Path planning for permutation-invariant multirobot formations

Stephen Kloder, Seth Hutchinson

Research output: Contribution to journalArticlepeer-review


In many multirobot applications, the specific assignment of goal configurations to robots is less important than the overall behavior of the robot formation. In such cases, it is convenient to define a permutation-invariant multirobot formation as a set of robot configurations, without assigning specific configurations to specific robots. For the case of robots that translate in the plane, we can represent such a formation by the coefficients of a complex polynomial whose roots represent the robot configurations. Since these coefficients are invariant with respect to permutation of the roots of the polynomial, they provide an effective representation for permutation-invariant formations. In this paper, we extend this idea to build a full representation of a permutation-invariant formation space. We describe the properties of the representation, and show how it can be used to construct collision-free paths for permutation-invariant formations.

Original languageEnglish (US)
Pages (from-to)650-665
Number of pages16
JournalIEEE Transactions on Robotics
Issue number4
StatePublished - Aug 2006
Externally publishedYes


  • Configuration spaces
  • Mobile robots
  • Multirobot systems
  • Path planning

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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