UAV Flight Path Control Using Contraction-Based Back-stepping Control

Tan Chun Kiat, Hungsun Son, Paw Yew Chai

DSO National Laboratories, Singapore.
School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore.

DOI: 10.4236/ojapps.2013.32B013                

Abstract

In this paper, a contraction-based backstepping nonlinear control technique was proposed. The proposed controller synthesis technique utilizes both the recursive nature of backstepping control and of contraction analysis. This approach results in a contracting closed-loop dynamics, with exponential stability. The use of the hierarchical contraction form in the control problem formulation also results in the exponential convergence of controlled variables and can be easily applied to non-autonomous systems. A flight path angle controller was synthesized and simulated using the proposed technique to demonstrate the exponential convergence achieved by the backstepping controller design.

Keywords

Backstepping; Contraction Theory

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. H. Stone, “The T-wing Tail-Sitter Unmanned Air Vehicle: From Design Concept to Research Flight Vehicle,” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 218, No. 6, 2004, pp. 417-433. doi:10.1243/0954410042794920
[2]	J. Carl G. Schaefer and L. J. Baskett, “GoldenEye: The Clandestine UAV,” in 2nd AIAA “Unmanned Unlimited” Systems, Technologies, and Operations, 2003, pp. 1-11.
[3]	J. Escareno, R. H. Stone, A. Sanchez and R. Lozano, “Modeling and Control Strategy for the Transition of a Convertible Tail-sitter UAV,” in European Control Conference, 2007.
[4]	O. Harkegard, “Flight Control Design Using Backstepping,” Linkoping University, 2003.
[5]	N. B. Knoebel and T. W. McLain, “Adaptive Quaternion Control of A Miniature Tailsitter UAV,” in 2008 American Control Conference, 2008, pp. 2340-2345. doi:10.1109/ACC.2008.4586841
[6]	A. A. Mian, M. I. Ahmad and D. Wang, “Backstepping based Nonlinear Flight Control Strategy for 6 DOF Aerial Robot,” in 2008 International Conference on Smart Manufacturing Application, 2008, pp. 146-151. doi:10.1109/ICSMA.2008.4505630
[7]	F. M. Subolic, “Agile Flight Control Techniques for a Fixed-Wing Aircraft,” Massachusetts Institute of Technology, 2009.
[8]	J. H. Yang and W. C. Hsu, “Adaptive Backstepping Control for Electrically Driven Unmanned Helicopter,” Control Engineering Practice, Vol. 17, No. 8, 2009, pp. 903-913. doi:10.1016/j.conengprac.2009.02.012
[9]	W. S. Lohmiller, “Contraction Analysis of Nonlinear Systems,” Massachusetts Institute of Technology, 1999.
[10]	W. Lohmiller and J. J. E. Slotine, “On Contraction Analysis for Non-linear Systems,” Automatica, Vol. 34, No. 6, 1998, pp. 683-696. doi:10.1016/S0005-1098(98)00019-3
[11]	W. Lohmiller and J. J. E. Slotine, “Control System Design for Mechanical Systems Using Contraction Theory,” IEEE Transactions on Automatic Control, Vol. 45, No. 5, 2000, pp. 984-989. doi:10.1109/9.855568
[12]	J. Jouffroy and J. J. E. Slotine, “Methodological Remarks on Contraction Theory,” 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) , Vol. 3, 2004, pp. 2537-2543.
[13]	J. Jouffryo, “Integrator Backstepping Using Contraction Theory: A Brief Methodological Note,” 2002, p. 238.
[14]	B. B. Sharma and I. N. Kar, “Contraction Theory-based Recursive Design of Stabilising Controller for A Class of Non-linear Systems,” IET Control Theory & Applications, Vol. 4, No. 6, 2010, p. 1005. doi:10.1049/iet-cta.2009.0060
[15]	M. Zamani and P. Ta-buada, “Towards Backstepping Design for Incremental Stability,” 49th IEEE Conference on Decision and Control (CDC) , 2010, pp. 2426-2431. doi:10.1109/CDC.2010.5717210
[16]	B. L. Stevens and F. L. Lewis, “Aircraft Control and Simulation,” John Wiley and Sons, 2003, p. 664.