3D underactuated formation tracking control on loops

This article considers the three dimensional problem of directing a family of underactuated vehicles to formation flying on closed convex plane curves. We show how the curve-extension design, projection-tracking method and consensus-based technique can be combined together to construct the formation tracking controller under the bidirectional commutation topology. With help of invariance-like theorem and the extension of Barbalat´s lemma, it is proved that the design control system is asymptotically stable if the commutation graph is connected. Simulation results demonstrate the effectiveness of the proposed approach.