A key aspect of foraging in robot swarms is optimizing the search efficiency when both the environment and target density are unknown. Hence, designing optimal exploration strategies is desirable. This paper proposes a novel approach that extends the individual Lévy walk to a collective one. To achieve this, we adjust the individual motion through applying an artificial potential field method originating from local communication. We demonstrate the effectiveness of the enhanced foraging by confirming that the collective trajectory follows a heavy-tailed distribution over a wide range of swarm sizes. Additionally, we study target search efficiency of the proposed algorithm in comparison with the individual Lévy walk for two different types of target distributions: homogeneous and heterogeneous. Our results highlight the advantages of the proposed approach for both target distributions, while increasing the scalability to large swarm sizes. Finally, we further extend the individual exploration algorithm by adapting the Lévy walk parameter α, altering the motion pattern based on a local estimation of the target density. This adaptive behavior is particularly useful when targets are distributed in patches.
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