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2017 | OriginalPaper | Chapter

6. Coordinate-Free Control of Multirobot Formations

Authors : Miguel Aranda, Gonzalo López-Nicolás, Carlos Sagüés

Published in: Control of Multiple Robots Using Vision Sensors

Publisher: Springer International Publishing

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Abstract

It is undoubtedly interesting, from a practical perspective, to solve the problem of multirobot formation stabilization in a decentralized fashion, while allowing the agents to rely only on their independent onboard sensors (e.g., cameras), and avoiding the use of leader robots or global reference frames. However, a key observation that serves as motivation for the work presented in this chapter is that the available controllers satisfying these conditions generally fail to provide global stability guarantees. In this chapter, we provide novel theoretical tools to address this issue; in particular, we propose coordinate-free formation stabilization algorithms that are globally convergent. The common elements of the control methods we describe are that they rely on relative position information expressed in each robot’s independent frame, and that the absence of a shared orientation reference is dealt with by introducing locally computed rotation matrices in the control laws. Specifically, three different nonlinear formation controllers for mobile robots are presented in the chapter. First, we propose an approach relying on global information of the team, implemented in a distributed networked fashion. Then, we present a purely distributed method based on each robot using only partial information from a set of formation neighbors. We finally explore formation stabilization applied to a target enclosing task in a 3D workspace. The developments in this chapter pave the way for novel vision-based implementations of control tasks involving teams of mobile robots, which is the leitmotif of the monograph. The controllers are formally studied and their performance is illustrated with simulations.

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Footnotes
1
Note that the analysis in this section is similar to finding the solution to the Procrustes orthogonal problem [45] and resembles the study in Sect. 6.2.2.1. Observe, however, that the cost functions for the control method we describe here and the one presented throughout Sect. 6.2 differ.
 
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Metadata
Title
Coordinate-Free Control of Multirobot Formations
Authors
Miguel Aranda
Gonzalo López-Nicolás
Carlos Sagüés
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-57828-6_6