Controlling Mobile Robot Teams from 1D Homographies

  • Miguel ArandaEmail author
  • Gonzalo López-Nicolás
  • Carlos Sagüés
Part of the Advances in Industrial Control book series (AIC)


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.


Planar Motion Motion Estimation Camera Motion Homography Matrix Trifocal Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Miguel Aranda
    • 1
    Email author
  • Gonzalo López-Nicolás
    • 2
  • Carlos Sagüés
    • 2
  1. 1.ISPRSIGMA Clermont, Institut PascalAubièreFrance
  2. 2.Instituto de Investigación en Ingeniería de AragónUniversidad de ZaragozaZaragozaSpain

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