θ-D based nonlinear tracking control of quadcopter

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.

[1]  M. Navabi,et al.  Development of access-based metrics for site location of ground segment in LEO missions , 2010 .

[2]  Rogelio Lozano,et al.  Discrete optimal control for a quadrotor UAV: Experimental approach , 2014, 2014 International Conference on Unmanned Aircraft Systems (ICUAS).

[3]  A. T. Kutay,et al.  Optimal path tracking control of a quadrotor UAV , 2014, 2014 International Conference on Unmanned Aircraft Systems (ICUAS).

[4]  Rogerio A. Enríquez-Caldera,et al.  LQR control for a quadrotor using unit quaternions: Modeling and simulation , 2013, CONIELECOMP 2013, 23rd International Conference on Electronics, Communications and Computing.

[5]  Congbo Luo.  Research on Flight Control of Quad-rotor Based on Backstepping and Adaptive Control Technology , 2016 .

[6]  Tayfun Çimen,et al.  State-Dependent Riccati Equation (SDRE) Control: A Survey , 2008 .

[7]  Guobao Zhang,et al.  Discrete-time sliding mode control for a quadrotor UAV , 2016 .

[8]  Ming Xin,et al.  A new method for suboptimal control of a class of nonlinear systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[9]  Samir Bouabdallah,et al.  Design and control of quadrotors with application to autonomous flying , 2007 .

[10]  Tansel Yucelen,et al.  Online solution of state dependent Riccati equation for nonlinear system stabilization , 2010, Proceedings of the 2010 American Control Conference.

[11]  Soon-Jo Chung,et al.  Exponential stability region estimates for the State-Dependent Riccati Equation controllers , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[12]  Holger Voos.  Nonlinear state-dependent Riccati equation control of a quadrotor UAV , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[13]  Raziyeh Babaie,et al.  Robust optimal motion planning approach to cooperative grasping and transporting using multiple UAVs based on SDRE , 2017 .

[14]  Salvatore Strano,et al.  A SDRE-based tracking control for a hydraulic actuation system , 2015 .

[15]  Hyo-Sung Ahn,et al.  Nonlinear Control of Quadrotor for Point Tracking: Actual Implementation and Experimental Tests , 2015, IEEE/ASME Transactions on Mechatronics.

[16]  Jinguo Liu,et al.  Fuzzy adaptive PD control for quadrotor helicopter , 2015, 2015 IEEE International Conference on Cyber Technology in Automation, Control, and Intelligent Systems (CYBER).

[17]  G. Cook,et al.  Suboptimal control for the nonlinear quadratic regulator problem , 1975, Autom..

[18]  Ming Xin,et al.  Integrated Guidance and Control of Missiles with Θ-D Method , 2004 .

[19]  M. Navabi,et al.  On reduction of longest accessibility gap in LEO sun-synchronous satellite missions , 2011 .

[20]  Shigenori Sano,et al.  Least square based sliding mode control for a quad-rotor helicopter and energy saving by chattering reduction , 2016 .

[21]  Liu Chun-Sheng,et al.  Optimal robust control for attitude of quad-rotor aircraft based on SDRE , 2015, 2015 34th Chinese Control Conference (CCC).

[22]  J. R. Cloutier,et al.  The capabilities and art of state-dependent Riccati equation-based design , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).