A geometric extension design for spherical formation tracking control of second-order agents in unknown spatiotemporal flowfields

This article proposes a solution to the problem of directing multiple second-order agents sphere landing, orbit tracking and formation moving around a family of given concentric spheres in unknown spatiotemporal flowfields. The flowfields put stress on each agent’s velocity and acceleration at once, and the specification of each one is composed of three known base vectors and unknown responding coefficients. First, our pervious two-dimensional geometric extension design is extended to deal with the extension of surface in three-dimensional space. Then, two new adaptive estimators and the cooperative control law are constructed to accomplish the robust spherical formation tracking motion by using the tools of adaptive backstepping, geometric extension and consensus. The asymptotic stability of system is proved when the bidirectional communication topology is connected. The effectiveness of the analytical result is verified by numerical simulations.