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The recent advancement of Deep Reinforcement Learning (DRL) contributed to robotics by allowing automatic controller design. The automatic controller design is a crucial approach for designing swarm robotic systems, which require more complex controllers than a single robot system to lead a desired collective behaviour. Although the DRL-based controller design method showed its effectiveness, the reliance on the central training server is a critical problem in real-world environments where robot-server communication is unstable or limited. We propose a novel Federated Learning (FL) based DRL training strategy (FLDDPG) for use in swarm robotic applications. Through the comparison with baseline strategies under a limited communication bandwidth scenario, it is shown that the FLDDPG method resulted in higher robustness and generalisation ability into a different environment and real robots, while the baseline strategies suffer from the limitation of communication bandwidth. This result suggests that the proposed method can benefit swarm robotic systems operating in environments with limited communication bandwidth, e.g., in high-radiation, underwater, or subterranean environments.