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Each agent is equipped with the same sensing, computing, and motion-control capabilities to achieve rendezvous based on the neighbors\u2019 states. First, a convex hull combination algorithm (CHCA) is designed, in which each agent solves a convex problem composed of perceived neighbors in the sensing region and chooses an optimal control strategy to move to the next position with guaranteed connectivity under low-density network topologies. Second, the relative neighborhood graph is incorporated into the CHCA (RNCHCA) as the constraint set to adapt to the high-density network topologies. The convergence and connectivity of the proposed algorithms are proved based on the geometric concept and case analyses. Finally, a large number of simulation results show that under the initially connected topologies with different densities, the RNCHCA can achieve a higher rendezvous speed than that achieved by the traditional circumcenter algorithm, particularly under high-density network topologies. <\/jats:p>","DOI":"10.1177\/01423312231187012","type":"journal-article","created":{"date-parts":[[2023,7,29]],"date-time":"2023-07-29T11:56:56Z","timestamp":1690631816000},"page":"771-784","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["Connectivity-preserving rendezvous in discrete-time multi-agent systems via relative neighborhood proximity graph"],"prefix":"10.1177","volume":"46","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9857-2140","authenticated-orcid":false,"given":"Guangqiang","family":"Xie","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Guangdong University of 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