A Unified SO(3) Approach to the Attitude Control Design for Quadrotors

This paper proposes a two-phased problem reformulation approach to solve the quadrotor UAV attitude control problem. Given an initial attitude, the objective is to design a control to drive it toward a desired value. The first phase begins with the definition of three types of errors pertaining to attitude discrepancy, followed by the utilization of virtual control with which the dynamics of quadrotor's attitude and angular velocity are then unified under the framework of SO(3), rendering the original control problem much more transparent to tackle. Through cancellation of certain unwanted terms emerging from the unification process, entry-wise treatment of the remaining matrix dynamics is then employed in the second phase to transform it further into the stabilization problem of a 3-dimensional linear time-invariant system that is fairly easy to solve since to which standard feedback designs such as linear quadratic regulator and pole placement are readily applicable. In addition to the classical designs, a specialized and structurally simple controller is provided to reduce the number of gains. To account for system parametric uncertainties, external disturbances, and sensor measurement errors and noises, a second controller based on classical H_∞ theory is presented to enhance the robustness of the design. A numerical example is given, and computer simulations are conducted to generate error and control trajectories to assess and compare the effectiveness of the presented designs.