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Integral backstepping control for trajectory and yaw motion tracking of quadrotors

Published online by Cambridge University Press:  05 October 2018

Alexander Poultney ,
Peiyan Gong  and
Hashem Ashrafiuon
Alexander Poultney
Affiliation:
Villanova University, Center for Nonlinear Dynamics and Control Villanova, PA 19085. E-mails: [email protected], [email protected]
Peiyan Gong
Affiliation:
Villanova University, Center for Nonlinear Dynamics and Control Villanova, PA 19085. E-mails: [email protected], [email protected]
Hashem Ashrafiuon*
Affiliation:
Villanova University, Center for Nonlinear Dynamics and Control Villanova, PA 19085. E-mails: [email protected], [email protected]
*
*Corresponding author. E-mail: [email protected].
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Summary

This work presents a novel trajectory tracking, hovering, and yaw motion control for quadrotors subject to unknown modeling uncertainties and disturbances. Nonlinear equations of motion are used to model the quadrotor's motion without any simplifying assumptions. An integral backstepping control is developed by defining the tracking errors, their integral, and their first through third time derivatives as the system states. The resulting surge force and roll and pitch moments are shown to asymptotically stabilize the error states subject to bounded disturbances and modeling uncertainties. Similarly, a yaw moment is derived through integral backstepping that simultaneously stabilizes yaw motion errors. The controller performance in simultaneous trajectory and yaw motion tracking is verified through both simulations and experiments.

Keywords

Quadrotor controlTrajectory trackingIntegral backstepping control
Type
Articles
Information
Robotica , Volume 37 , Issue 2 , February 2019 , pp. 300 - 320
Copyright
Copyright © Cambridge University Press 2018 

