Backstepping based PID Control Strategy for an Underactuated Aerial Robot

Abstract

In this paper a nonlinear model of an underactuated quad rotor aerial robot is derived, based on Newton-Euler formalism, and backstepping based PID control strategy is implemented for the derived model. Model derivation comprises determining equations of motion of the quad rotor in three dimensions and seeking to approximate actuation forces through modeling of aerodynamic coefficients and electric motor dynamics. The derived MIMO model, constituted of translational and rotational subsystem, is dynamically unstable. A nonlinear control strategy is therefore implemented for the quad rotor aerial robot. The control strategy includes integral backstepping control for the translational subsystem and backstepping based PID control for the rotational subsystem. The stability of the control design is ensured by Lyapunov stability theorem. The performance of the nonlinear control strategy is evaluated using nonlinear simulation. The simulation results, obtained from backstepping based PID, are compared with conventional optimized PID controller. For the conventional PID controller, the optimization algorithm used is to minimize the Integral of Absolute Error (IAE). Results of comparison validate effectiveness of the backstepping based PID control strategy for the underactuated aerial robot near quasi stationary flight.