Robust Geometric Navigation of a Quadrotor UAV on SE(3)

In this paper, a robust geometric navigation algorithm, designed on the special Euclidean group SE(3), of a quadrotor is proposed. The equations of motion for the quadrotor are obtained using the Newton–Euler formulation. The geometric navigation considers a guidance frame which is designed to perform autonomous flights with a convergence to the contour of the task with small normal velocity. For this purpose, a super twisting algorithm controls the nonlinear rotational and translational dynamics as a cascade structure in order to establish the fast and yet smooth tracking with the typical robustness of sliding modes. In this sense, the controller provides robustness against parameter uncertainty, disturbances, convergence to the sliding manifold in finite time, and asymptotic convergence of the trajectory tracking. The algorithm validation is presented through experimental results showing the feasibility of the proposed approach and illustrating that the tracking errors converge asymptotically to the origin.

[1]  M. Tadjine,et al.  Classical and second order sliding mode control solution to an attitude stabilization of a four rotors helicopter: From theory to experiment , 2011, 2011 IEEE International Conference on Mechatronics.

[2]  Amit K. Sanyal,et al.  Integrated Guidance and Feedback Control of Underactuated Robotics System in SE(3) , 2018, J. Intell. Robotic Syst..

[3]  H. J. Jayakrishnan,et al.  Position and Attitude control of a Quadrotor UAV using Super Twisting Sliding Mode , 2016 .

[4]  Luis F. Luque-Vega,et al.  Robust block second order sliding mode control for a quadrotor , 2012, J. Frankl. Inst..

[5]  J. Gordon Leishman,et al.  Principles of Helicopter Aerodynamics , 2000 .

[6]  Amit K. Sanyal,et al.  Attitude State Estimation with Multirate Measurements for Almost Global Attitude Feedback Tracking , 2012 .

[7]  Luis Amezquita-Brooks,et al.  Towards a standard design model for quad-rotors: A review of current models, their accuracy and a novel simplified model , 2017 .

[8]  Anand Sánchez-Orta,et al.  Position–Yaw Tracking of Quadrotors , 2015 .

[9]  Tansel Yucelen,et al.  Morse-Lyapunov-Based Control of Rigid Body Motion on TSE(3) via Backstepping , 2018 .

[10]  Nicolas Petit,et al.  The Navigation and Control technology inside the AR.Drone micro UAV , 2011 .

[11]  Rogelio Lozano,et al.  Sliding mode collision-free navigation for quadrotors using monocular vision , 2018, Robotica.

[12]  Anand Sánchez-Orta,et al.  Nonlinear ellipsoid based attitude control for aggressive trajectories in a quadrotor: Closed-loop multi-flips implementation , 2018, Control Engineering Practice.

[13]  Luis Amezquita-Brooks,et al.  Experimental assessment of wind gust effect on PVTOL aerial vehicles using a wind tunnel , 2015, 2015 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC).

[14]  Antonio Barrientos,et al.  Mini-quadrotor attitude control based on Hybrid Backstepping & Frenet-Serret theory , 2010, 2010 IEEE International Conference on Robotics and Automation.

[15]  Rita Cunha,et al.  A nonlinear position and attitude observer on SE(3) using landmark measurements , 2010, Syst. Control. Lett..

[16]  Amit K. Sanyal,et al.  Almost global finite‐time stabilization of rigid body attitude dynamics using rotation matrices , 2016 .

[17]  Taeyoung Lee,et al.  Dynamics of connected rigid bodies in a perfect fluid , 2008, 2009 American Control Conference.

[18]  Jaime A. Moreno,et al.  Strict Lyapunov Functions for the Super-Twisting Algorithm , 2012, IEEE Transactions on Automatic Control.

[19]  Sung Kyung Hong,et al.  Nonlinear Control for Autonomous Trajectory Tracking while Considering Collision Avoidance of UAVs Based on Geometric Relations , 2019, Energies.

[20]  Leonid M. Fridman,et al.  Super twisting control algorithm for the attitude tracking of a four rotors UAV , 2012, J. Frankl. Inst..

[21]  Amit K. Sanyal,et al.  Integrated guidance and nonlinear feedback control of underactuated unmanned aerial vehicles in SE(3) , 2017 .

[22]  J. Aubin,et al.  Differential inclusions set-valued maps and viability theory , 1984 .

[23]  Octavio Garcia,et al.  Time-parametrization control of quadrotors with a robust quaternion-based sliding mode controller for aggressive maneuvering , 2013, 2013 European Control Conference (ECC).

[24]  A. D. Lewis,et al.  Geometric control of mechanical systems : modeling, analysis, and design for simple mechanical control systems , 2005 .

[25]  Sergio Salazar,et al.  Test bed for applications of heterogeneous unmanned vehicles , 2017 .

[26]  O. Garcia,et al.  Embedded Super Twisting Control for the Attitude of a Quadrotor , 2016, IEEE Latin America Transactions.

[27]  Peter I. Corke,et al.  Multirotor Aerial Vehicles: Modeling, Estimation, and Control of Quadrotor , 2012, IEEE Robotics & Automation Magazine.

[28]  Martin Horn,et al.  Stability proof for a well-established super-twisting parameter setting , 2017, Autom..

[29]  Rogelio Lozano,et al.  Unmanned Aerial Vehicles Embedded Control , 2013 .

[30]  Rogelio Lozano,et al.  Second order sliding mode controllers for altitude control of a quadrotor UAS: Real-time implementation in outdoor environments , 2017, Neurocomputing.

[31]  Emilio Frazzoli,et al.  Trajectory tracking control design for autonomous helicopters using a backstepping algorithm , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[32]  Taeyoung Lee,et al.  Geometric tracking control of a quadrotor UAV on SE(3) , 2010, 49th IEEE Conference on Decision and Control (CDC).

[33]  Lorenzo Marconi,et al.  Output regulation on the Special Euclidean Group SE(3) , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[34]  Taeyoung Lee,et al.  Nonlinear Robust Tracking Control of a Quadrotor UAV on SE(3) , 2013 .