For mobile robotic networks in industrial scenarios, reliable and energy-efficient communications are crucial yet challenging. Fortunately, collaborative beamforming (CB) emerges as a promising solution, which can increase the transmission gain and reduce the transmit power of robots by constructing a mobile robot-enabled virtual antenna array (MRVAA). The performance of CB is tightly related to robot positions, necessitating proper robot selection. However, robot selection may expose the network to the risk of unbalanced energy distribution, reducing network lifetime. Additionally, the mobility and variable numbers of robots require flexible and scalable robot selection algorithms. To tackle these challenges, we first formulate a multi-objective optimization problem to reduce the maximum sidelobe level (MSLL) of MRVAA while minimizing the standard deviation of the network energy distribution (SDNED) by selecting robots for CB. Then, based on distributed multi-agent learning (MARL), we propose an effective and scalable robot selection algorithm with energy considered (RoSE) to solve the problem, where difference-rewards function (DRF) and policy sharing are designed for enhancing convergence rate and policy stability. Simulation results show that the RoSE has the scalability to positions and numbers of robots. Furthermore, RoSE surpasses existing selection algorithms in network lifetime and time efficiency, while still maintaining comparable MSLL.
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