# Formation of multiple groups of mobile robots: multi-timescale convergence perspective

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## Abstract

Multiple objects of different shapes combined together build a composite structure in automated industry. To carry those objects of different shapes, different numbers of robots are required to be in the formations which comply with the shapes of those objects. This paper introduces a transformation that separates the combined dynamics of a formation of multiple groups of robots into translational dynamics of centroid, intra-group shape dynamics, and inter-group shape dynamics, using the geometry of a shape. Partitioning the intra-group shape vectors, gives one the freedom to choose the number of groups required in a formation (with multiple groups). On the other hand, the inter-group shape vectors as opposed to the existing literature on single group of robots, extend further the connectivity among the groups. Therefore, they determine the geometric shape of the groups when connected. At first the transformation is applied on the combined dynamics of robots for the purpose of partitioning. Then singular perturbation-based control laws are designed to show through simulation results, that the convergence of different groups, the overall shape of groups combined together, and the tracking occur at different time. This ensures that one dynamics does not need to wait for the convergence of others. This saves time as opposed to sequential completion of various operations of the mission.

## Keywords

Formation control Multi-level topology Multi-timescale analysis Singular perturbation Obstacle avoidance## Supplementary material

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