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

Published online by Cambridge University Press:  05 August 2019

O. Garcia Open the ORCID record for O. Garcia [Opens in a new window] ,
E. G. Rojo-Rodriguez Open the ORCID record for E. G. Rojo-Rodriguez [Opens in a new window] ,
A. Sanchez ,
D. Saucedo  and
A. J. Munoz-Vazquez Open the ORCID record for A. J. Munoz-Vazquez [Opens in a new window]
O. Garcia*
Affiliation:
Aeronautics Department, Aerospace Engineering Research and Innovation Center, Faculty of Mechanical and Electrical Engineering, Autonomous University of Nuevo Leon, Apodaca, NL, Mexico E-mails: octavio.garcias@uanl.mx; erik.rojordr@uanl.edu.mx
E. G. Rojo-Rodriguez
Affiliation:
Aeronautics Department, Aerospace Engineering Research and Innovation Center, Faculty of Mechanical and Electrical Engineering, Autonomous University of Nuevo Leon, Apodaca, NL, Mexico E-mails: octavio.garcias@uanl.mx; erik.rojordr@uanl.edu.mx
A. Sanchez
Affiliation:
Aeronautics Department, Robotics and Advanced Manufacturing Department, CINVESTAV, Saltillo, Coahuila, Mexico E-mail: anand.sanchez@cinvestav.mx
D. Saucedo
Affiliation:
National Polytechnic Institute, UPIIG, Silao de la Victoria, Guanajuato, Mexico E-mail: dsaucedog@ipn.mx
A. J. Munoz-Vazquez
Affiliation:
Computer Science Department, CONACYT-School of Engineering, Autonomous University of Chihuahua, Campus II, Chihuahua, Mexico E-mail: aldo.munoz.vazquez@gmail.com
*
*Corresponding author. E-mail: octavio.garcias@uanl.mx
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Summary

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.

Keywords

Quadrotor UAVGeometric navigationGuidance frameSuper twisting algorithm
Type
Articles
Information
Robotica , Volume 38 , Issue 6 , June 2020 , pp. 1019 - 1040
Copyright
© Cambridge University Press 2019

