Modeling and Control Design for Quadrotors: A Controlled Hamiltonian Systems Approach

In this paper, a new mathematical model of quadrotor is proposed by using the Hamiltonian approach, which has more advantages than Newtonian and Lagrangian approaches in some aspects such as compactness, easiness of controller design, and its symplectic structure. The Hamiltonian model of a quadrotor is a first-order differential equation whose states include generalized position and momentum that contain information about both the corresponding velocity and generalized mass. A nonlinear controller is proposed based on the proposed symplectic Hamiltonian model. The controller includes two sub-controllers-attitude sub-controller and position sub-controller. Furthermore, the stability of the designed controller is verified by Lyapunov stability theorem and the controller is provided with exponential stability. The effectiveness of the proposed model and the designed controller is demonstrated not only by software-in-the-loop simulations but also by hardware-in-the-loop simulations. Real-time experimental results show that the proposed controller is able to carry out the tasks of taking off, tracking fixed point, hovering, and landing.