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Cascaded control for balancing an inverted pendulum on a flying quadrotor

  • Chao Zhang (a1) (a2), Huosheng Hu (a2), Dongbing Gu (a2) and Jing Wang (a1)


This paper is focused on the flying inverted pendulum problem, i.e., how to balance a pendulum on a flying quadrotor. After analyzing the system dynamics, a three loop cascade control strategy is proposed based on active disturbance rejection control (ADRC). Both the pendulum balancing and the trajectory tracking of the flying quadrotor are implemented by using the proposed control strategy. A simulation platform of 3D mechanical systems is deployed to verify the control performance and robustness of the proposed strategy, including a comparison with a Linear Quadratic Controller (LQR). Finally, a real quadrotor is flying with a pendulum to demonstrate the proposed method that can keep the system at equilibrium and show strong robustness against disturbances.


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1. Boubaker, O., “The inverted pendulum benchmark in nonlinear control theory: a survey,” Int. J. Adv. Robot. Sy. 10, 233242 (2013).
2. Grasser, F., D'Arrigo, A., Colombi, S. and Rufer, A. C., “Joe: A mobile, inverted pendulum,” IEEE Trans. Indust. Electron. 49 (1), 107114 (2002).
3. Wang, J.-J., “Simulation studies of inverted pendulum based on PID controllers,” Simul. Modelling Pract. Theory 19 (1), 440449 (2011).
4. Jung, S., Cho, H.-T. and Hsia, T. C., “Neural network control for position tracking of a two-axis inverted pendulum system: Experimental studies,” IEEE Trans. Neural Netw. 18 (4), 10421048 (2007).
5. Bloch, A. M., Leonard, N. E. and Marsden, J. E., “Controlled lagrangians and the stabilization of mechanical systems. I. The first matching theorem,” IEEE Trans. Autom.Control 45 (12), 22532270 (2000).
6. Cai, G., Dias, J. and Seneviratne, L., “A survey of small-scale unmanned aerial vehicles: Recent advances and future development trends,” Unmanned Syst. 2 (02), 175199 (2014).
7. How, J. P., Fraser, C., Kulling, K. C., Bertuccelli, L. F., Toupet, O., Brunet, L., Bachrach, A. and Roy, N., “Increasing autonomy of uavs,” Robot. Autom. Mag. IEEE 16 (2), 4351 (2009).
8. Lupashin, S., Hehn, M., Mueller, M. W., Schoellig, A. P., Sherback, M. and DAndrea, R., “A platform for aerial robotics research and demonstration: The flying machine arena,” Mechatronics 24 (1), 4154 (2014).
9. Michael, N., Mellinger, D., Lindsey, Q. and Kumar, V., “The grasp multiple micro-uav testbed,” Robot. Autom. Mag. IEEE 17 (3), 5665 (2010).
10. Hehn, M. and D'Andrea, R., “A Flying Inverted Pendulum,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China (2011) pp. 763–770.
11. Figueroa, R., Faust, A., Cruz, P., Tapia, L. and Fierro, R., “Reinforcement Learning for Balancing a Flying Inverted Pendulum,” Proceedings of the 11th World Congress on Intelligent Control and Automation, IEEE. Shenyang, China (2014) pp. 1787–1793.
12. Raimundez, C., Camano, J. L. and Barreiro, A., “Stabilizing an Inverted Spherical Pendulum using a Scale Quad-Rotor,” Proceedings of the IEEE 4th Annual International Conference on Cyber Technology in Automation, Control and Intelligent Systems (CYBER), Hong Kong, China (2014) pp. 111–116.
13. Sandoval, J., Kelly, R. and Santibanez, V., “On the Controlled Lagrangian of an Inverted Pendulum on a Force-Driven Cart,” Proceedings of the Control Conference (ECC), 2015 European, IEEE. Linz, Austria (2015) pp. 992–997.
