Abstract

In many multi-robot 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 multi-robot 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 permutationinvariant formations.

Citations