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Visual Servoing of a Spherical Inverted Pendulum on a Quadrotor Using Backstepping Controller

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Vision-based Robot applications have taken a lot of attention, with the development of electronic and computer technology. In this paper, a visual servoing method is used to control the stability of the Spherical Inverted Pendulum at its equilibrium upright position. The main objective of this study will be attended in four steps. The first step consists of a real time acquisition of images from a vision system. In the second step, an algorithm is proposed that will allow determining accurately the position of the pendulum from the acquired images. In the third step, the difference between the current position and the equilibrium upright position is calculated. The last step consists of developing a strategy of a command from this difference of positions. The command that will be generated is based on the Backstepping control to make the Quadrotor actions in such a way to bring the spherical inverted pendulum in its upright position. The implementation of the proposed method is carried out using Matlab Simulink and Virtual Reality environment.
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Spherical Inverted Pendulum; Quadrotor; Visual Servoing; Backstepping; Nonlinear Control

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A. Castro, C. Adams and W. Singhose, "Dynamic response characteristics of a two-wheeled inverted-pendulum transporter," 52nd IEEE Conference on Decision and Control, Firenze, 2013, pp. 1532-1537.

J. Jovic, V. Bonnet, C. Fattal, P. Fraisse, Ch. AzevedoCoste, A new 3D center of mass control approach for FES-assisted standing: First experimental evaluation with a humanoid robot, Medical Engineering & Physics, Volume 38, Issue 11, 2016, Pages 1270-1278,

S. T. Kao, W. J. Chiou, and M. T. Ho, "Balancing of a spherical inverted pendulum with an omni-directional mobile robot," 2013 IEEE International Conference on Control Applications (CCA), Hyderabad, 2013, pp. 760-765.

C. C. Tsai, C. C. Yu, and C. S. Chang, "Aggregated hierarchical sliding-mode control for spherical inverted pendulum," 2011 8th Asian Control Conference (ASCC), Kaohsiung, 2011, pp. 914-919

A. Ghanbari and M. Farrokhi, "Decentralized Neuro-Fuzzy Controller Design Using Decoupled Sliding-Mode Structure for Two-Dimensional Inverted Pendulum," 2006 IEEE International Conference on Engineering of Intelligent Systems, Islamabad, 2006, pp. 1-6.

M. Hehn and R. D'Andrea, "A flying inverted pendulum," 2011 IEEE International Conference on Robotics and Automation, Shanghai, 2011, pp. 763-770.

F. Cai, T. Lai, Q. Chai and W. Wang, "Trajectory tracking problem of a quad-rotor Pendulum," 2016 Chinese Control and Decision Conference (CCDC), Yinchuan, 2016, pp. 578-582.

C. Raimúndez, J. L. Camaño, and A. Barreiro, "Stabilizing an inverted spherical pendulum using a scale quad-rotor," The 4th Annual IEEE International Conference on Cyber Technology in Automation, Control and Intelligent, Hong Kong, 2014, pp. 111-116.

A. M. Bloch, N. E. Leonard, and J. E. Marsden, "Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem," in IEEE Transactions on Automatic Control, vol. 45, no. 12, pp. 2253-2270, Dec 2000.

T. Ibuki, Y. Tadokoro, Y. Fujita and M. Sampei, "3D inverted pendulum stabilization on a quadrotor via bilinear system approximations," 2015 IEEE Conference on Control Applications (CCA), Sydney, NSW, 2015, pp. 513-518.

Y. Fujita, T. Ibuki, and M. Sampei, "Bilinear system approximation-based inverted pendulum stabilization in three dimensions," 2014 Proceedings of the SICE Annual Conference (SICE), Sapporo, 2014, pp. 1023-1028.

Zhang, C., Hu, H., Gu, D., & Wang, J. (2017). Cascaded control for balancing an inverted pendulum on a flying quadrotor. Robotica, 35(6), 1263-1279.

García Carrillo L.R., DzulLópez A.E., Lozano R., Pégard C. (2013) Modeling the Quad-Rotor Mini-Rotorcraft. In: Quad Rotorcraft Control. Advances in Industrial Control. Springer, London. pp 23-34.

Vijayan, A., Ashok, S., A MIMO Approach to Supervisory Control in Robot Visual Feedback, (2017) International Review on Modelling and Simulations (IREMOS), 10 (1), pp. 16-25.

Chandramohan, G., Subramanian, S., An Efficient Hybrid Segmentation Algorithm for Computer Tomography Image Segmentation, (2014) International Review on Computers and Software (IRECOS), 9 (9), pp. 1576-1582.

Corke, P.I.: Robotics, Vision & Control: Fundamental Algorithms in MATLAB. Springer, Heidelberg (2011)

M Belkheiri, ARabhi, A ElHajjaji, C Pegard. Different linearization control techniques for a quadrotor system. Communications, Computing and Control Applications (CCCA), Dec 2012, Marseille, France.

T. Lee, M. Leok and N. H. McClamroch, "Nonlinear robust tracking control of a quadrotor UAV on SE(3)," 2012 American Control Conference (ACC), Montreal, QC, 2012, pp. 4649-4654.

M. Imran Rashid and S. Akhtar, "Adaptive control of a quadrotor with unknown model parameters," Proceedings of 2012 9th International Bhurban Conference on Applied Sciences & Technology (IBCAST), Islamabad, 2012, pp. 8-14.

S. Krafes, Z. Chalh and A. Saka, "Review: Linear, nonlinear and intelligent controllers for the inverted pendulum problem," 2016 International Conference on Electrical and Information Technologies (ICEIT), Tangiers, 2016, pp. 136-141.

H. K. Khalil, Nonlinear Systems, vol. 3. Englewood Cliffs, NJ, USA: Prentice-Hall, 2002

Iswanto, I., Ataka, A., Inovan, R., Wahyunggoro, O., Imam Cahyadi, A., Disturbance Rejection for Quadrotor Attitude Control Based on PD and Fuzzy Logic Algorithm, (2016) International Review of Automatic Control (IREACO), 9 (6), pp. 405-412.

Agustinah, T., Isdaryani, F., Nuh, M., Tracking Control of Quadrotor Using Static Output Feedback with Modified Command-Generator Tracker, (2016) International Review of Automatic Control (IREACO), 9 (4), pp. 242-251.

Belhadri, K., Kouadri, B., Zegai, M., Adaptive Neural Control Algorithm Design for Attitude Stabilization of Quadrotor UAV, (2016) International Review of Automatic Control (IREACO), 9 (6), pp. 390-396.

Azouz, N., Bennaceur, S., Modeling and Stabilization of a Mini Quadrotor Helicopter, (2016) International Journal on Engineering Applications (IREA), 4 (2), pp. 55-66.

Bouallegue, S., Khoud, K., Integral Backstepping Control Prototyping for a Quad Tilt Wing Unmanned Aerial Vehicle, (2016) International Review of Aerospace Engineering (IREASE), 9 (5), pp. 152-161.


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