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.

[1]  Ashfaq Ahmad Mian,et al.  Dynamic modeling and nonlinear control strategy for an underactuated quad rotor rotorcraft , 2008 .

[2]  A. Tayebi,et al.  Attitude stabilization of a four-rotor aerial robot , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[3]  S. Sastry,et al.  NONLINEAR CONTROL OF A HELICOPTER BASED UNMANNED AERIAL VEHICLE MODEL , 2001 .

[4]  I. C. Cheeseman.  Helicopter Performance, Stability and Control. R. W. Prouty. PWS Engineering, 20 Park Plaza, Boston, MA 02116, USA. 1986. Distributed by Routledge, Chapman & Hall Ltd., Andover. 731 pp. Illustrated. £43.95. , 1989 .

[5]  A.,et al.  Principles and Practice of Automatic Process Control , 2007 .

[6]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[7]  P. McKerrow,et al.  Modelling the Draganflyer four-rotor helicopter , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[8]  Rogelio Lozano,et al.  Modelling and Control of Mini-Flying Machines , 2005 .

[9]  Rogelio Lozano,et al.  Real-time stabilization and tracking of a four rotor mini-rotorcraft , 2003 .

[10]  Roland Siegwart,et al.  Backstepping and Sliding-mode Techniques Applied to an Indoor Micro Quadrotor , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[11]  I. Kanellakopoulos,et al.  Integral-Action Nonlinear Control of Induction Motors 1 , 1993 .

[12]  Robert Mahony,et al.  Design of a four-rotor aerial robot , 2002 .

[13]  Raymond W. Prouty,et al.  Helicopter performance, stability, and control , 1986 .

[14]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .