Multi-robot rendezvous in the plane

In this paper, we discuss a multi-robot rendezvous problem. The aim is to design decentralized control laws for N robots moving in the horizontal plane in order to reach an unpredictably moving point at the same time. The rendezvous problem is modeled using the relative kinematics equations. Our control laws are derived using the integration of geometrical rules with the relative kinematics model. Two approaches are used, namely reference-robot and leader-follower. In the first approach the robots move independently from each other, but they depend on the motion of the reference trajectory. In the second approach the motion of each following robot depends only on its leader, and the motion of one leader depends on the motion of the reference trajectory. Each follower has one leader. For both approaches, two control laws are derived for each robot. Our strategy is illustrated using various simulation examples.