Multirobot rendezvous control and coordination strategies have garnered significant interest in recent years because of their potential applications in decentralized tasks. In this paper, we introduce a coordinate-free rendezvous control strategy to enable multiple robots to gather at different locations (dynamic leader robots) by tracking their hierarchy in a connected interaction graph. A key novelty in this strategy is the gathering of robots in different groups rather than at a single consensus point, motivated by autonomous multipoint recharging and flocking control problems. We show that the proposed rendezvous strategy guarantees convergence and maintains connectivity while accounting for practical considerations such as robots with limited speeds and an obstacle-rich environment. The algorithm is distributed and handles minor faults such as a broken immobile robot and a sudden link failure. In addition, we propose an approach that determines the locations of rendezvous points based on the connected interaction topology and indirectly optimizes the total energy consumption for rendezvous in all robots. Through extensive experiments with the Robotarium multirobot testbed, we verified and demonstrated the effectiveness of our approach and its properties.