On the Weighting of Control Signals in a Multi-robot System: A Formation-Based Analysis

This work presents a strategy to guide an n-robot convoy in a rigid virtual structure, split into n-2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n-2$$\end{document} triangular formations. Each set of three robots represents one formation, and transformation functions relate the robots’ position to the formation’s pose and shape, and vice versa. Each triangular formation has its own constructive sequence (clockwise or counterclockwise), which depends on the robots’ position, and is crucial for the control navigation. As first contribution, we propose a strategy based on cross-product concept to identify automatically the current and the desired triangle sequence. Furthermore, once knowing each robot can belong up to three formations, our second contribution is a control signals weighting, to improve simultaneous convergence of the whole formation. Finally, we present real experiments with four Pioneer-3DX robots performing a trajectory tracking task to validate our proposal.