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.