14. Abdessameud, A., Polushin, I. and Tayebi, A., “Motion coordination of thrust-propelled underactuated vehicles with intermittent and delayed communications,” Syst. Control Lett. 79, 1522 (2015).
15. Guo, L. and Cao, S., “Anti-disturbance control theory for systems with multiple disturbances: A survey,” ISA Trans. 53 (4), 846849 (2014).
16. Ohishi, K., Nakao, M., Ohnishi, K. and Miyachi, K., “Microprocessor-controlled dc motor for load-insensitive position servo system,” IEEE Trans. Indust. Electron. 1 (IE–34), 4449 (1987).
17. Li, S. and Yang, J., “Robust autopilot design for bank-to-turn missiles using disturbance observers,” IEEE Trans. Aerosp. Electron. Syst. 49 (1), 558579 (2013).
18. Xing, D., Su, J., Liu, Y. and Zhong, J., “Robust approach for humanoid joint control based on a disturbance observer,” Control Theory Appl. IET 5 (14), 16301636 (2011).
19. Tan, K. K., Lee, T. H., Dou, H. F., Chin, S. J. and Zhao, S., “Precision motion control with disturbance observer for pulsewidth-modulated-driven permanent-magnet linear motors,” IEEE Trans. Magn. 39 (3), 18131818 (2003).
20. Han, J., “From PID to active disturbance rejection control,” IEEE Trans. Indust. Electron. 56 (3), 900906 (2009).
21. Ramirez-Neria, M., Sira-Ramirez, H., Garrido-Moctezuma, R. and Luviano-Juárez, A., “Linear active disturbance rejection control of underactuated systems: The case of the furuta pendulum,” ISA Trans. 53 (4), 920928 (2014).
22. Zhang, C. and Zhu, J., “On Stabilization and Disturbance Rejection for the Inverted Pendulum,” Proceedings of the IEEE International Conference on Systems, Man and Cybernetics (SMC), San Diego, CA (2014) pp. 3750–3754.
23. Esteban, S., Gordillo, F. and Aracil, J., “Three-time scale singular perturbation control and stability analysis for an autonomous helicopter on a platform,” Int. J. Robust Nonlinear Control 23 (12), 13601392 (2013).
24. Wood, G. D. and Kennedy, D. C., “Simulating mechanical systems in simulink with simmechanics,” Technical Report 91124v00, The Mathworks Report Inc., Natick, MA, (2003).
25. Gurdan, D., Stumpf, J., Achtelik, M., Doth, K.-M., Hirzinger, G. and Rus, D., “Energy-Efficient Autonomous Four-Rotor Flying Robot Controlled at 1 KHz,” Proceedings of the IEEE International Conference on Robotics and Automation, Roma, Italy (2007) pp. 361–366.
26. Kendoul, F., “Survey of advances in guidance, navigation and control of unmanned rotorcraft systems,” J. Field Robot. 29 (2), 315378 (2012).
27. Gao, Z., “Scaling and Bandwidth-Parameterization Based Controller Tuning,” Proceedings of the American Control Conference, vol. 6 Denver, Colorado, USA (2006) pp. 4989–4996.
28. Sa, I. and Corke, P., “System Identification, Estimation and Control for a Cost Effective Open-Source Quadcopter,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Saint Paul, MN, USA (2012) pp. 2202–2209.
29. Nasir, A. N. K., Ahmad, M. A. and Rahmat, M. F., “Performance Comparison between LQR and PID Controllers for an Inverted Pendulum System,” Proceedings of the International Conference on Power Control and Optimization: Innovation in Power Control for Optimal Industry, AIP Publishing, vol. 1052 Chiangmai, Thailand (2008) pp. 124–128.


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Cascaded control for balancing an inverted pendulum on a flying quadrotor

  • Chao Zhang (a1) (a2), Huosheng Hu (a2), Dongbing Gu (a2) and Jing Wang (a1)


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