Three-dimensional multirobot formation control for target enclosing

This paper presents a novel method that enables a team of aerial robots to enclose a target in 3D space by attaining a desired geometric formation around it. We propose an approach in which each robot obtains its motion commands using measurements of the relative position of the other agents and of the target, without the need for a central coordinator. As contribution, our method permits any desired 3D target enclosing configuration to be defined, in contrast with the planar circular patterns commonly encountered in the literature. The proposed control strategy relies on the minimization of a cost function that captures the collective motion objective. In our method, the robots do not need to use a common reference frame. This coordinate independence is achieved through the introduction in the cost function of a rotation matrix computed locally by each robot. We prove that our motion controller is exponentially stable, and illustrate its performance through simulations.