Optimal Control using Backstepping Technique of a Quadrotor Helicopter

In this paper a novel optimal hierarchical controller for a quadrotor is proposed. It is based on optimal control theory and backstepping technique. The used dynamic model of the quadrotor is obtained via Euler-Lagrange formalism and written in a convenient canonical form which represents three interconnected subsystems: under-actuated subsystem, fully-actuated subsystem and propeller subsystem. This representation is suited for the application of the backstepping technique. The control law is designed step by step. The control law of each step is based on optimal control theory; it gives the expression of the virtual control input of the corresponding step which is optimal regarding a performance index. This new technique simplifies the design of the optimal controller by breaking down the complex nonlinear systems into smaller sub-systems. The performance of the proposed method is tested by simulation by considering the control of the 3D absolute position and the yaw angle.