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Abstract Random walks are fundamental building blocks for swarm robotics, as they enable exploration of unknown environments, area coverage and interaction with peers without requiring large computational abilities. As a matter of fact, random walks are employed in numerous swarm robotics studies. While implementing a random walk is relatively straightforward, choosing the best approach for a specific task is not, as the macroscopic properties of the system (e.g., diffusion) heavily depend on the specificities of the random walk model. In this study, we focus on a comprehensive random walk model, namely the Lévy-Modulated Correlated Random Walk, which can be easily parametrised to implement different kinds of random walks, from Brownian motion to Lévy walks. We perform a thorough evaluation of the macroscopic properties associated to different parameterisations, also largely varying the swarm size to identify the effect of robot density and collisions. We perform target search experiments with real and simulated Kilobots, both in bounded and open space. In bounded space, we evaluate the effects of different wall avoidance strategies. In open space, we determine the impact of different densities of the robots during the initial deployment around a central place. We quantify diffusion properties, search efficiency and probability of interaction with peers, hence providing a precise picture about the expected effects of different random walk models. The results can support the implementation of more complex behaviours in swarm robotics based on random walks, both with Kilobots and with any other robotics platform moving in 2D.