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2017 | OriginalPaper | Chapter

4. Controlling Mobile Robot Teams from 1D Homographies

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

As Chaps. 2 and 3 of the monograph have illustrated, an effective way to address vision-based control when the robots (and their attached cameras) move in a planar environment is to use omnidirectional vision and 1D multiview models. This provides interesting properties in terms of accuracy, simplicity, efficiency and robustness. After exploring the use of the 1D trifocal tensor model, in this chapter we turn our attention to the 1D homography. This model can be computed from just two views but, compared with the trifocal constraint, presents additional challenges: namely, it is dependent on the structure of the scene, and does not permit direct estimation of camera motion. The chapter presents a novel method that overcomes the latter issue by allowing to compute the planar motion between two views from two different 1D homographies. Additionally, this motion estimation framework is applied to a multirobot control task in which multiple robots are driven to a desired formation having arbitrary rotation and translation in a two-dimensional workspace. In particular, each robot exchanges visual information with a set of predefined formation neighbors, and performs a 1D homography-based estimation of the relative positions of these adjacent robots. Then, using a rigid 2D transformation computed from the relative positions, and the knowledge of the position of the group’s global centroid, each robot obtains its motion command. The robots’ individual motions within this distributed formation control scheme naturally result in the full team reaching the desired global configuration. Results from simulations and tests with real images are presented to illustrate the feasibility and effectiveness of the methodologies proposed throughout the chapter.

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Footnotes
1
The manner in which this computation can be carried out is studied in detail in Chap. 5 of the monograph. That chapter also proposes the use of rigid transformations but, unlike what is done here, the transformations take the form of homographies computed from image data, which are exploited in a multirobot control task. A more in-depth discussion of how these rigid transformations can be parameterized and computed is provided in Chap. 5.
 
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Metadata
Title
Controlling Mobile Robot Teams from 1D Homographies
Authors
Miguel Aranda
Gonzalo López-Nicolás
Carlos Sagüés
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-57828-6_4