms using received signal strength indicator (RSSI) data from the radio. Reference [40] addressed a simple rendezvous algorithm using RSSI data from the radio. Reference [40] used a small, low-cost, modular robotics platform in 2D environments. Reference [40] explored the potential for using RSSI in platforms equipped with radios in order to rendezvous at a desired location or agent. The authors of [39] addressed multi-robot rendezvous with range-only measurements. However, references [39; 40] considered simple 2D environments with no obstacles. In addition, [39; 40] did not show that their rendezvous algorithm is provably complete in achieving multi-robot rendezvous. Moreover, [39; 40] did not consider how to handle the case where a UUV is broken. In [41], the authors applied radars with a variable sensing range in order to make all robots rendezvous in 3D environments. However, obstacle environments were not considered in [41]. Unknown obstacles can block the communication link between robots in practice.