Distributed backstepping control of multiple thrust-propelled vehicles on a balanced graph

We propose novel exponentially-converging distributed flocking and formation-centroid backstepping control frameworks for multiple under-actuated thrust-propelled vehicles in SE(3), each consisting of the under-actuated Cartesian dynamics on E(3) with one-dimensional thrust-force input and the fully-actuated attitude kinematics on SO(3) with angular-rates inputs; and evolving on a strongly-connected balanced information graph G. Simulations are also performed to illustrate the theory.