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References

1. Mahony, R., Kumar, V. and Corke, P., “Multirotor aerial vehicles: Modeling, estimation and control of quadrotor,” IEEE Robot. Autom. Mag. 19 (3), 20–32 (2012).Google Scholar
2. Hua, M.-D., Hamel, T., Morin, P. and Samson, C., “Introduction to feedback control of underactuated VTOL vehicles,” IEEE Control Syst. Mag. 33 (1), 61–75 (2013).Google Scholar
3. Sanchez-Orta, A., Perra-Vega, V., Espinosa, C. zaguirre and Garci, O., “Positionyaw tracking of quadrotors,” J. Dyn. Syst. Meas. Control 137 (6), 061011 (2015).Google Scholar
4. Nieuwstadt, M. V. and Murray, R., “Real-time trajectory generation for differentially flat systems,” Int. J. Robust Nonlinear Control 8 (11), 995–1020 (1998).Google Scholar
5. Mellinger, D. and Kumar, V., “Minimum Snap Trajectory Generation and Control for Quadrotors,” Proceedings of the IEEE Conference on Decision and Control (2011) pp. 2520–2525.Google Scholar
6. Thomas, J., Loianno, G., Sreenath, K. and Kumar, V., “Toward Image Based Visual Servoing for Aerial Grasping and Perching,” Proceedings of the IEEE International Conference on Robotics and Automation (2014) pp. 2113–2118.Google Scholar
7. Zhou, D. and Schwager, M., “Vector Field Following for Quadrotors Using Differential Flatness,” Proceedings of the IEEE International Conference on Robotics and Automation (2014) pp. 6567–6572.Google Scholar
8. Bouabdallah, S. and Siegwart, R., “Full Control of a Quadrotor,” IEEE/RS Int. Conference on Intelligent Robots and Systems (2007) pp. 153–158.Google Scholar
9. Adigbeli, P., “Nonlinear Attitude and Position Control of A Micro Quadrotor Using Sliding Mode and Backstepping Techniques,” Proceedings of the 3rd US-European Competition and Workshop on Micro Air Vehicle Systems (2007) pp. 1–9.Google Scholar
10. Xu, R. and Özgüne, U., “Sliding mode control of a class of underactuated systems,” Automatica 44 (1), 233–241 (2008).Google Scholar
11. Runcharoon, K. and Srichatrapimuk, V., “Sliding Mode Control of Quadrotor,” Proceedings of the International Conference on Technological Advances in Electrical, Electronics and Computer Engineering (2013) pp. 552–557.Google Scholar
12. Dydek, Z., Annaswamy, A. and Lavretsky, E., “Adaptive control of quadrotor UAVs: A design trade study with flight evaluations,” IEEE Transactions on Control Systems Technology 21 (4), 1400–1406 (2013).Google Scholar
13. Yesildirek, A. and Imran, B., “Nonlinear Control of Quadrotor Using Multi Lyapunov Functions,” Proceedings of the American Control Conference (2014) pp. 3844–3849.Google Scholar
14. Zheng, E.-H., Xiong, J.-J. and Luo, J.-L., “Second order sliding mode control for a quadrotor UAV,” ISA Trans. 53, 1350–1356 (2014).Google Scholar
15. Choi, Y.-C. and Ahn, H.-S., “Nonlinear control of quadrotor for point tracking: Actual implementation and experimental tests,” IEEE/ASME Trans. Mechatronics 20 (3), 1179–1192 (2015).Google Scholar
16. Zhao, B., Zhang, B. X. Y. and Zhang, X., “Nonlinear robust adaptive tracking control of a quadrotor uav via immersion and invariance methodology,” IEEE Trans. Ind. Electron. 62 (5), 2891–2902 (2015).Google Scholar
17. Yu, Y., Guo, Y., Pan, X. and Sun, C., “Robust Backstepping Tracking Control of Uncertain MIMO Nonlinear Systems with Application to Quadrotor UAVs,” Proceeding of the IEEE International Conference on Information and Automation (2015) pp. 2868–2873.Google Scholar
18. Tayebi, A. and McGilvray, S., “Attitude stabilization of a VTOL quadrotor aircraft,” IEEE Trans. Control Syst. Technol. 14 (3), 562–571 (2006).Google Scholar
19. Yeh, F.-K., “Sliding-mode controller design for a mini-UAV with propellers,” Trans. Japan Soc. Aeronaut. Space Sci. 55 (1), 30–36 (2012).Google Scholar
20. Lee, T., “Robust adaptive attitude tracking on SO(3) with an application to a quadrotor UAV,” IEEE Trans. Control Syst. Technol. 21 (5), 1924–1930 (2013).Google Scholar
21. Xian, B., Zhao, B., Zhang, Y. and Zhang, X., “Nonlinear control of a quadrotor with deviated center of gravity,” J. Dyn. Syst. Meas. Control 139 (1), 011003 (2017).Google Scholar
22. Liu, H., Li, D., Yu, Y. and Zhong, Y., “Robust trajectory tracking control of uncertain quadrotors without linear velocity measurements,” IET Control Theory Appl. 9 (11), 1746–1755 (2015).Google Scholar
