Enhanced Foraging in Robot Swarms Using Collective L´ evy Johannes Nauta 1 and Stef van Havermaet and Pieter Simoens and Yara Khaluf Abstract. 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 de- sirable. This paper proposes a novel approach that extends the in- dividual L´ evy 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 collec- tive 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 L´ evy walk for two different types of target distributions: homogeneous and hetero- geneous. Our results highlight the advantages of the proposed ap- proach for both target distributions, while increasing the scalability to large swarm sizes. Finally, we further extend the individual explo- ration algorithm by adapting the L´ evy 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. 1 Introduction Coordination and self-organization in swarm robotics are key fea- tures that are inspired from natural social systems such as ant colonies [27], and enable a large group of robots to achieve collec- tive efficiency that is not achieved by individual robots [29, 6, 12]. In robot swarms, each robot builds its knowledge of the world lo- cally through its limited perception. Nevertheless, robots exploit di- rect and indirect communication to increase their effectiveness as a group by sharing information and make decisions conjointly. One of the well-studied examples in robot swarms is foraging, which is behavior commonly observed in social animals [4]. This task is in- tensively studied in robot swarms due to its importance as a metaphor for a large spectrum of robotic applications, including search and res- cue, and resource exploitation (e.g., harvesting). In foraging, the collective system searches for targets in an un- known environment. Such exploration attempts are bound to con- straints, such as energy expenditure, and thus need to be optimized in order to ensure the survival of the swarm. Several studies have shown that when foraging considers individuals, random searches can be optimized depending on the distribution over targets [31, 23, 25, 38]. In these studies, random searches which follow L´ evy walk patterns have been found to be more efficient than alternatives, such as the correlated random walk [3] and Brownian motion. In random walks, the trajectory of an individual is described by a sequence of flights, whose length and direction are chosen randomly. In the specific case 1 Ghent University, Belgium, email: johannes.nauta@ugent.be of L´ evy walks, the flight lengths ℓ are sampled from a power-law distribution p(ℓ) ∼ ℓ -(α+1) , (1) where 0 <α< 2 is the L´ evy parameter. In contrast to many exponentially decaying distributions, such as the normal distribu- tion, power-law distributions have tails which are fat. This results in statistically relevant large values being sampled from the distri- bution, corresponding to execution of long flights in the case of a L´ evy walk (for an extensive review, we refer the interested reader to [37]). Hence, L´ evy walks alternate long bouts of straight line motion with Brownian-like motion, furthermore displaying scale-free behav- ior typical of power-laws. Exactly these long flights are responsible for the increase in the search efficiency needed for foraging animals to survive. In more detail, random searches with L´ evy parameter α ≈ 1 opti- mize the random search for an individual over a wide range of target distributions, such as homogeneous, sparse distributions [31, 3], het- erogeneous, patchy distributions [34, 36, 35] and scale-free, fractal- like distributions [11]. Furthermore, L´ evy walks are of interest due to the wide range of motion behavior that they encompass. For α → 0, we enter the ballistic regime where each individual only displays straight line motion. For α ≥ 2, the resulting motion is Brownian due to the power-law distribution converging to the normal distribu- tion due to the central limit theorem. Intermediate values 0 <α< 2 show motion patterns in between both extremes, including an opti- mal value at α opt ≈ 1 that interchanges long flight lengths with more Brownian-like behavior. While individual foraging can be optimized by having the forager follow a L´ evy walk, collective foraging is not optimized by simply having each individual follow a L´ evy walk, due to physical limita- tions and finite size effects. In cases where the density of the swarm is high, collisions between individuals become increasingly likely, resulting in truncation of the current flight due to collision avoidance. Hence, the collective system as a whole might not display the char- acteristics typical for a L´ evy flight, i.e. a power-law distribution over flight lengths. To the best of our knowledge, it is currently unclear if the resulting collective motion actually resembles a L´ evy walk for an increasing swarm density. The purpose of this study is therefore twofold; (i) we first aim to understand the influence of the swarm density on the collective behavior of the random search, and (ii) pro- vide an engineered approach to increase the search efficiency of the collective system. Specifically, we (i) analyze the distribution of the collective flight lengths, for which we show that this does not fol- low a L´ evy characteristic power-law anymore above a certain (criti- cal) swarm size. Afterwards, we (ii) develop a random walk strategy for each individual which ensures power-law distributions for larger Walks ECAI 2020 G.D. Giacomo et al. (Eds.) © 2020 The authors and IOS Press. This article is published online with Open Access by IOS Press and distributed under the terms of the Creative Commons Attribution Non-Commercial License 4.0 (CC BY-NC 4.0). doi:10.3233/FAIA200090 171