Unified Position and Attitude Control of A Fully Nonlinear Quadrotor*
This paper presents a departure from hierarchical cascade methods to control the position and attitude of a fully nonlinear quadrotor. The paper presents a nonlinear feedback control scheme that simultaneously controls position and attitude. The proposed method is based on a generalization of the Gauss's Principle of Least Constraint (GPLC) for higherorder constrained dynamical systems. By double differentiating the rigid-body position dynamics of a fully nonlinear quadrotor with respect to time, the translational and rotational dynamics become fully coupled at the levels of snap and angular acceleration, and the quadrotor is turned into a fully actuated system in a reduced configuration space. A generalized Baumgarte's error stabilization (BES) is developed to asymptotically drive constraint errors to zero. The nonlinear control law is due purely to the natural evolution of constrained system dynamics. To the best of our knowledge, this is the first instance that GPLC and BES are both extended to higher-order systems and that the control scheme for the position and attitude of a quadrotor is unified into one step by making use of its fully nonlinear constrained dynamics. The efficiency and efficacy of the proposed method is demonstrated by numerical experiments on a quadrotor tracking a prescribed conical spiral.
