Cooperative adaptive flow estimation for spherical formation tracking control with directed communication

This article considers the robust cooperative control problem of multiple double-integrator agents' formation moving around a set of given curves on spheres, where each agent suffers an unknown spatiotemporal flowfield and the communication topology among agents is directed. The flow specification is composed of a general direction matrix and a responding unknown flow speed vector, which includes almost all forms of flowfield in the literature. A new second-order adaptive update law is given for estimating the flow speed vector by using the tool of adaptive backstepping, which is incorporated into our previous geometric extension design for the purpose of designing the robust spherical formation tracking control law. A potential function is used to avoid each agent's movement to the undefined angle on the points between the poles of sphere. The asymptotic stability of the system is proved when the directed communication topology is strongly connected. The effectiveness of the analytical results is verified by a numerical simulation.