23. Sanz, R., Garcia, P., Zhong, Q.-C. and Albertos, P., “Robust control of quadrotors based on an uncertainty and disturbance estimator,” J. Dyn. Syst. Meas. Control 138 (7), 071006 (2016).Google Scholar
24. Hua, M.-D., Hamel, T., Morin, P. and Samson, C., “A control approach for thrust-propelled underactuated vehicles and its application to VTOL drones,” IEEE Trans. Autom. Control 54 (8), 1837–1853 (2009).Google Scholar
25. Madani, T. and Benallegue, A., “Backstepping Control for a Quadrotor Helicopter,” Proceedings of the IEEE/RSJ Int. Conference on Intelligent Robots and Systems (2006) pp. 3255–3260.Google Scholar
26. Mian, A. and Wang, D., “Nonlinear Flight Control Strategy for an Underactuated Quadrotor Aerial Robot,” Proceedings of the IEEE International Conference on Networking, Sensing and Control (2008) pp. 938–942.Google Scholar
27. Das, A., Lewis, F. and Subbarao, K., “Backstepping approach for controlling a quadrotor using lagrange form dynamics,” J. Intell. Robot. Syst. 56 (1), 127–151 (2009).Google Scholar
28. Fang, Z. and Gao, W., “Adaptive Integral Backstepping Control of a Micro-Quadrotor,” Proceedings of the International Conference on Intelligent Control and Information Processing (2011) pp. 910–915.Google Scholar
29. Raffo, G., Ortega, M. and Rubio, F., “An integral predictive/nonlinear h ∞ control structure for a quadrotor helicopter,” Automatica 46, 29–39 (2010).Google Scholar
30. Lee, T., Leoky, M. and McClamroch, N., “Geometric Tracking Control of a Quadrotor UAV on SE(3),” Proceedings of the IEEE Conference on Decision and Control (2010) pp. 5420–5425.Google Scholar
31. Mellinger, D., Michael, N. and Kumar, V., “Trajectory generation and control for precise aggressive maneuvers with quadrotors,” Int. J. Robot. Res. 31 (5), 664–674 (2012).Google Scholar
32. Lee, T., Leoky, M. and McClamroch, N., “Nonlinear robuts tracking control of a quadrotor UAV on SE(3),” Asian J. Control 15 (2), 391–408 (2013).Google Scholar
33. Goodarzi, F., Lee, D. and Lee, T., “Geometric adaptive tracking control of a quadrotor unmanned aerial vehicle on se(3) for agile maneuvers,” J. Dyn. Syst. Meas. Control 137 (9), 091007 (2015).Google Scholar
34. Rosales, C., Gandolfo, D., Scaglia, G., Jordan, M. and Carelli, R., “Trajectory tracking of a mini four-rotor helicopter in dynamic environments - a linear algebra approach,” Robotica 33 (8), 1682–1652 (2015).Google Scholar
35. Zuo, Z., “Trajectory trajectory tracking control design with command filtered compensation for a quadrotor,” IET Control Theory Appl. 4 (11), 2343–2355 (2010).Google Scholar
36. Abdessameuda, A. and Tayebi, A., “Global trajectory tracking control of vtol-uavs without linear velocity measurements,” Automatica 46 (6), 1053–1059 (2010).Google Scholar
37. Ding, X., Wang, X., Yu, Y. and Zha, C., “Dynamics modeling and trajectory tracking control of a quadrotor unmanned aerial vehicle,” J. Dyn. Syst. Meas. Control 139 (2), 021004.Google Scholar
38. Cabecinhas, D., Cunha, R. and Silvestre, C., “A nonlinear quadrotor trajectory tracking controller with disturbance rejection,” Control Eng. Pract. 26, 1–10 (2014).Google Scholar
39. Kobilarov, M., “Trajectory Tracking of A Class of Underactuated Systems with External Disturbances,” Proceedings of the American Control Conference (2013) pp. 1044–1049.Google Scholar
40. Ramirez-Rodriguez, H., Parra-Vega, V. and Garcia-Salazar, O., “Robust backstepping control based on integral sliding modes for tracking of quadrotors,” J. Intell. Robot. Syst. 73, 51–66 (2014).Google Scholar
41. Poultney, A., Gong, P. and Ashrafiuon, H., “Robust Integral Backstepping Control of Quadrotors,” Proceedings of the ASME Dynamic Systems and Control Conference, vol. 2 (2017) p. V002T12A001.Google Scholar
42. Jazar, R., Advanced Dynamics: Rigid Body, Multibody, snf Aerospace Applications (John Wiley & Sons, Inc., Hoboken, NJ, 2011).Google Scholar
43. Khalil, H., Nonlinear Systems (Prentice-Hall, Upper Saddle River, NJ 2002).Google Scholar
44. Einicke, G. and White, L., “Robust extended kalman filtering,” IEEE Trans. Signal Process. 47 (9), 2596–2599 (1999).Google Scholar