A New Characterization of Mobility for Distance-Bearing Formations of Unicycle Robots

Fabio Morbidi, Estelle Bretagne
2018 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)  
In this paper, we present a new characterization of mobility for formations of unicycle robots defined by distance-bearing constraints. In fact, by introducing a simple reduction procedure which associates a prescribed formation with a "macro-robot", we extend the classification by type proposed by Campion et al., to multi-agent systems. To simplify the classification task, which only leverages the nonslip condition for a conventional centered wheel, we assume that the robots are disposed at
more » ... vertices of a regular convex polygon. We demonstrate the practical utility of the notion of macrorobot in a trajectory-tracking control problem for a formation of unicycles. ⎤ ⎦ , the elementary rotation matrix of an angle θ about the z-axis. ∀ x, y ∈ R n , x, y = n i=1 x i y i , and x = x, x 1/2 . f (t) ∈ C k means that the vector-valued function f (t) is of differentiability class C k . Finally, I n×n and 0 m×n denote the n × n identity matrix and the m × n matrix of zeros, respectively, and nul(A) the nullity of matrix A ∈ R m×n , i.e. the dimension of the kernel of A.
doi:10.1109/iros.2018.8593984 dblp:conf/iros/MorbidiB18 fatcat:wnuwr2j7sbaj5pjde2ncyuhusy