A Distributed Constrained Optimization Approach for Spatiotemporal Connectivity-Preserving Rendezvous of Multi-Robot Systems

This paper studies a spatiotemporal connectivity-preserving rendezvous problem for a group of mobile robots. With the available battery and communication cost being taken into account, this problem is split into two sub-problems. Firstly, robots need to choose optimal strategies by solving a distributed constrained optimization problem to determine when and where to meet before moving. Consensus-based distributed gradient algorithms are developed to solve this subproblem. Subsequently, once the optimal solution is obtained and provided to only a subset of robots, a fixed-time distributed controller is designed to solve a connectivity-preserving rendezvous control problem. It is shown that the robot team under the proposed designs can achieve the spatiotemporal connectivity-preserving rendezvous task, while minimizing the energy consumption.