Alignment of Three Robots without Communication nor Localization*

Frédéric Guinand (1, 2) , François Guerin (3) , Mark Bastourous (1)

1 RI2C - LITIS - Equipe Réseaux d'interactions et Intelligence Collective
2 UKSW - Cardinal Stefan Wyszyński University
3 GREAH - Groupe de Recherche en Electrotechnique et Automatique du Havre

This paper presents a decentralized method for aligning three robots without communication and without explicit localization. Each robot is assumed to be equipped with an omnidirectional camera and is assumed to be able to detect the two other robots in the images produced by its own camera. Each robot decides of its own movements based on the continuous measures of angles between itself and the others. We present both the algorithm that performs such a task and its theoretical analysis. We prove the correctness of the algorithm when the robots are reduced to points, when collisions are not considered and when the initial formation is not an equilateral triangle. When collisions are considered, the probability for the algorithm to be successful is greater than 1 − 1 36. We then present some simulation for which a security distance d sec has been introduced. During the execution of the algorithm by each robot, if the distance between any two robots is lower than this security distance we suppose that a collision is likely to occur and consider that the Algorithm has failed. Simulation results report that the larger d sec , the bigger the percentage of failures. However runs are always successful when d sec = 0 which suggests that the theoretical bound is not tight and could be improved. In addition, simulations reveal that the main source of failures was not the one expected by the theoretical analysis.

Domaines: Informatique [cs]; Robotique [cs.RO]

Frédéric Guinand, François Guerin, Mark Bastourous. Alignment of Three Robots without Communication nor Localization*. 2019 IEEE International Conference on Systems, Man and Cybernetics (SMC), Oct 2019, Bari, Italy. pp.647-654, ⟨10.1109/SMC.2019.8914442⟩. ⟨hal-02501345⟩