Controlled Lagrangians control for a quadrotor helicopter

The controller design technique based on Controlled Lagrangians (CL) is presented for a quadrotor helicopter with under-actuation degree 2. Firstly, the dynamic model of the quadrotor used for controller design is introduced, and the model is linearized at its equilibrium. Then, the CL method is used for the linearized system to design its controller and the matching conditions satisfied for the controller are derived. Stability analysis shows that the controlled closed-loop system is asymptotically stable. The proposed method solves the under-actuated problem for quadrotor and avoids the dependence of control law design under the time-scale separation assumption. Finally, simulation results for the quadrotor helicopter to hovering in a certain position are illustrated to verify effectiveness of the proposed method.