Cooperative concurrent targeting for planar arrays of point sources

Abstract

Motivated by practical applications in satellite formations and directional antenna arrays, the problem of targeting a planar array of point sources at one common object of interest is proposed and then solved using novel distributed coordination strategies. These point sources are arbitrarily located on the x–y plane and the boundary point sources, whose either x or y coordinate is extremal, already orient to the non-coplanar target point. The only global information shared among the remaining point sources is the positive directions of the global coordinate axes x and y, and hence, they have to rely on sensing the changes of the orientation angles of their nearest neighbors to adjust their own orientation. We prove that under our control law, the orientation lines will asymptotically intersect at the same point of concurrency as the boundary point sources. The main idea behind the designed control law is the intuitive argument from Euclidean geometry that reducing the differences between the distances to the x–y plane of the pairwise intersection points of the orientation lines leads to realizing concurrent targeting. We further show the boundedness and exponential convergence speed of the orientation angles.