Spherical formation tracking control of second-order nonlinear agents with directed communication

This article proposes a solution to the problem of forcing multiple agents to formation tracking a family of given concentric spheres when the communication topology is directed. Each agent under consideration has intrinsic second-order nonlinear dynamics. By using our previous concentric compression method, the cooperative control system can be regarded as a cascade system composed of the spherical tracking subsystem and the formation subsystem with the spherical tracking error as input. The algorithm for directed interaction is constructed by separately designing the control input projected onto the normal vector to the surface of sphere and the direction of spherical meridian for the spherical tracking subsystem, and the control input projected onto the direction of spherical parallel for formation motion. The asymptotic stability of the system is proved by using the tools of Input-to-State stability (ISS) theory. The effectiveness of the analytical results is verified by numerical simulations.