Probabilistic Analysis of Long-Term Swarm Performance under Spatial Interferences Yara Khaluf 1 , Mauro Birattari 2 , and Franz Rammig 1 1 Heinz Nixdorf Institut, University of Paderborn F¨ urstenallee 11, 33102 Paderborn, Germany {yara,franz}@hni.uni-paderborn.de https://www.hni.uni-paderborn.de/ 2 IRIDIA, Universit´ e Libre de Bruxelles B-1050 Brussels, Belgium mbiro@ulb.ac.be http://iridia.ulb.ac.be Abstract. Swarm robotics is a branch of collective robotics that out- performs many other systems due to its large number of robots. It allows for performing several tasks that are beyond the capability of a single or multi robot systems. Its global behaviour emerges from the local rules implemented on the level of its individual robots. Thus, estimating the obtained performance in a self-organized manner represents one of the main challenges, especially under complex dynamics like spatial inter- ferences. In this paper, we exploit the central limit theorem (CLT) to analyse and estimate the swarm performance over long-term deadlines and under potential spatial interferences. The developed model is tested on the well-known foraging task, however, it can be generalized to be applied on any constrictive robotic task. Keywords: Swarm robotics, Time-constrained tasks, Central limit theorem. 1 Introduction Swarm robotics is a high density multi-robot system, where the global behaviour emerges from local rules implemented on the level of individual robots. These systems are characterized by a set of advantages including: redundancy, scala- bility and flexibility which introduce them as a promising approach for a large spectrum of tasks. Spatial interferences, on the other hand, affect significantly the performance of the single robot and consequently the collective performance of the swarm. A well-studied example is the foraging, where robots are exploited to retrieve scattered objects to a special area called ”nest”. As noted in [5,10], the increment of the robots’ number in a task like foraging, decreases the performance of a single robot which represents the number of retrieved objects per time unit. In the case of swarm performance, it may increase by adding robots up to an A.-H. Dediu et al. (Eds.): TPNC 2013, LNCS 8273, pp. 121–132, 2013. c  Springer-Verlag Berlin Heidelberg 2013