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Path planning for permutation-invariant multirobot formations

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2 Author(s)
Kloder, S. ; Beckman Inst. for Adv. Sci. & Technol., Illinois Univ., Urbana, IL ; Hutchinson, S.

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

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Robotics, IEEE Transactions on  (Volume:22 ,  Issue: 4 )