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References

Amezquita-Brooks, L. A., Liceaga-Castro, E., Gonzalez-Sanchez, M., Garcia-Salazar, O. and Martinez-Vazquez, D., “A towards a standard design model for quad-rotors: A review of current models, their accuracy and a novel simplified model,” Progress Aerospace Sci., Elsevier 95(8), 1–23 (2017).CrossRefGoogle Scholar
Lozano, R., Unmanned Aerial Vehicles Embedded Control (John Wiley-ISTE Ltd, USA, 2010).Google Scholar
Sanchez, A., Parra-Vega, V., Garcia, O., Ruiz-Sanchez, F. and Ramos-Velasco, L. E., “Time-Parametrization Control of Quadrotors with a Robust Quaternion-based Sliding Mode Controller for Aggressive Maneuvering,” 2013 European Control Conference (ECC), Zurich, Switzerland (2013) pp. 3876–3881.Google Scholar
Lee, T., Leok, M. and McClamroch, N. H., “Dynamics of Connected Rigid Bodies in a Perfect Fluid,” Proceedings of the IEEE American Control Conference (ACC), St. Louis, MO (2009).CrossRefGoogle Scholar
Lee, T., Leok, M. and McClamroch, N. H., “Geometric Tracking Control of a Quadrotor UAV on SE(3),” Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, GA (2010) pp. 5420–5425.Google Scholar
Lee, T., Leok, M. and McClamroch, N. H., “Nonlinear robust tracking control of a quadrotor UAV on SE(3),” Asian J. Control 15(2), 391–408 (2013).CrossRefGoogle Scholar
Vasconcelos, J. F., Cunha, R., Silvestre, C. and Oliveira, P., “A nonlinear position and attitude observer on SE(3) using landmark measurements,” Syst. Control Lett. 59(3–4), 155–166 (2010).CrossRefGoogle Scholar
Colorado, J., Barrientos, A., Martinez, A., Lafaverges, B. and Valente, J., “Mini-Quadrotor Attitude Control Based on Hybrid Backstepping and Frenet–Serret Theory,” Proceedings of the 2010 IEEE International Conference on Robotics and Automation (ICRA 2010), Anchorage, AK (2010) pp. 1617–1622.Google Scholar
Sanyal, A. K. and Nordkvist, N., “Attitude state estimation with multi-rate measurements for almost global attitude feedback tracking,” AIAA J. Guidance Control Dyn. 35(3), 868–880 (2012).CrossRefGoogle Scholar
Pylorof, D. and Bakolas, E., “Tracking a Maneuvering Target with an Underactuated UAV in the SE(3) Space,” AIAA Guidance, Navigation, and Control Conference, AIAA SciTech Forum (2015) pp. 1–12.Google Scholar
Bohn, J. and Sanyal, A. K., “Almost global finite-time stabilization of rigid body attitude dynamics using rotation matrices,” Int. J. Robust Nonlinear Control 26(9), 2008–2022 (2016).CrossRefGoogle Scholar
Viswanathan, S. P., Sanyal, A. K. and Samiei, E., “Integrated guidance and feedback control of underactuated robotics system in SE(3),” J. Intell. Robot. Syst. 89(1–2), 251–263 (2018).CrossRefGoogle Scholar
Viswanathan, S. P., Sanyal, A. K. and Izadi, M., “Integrated Guidance and Nonlinear Feedback Control of Underactuated Unmanned Aerial Vehicles in SE(3),” AIAA Guidance, Navigation and Control Conference, AIAA SciTech Forum (2017) pp. 1–12.Google Scholar
Nazari, M., Maadani, M., Butcher, E. A. and Yucelen, T., “Morse-Lyapunov-Based Control of Rigid Body Motion on TSE(3) via Backstepping,” 2018 AIAA Guidance, Navigation and Control Conference, AIAA SciTech Forum (2018) pp. 1–12.Google Scholar
Mahony, R., Kumar, V. and Corke, P., “Multirotor aerial vehicles: Modeling, estimation, and control of quadrotor,” IEEE Robot. Auto. Mag. 19(3), 20–32 (2012).CrossRefGoogle Scholar
de Marco, S., Marconi, L., Hamel, T. and Mahony, R., “Output Regulation on the Special Euclidean Group SE(3),” IEEE 55th Conference on Decision and Control (CDC 2016), Las Vegas, NV (2016).CrossRefGoogle Scholar
Ha, L. N. N. T., Bui, D. H. P. and Hong, S. K., “Nonlinear control for autonomous trajectory tracking while considering collision avoidance of UAVs based on geometric relations,” Energies 12(8), 1551 (2019).CrossRefGoogle Scholar
Derafa, L., Benallegue, A. and Fridman, L., “Super twisting control algorithm for the attitude tracking of a four rotors UAV,” J. Franklin Inst. 349(2), 685–699 (2012).CrossRefGoogle Scholar
Jayakrishnan, H. J., “Position and Attitude Control of a Quadrotor UAV Using Super Twisting Sliding Mode,” IFAC 2016 (2016) pp. 284–289.Google Scholar
Bouchoucha, M., Seghour, S. and Tadjine, M., “Classical and Second Order Sliding Mode Control Solution to an Attitude Stabilization of a Four Rotors helicopter: From Theory to Experiment,” 2011 IEEE International Conference on Mechatronics (ICM), Istanbul, Turkey (2011).Google Scholar
Munoz, F., Gonzalez-Hernandez, I., Salazar, S. and Espinoza, E. S., “Second order sliding mode controllers for altitude control of a quadrotor UAS: Real-time implementation in outdoor environments,” Neurocomputing 233, 61–71 (2017).CrossRefGoogle Scholar
Luque-Vega, L., Castillo-Toledo, B. and Loukianov, A. G., “Robust block second order sliding mode control for a quadrotor,” J. Franklin Inst. 349(2), 719–739 (2012).CrossRefGoogle Scholar
Sanchez, A., Parra-Vega, V., Izaguirre, C. and Garcia, O., “Position-yaw tracking of quadrotors,” J. Dyn. Syst. Measurement Control 137(6), 1–12 (2015).Google Scholar
Escobar, A. G., Alazki, H., Valenzuela, J. E. and Garcia, O., “Embedded super twisting control for the attitude of a quadrotor,” IEEE Latin America Trans. 14(9), 3974–3979 (2016).Google Scholar
Mercado, D., Castillo, P. and Lozano, R., “Sliding mode collision-free navigation for quadrotors using monocular vision,” 36(10), 1–17 (2018).CrossRefGoogle Scholar
Stengel, R. F., Flight Dynamics (Princeton University Press, USA, 2004).Google Scholar
Leishman, J. G., Principles of Helicopter Aerodynamics (Cambridge University Press, USA, 2006).Google Scholar
Martinez, O., Amezquita-Brooks, L., Liceaga-Castro, E., Garcia, O. and Martinez, D., “Experimental Assessment of Wind Gust Effect on PVTOL Aerial Vehicles Using a Wind Tunnel,” Proceedings of the 2015 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC), Ixtapa, Mexico (2015).CrossRefGoogle Scholar
Oliva-Palomo, F.Sanchez-Orta, A., Castillo, P. and Alazki, H., “Nonlinear ellipsoid based attitude control for aggressive trajectories in a quadrotor: Closed-loop multi-flips implementation,” Control Eng. Pract. 77(8), 150–161 (2018).CrossRefGoogle Scholar
Aubin, J. P. and Cellina, A., Differential Inclusions: Set-Valued Maps and Viability Theory (Springer Science & Business Media, Germany, 2012).Google Scholar
Moreno, J. A. and Osorio, M., “Strict Lyapunov functions for the super-twisting algorithm,” IEEE Trans. Auto. Control 57(4), 1035–1040 (2012).CrossRefGoogle Scholar
Bullo, F. and Lewis, A. D., Geometric Control of Mechanical Systems: Modeling, Analysis, and Design for Simple Mechanical Control Systems (Springer, New York, 2005).CrossRefGoogle Scholar
Frazzoli, E., Dahleh, M. A. and Ferron, E., “Trajectory Tracking Control Design for Autonomous Helicopters Using a Backstepping Algorithm,” Proceedings of the IEEE American Control Conference (ACC), Chicago IL (2000) pp. 4102–4107.Google Scholar
Seeber, R. and Horn, M., “Stability proof for a well-established super-twisting parameter setting,” Automatica 84, 241–243 (2017).CrossRefGoogle Scholar
Bristeau, P. J., Callou, F., Vissiere, D. and Petit, N., “The Navigation and Control Technology Inside the AR.Drone Micro UAV,” Proceedings of the 18th IFAC World Congress, Milano, Italy (2011) pp. 1477–1484.Google Scholar
Munoz Palacios, F., Espinoza Quesada, E. S., Sanahuja, G., Salazar, S., Garcia Salazar, O. and Garcia Carrillo, L. R., “Test bed for applications of heterogeneous unmanned vehicles,” Int. J. Adv. Robot. Syst. (IJARS) 14(1), 1–14 (2017).Google Scholar