Three-dimensional distributed tracking control for multiple quadrotor helicopters

This paper deals with the cooperative tracking control of a team of underactuated quadrotors in three-dimensional space when the reference signal is not available to all the vehicles. Using the Backstepping and filtering design technique and results from graph theory, a distributed cooperative controller consisting of two interconnected blocks is proposed. The first block, which is based on local distributed controllers, guarantees that the centroid of the three-dimensional formation asymptotically follows a desired path corresponding to the desired formation trajectory. The second block ensures that the attitude dynamics of the quadrotor will converge asymptotically to their actual values, which are constrained within a predefined set, such that singularities are avoided in the quadrotor's dynamics. Due to the coupling property between the translational and rotational dynamics, the equilibrium point of the complete closed-loop system is shown to be asymptotically stable. Numerical simulations are illustrated to show that the theoretical conclusions are effective.