θ-D based nonlinear tracking control of quadcopter

Abstract

In this paper, two nonlinear suboptimal control techniques are investigated to effectively design flight control system for a quadcopter. Quadcopters have nonlinear, multi-input multi-output (MIMO), coupled and underactuated dynamics. First, State Dependent Riccati Equation (SDRE) method is utilized to tackle infinite-time nonlinear optimal control problem of quadcopter flight through precise approximation of Hamilton Jacobi Bellman (HJB) equation. Then, to obtain closed-form optimal controller and elude inordinate computation requirement of SDER method, we apply θ−D technique to perturb the optimal cost, resulting in declining HJB equation to a set of recursive algebraic Lyapunov equations. These methods guarantee stability of closed-loop system, force the states to follow desired reference signals and compensate nonlinear terms. Finally, the performance of nonlinear control algorithms are evaluated by numerical simulations. Results illustrate the effectiveness of presented controllers in stabilization and altitude tracking, particularly with large initial conditions, while Linear Quadratic Regulator (LQR) fails to keep tracking error below the requirements and find an optimal feedback gain.