# Robust Distributed Rendezvous Using Multiple Robots with Variable Range Radars
## 2 Literature Review  
Considering 2D environments, many papers [16; 17; 18; 19; 20; 21] addressed distributed rendezvous algorithms. Reference [18] addressed distributed rendezvous algorithms, considering limited visibility of identical robots. Reference [16] addressed connectivity-preserving control strategies for the rendezvous problem. Considering 2D environments, [17] addressed distributed rendezvous algorithms considering robots with bounded control inputs. Reference [13] presented rendezvous controllers based on local sensing measurements of every robot. Reference [22] presented distributed rendezvous controllers so that multiple robots rendezvous at multiple rendezvous points simultaneously. Considering cluttered 3D environments, [23] addressed distributed control laws to make all spherical underwater robots rendezvous. However, [23] requires that a robot can be identified using local sensors and that a tree structure is built based on local sensing measurements. However, the radar sensors considered in our paper cannot be used to identify one robot from another. The authors of [9; 24; 25] proposed a distributed controller to achieve rendezvous, even when some robots in the system are broken. The references [9; 24; 25] assumed that a broken robot does not move or does not follow a prescribed policy. Reference [9] assumed that probabilities associated with robot failures are available, and their rendezvous algorithms rely on these probability distributions to compute stochastic optimal control strategies to maximize performance in an expected sense. However, in practice, robot failure probabilities may not be available. In our paper, we do not use the probabilities associated with robot failures. Recall [9; 24; 25] assumed that a broken robot does not move or does not follow a prescribed policy. However, our paper considers the case where a robot is completely broken. For instance, enemy attacks can completely destroy a robot, as plotted in Figure 1. This distinguishes our paper from [9; 24; 25]. For achieving distributed rendezvous in arbitrary dimensions, circumcenter algorithms were proposed in [13; 14; 15] to avoid the loss of existing links between robots. Circumcenter algorithms do not require that a robot can be identified using local sensors. Thus, circumcenter algorithms are suitable for distributed rendezvous using radar sensors. Furthermore, in circumcenter algorithms, a tree structure does not have to be built based on local sensing measurements. The proposed rendezvous controls with variable range radars are based on circumcenter algorithms. Similarly to circumcenter algorithms, our rendezvous approach can handle arbitrary dimensions and does not require that a robot can be identified using local sensors. As far as we know, other papers on rendezvous controls did not consider sensor specifications required for multi-robot rendezvous. Our paper is distinct from [13; 14; 15] since we consider robots with specific sensors: variable range radars. Circumcenter algorithms in [13; 14; 15] require the initial connectivity assumption. To the best of our knowledge, every distributed rendezvous control in the literature requires the initial connectivity assumption. In our paper, we control the sensing range of each robot adaptively in order to achieve distributed rendezvous even in the case where the initial connectivity assumption does not hold. Considering 3D environments, we design a distributed rendezvous control with a variable sensing range so that the network connectivity is maintained (or recovered) during a robot's maneuvering. Once the rendezvous is achieved, the sensing range of every robot can decrease in order to reduce the power consumption of its radar. To the best of our knowledge, our article is novel in applying radars with a variable sensing range in order to make all heterogeneous robots rendezvous in 3D environments. Our distributed rendezvous control is unique since we do not require the initial connectivity assumption.