AUTHORS: Ákos Odry, István Kecskés, Ervin Burkus, Péter Odry

Download as PDF

ABSTRACT: This paper describes the design and optimization results of a cascade fuzzy control structure developed and applied for the stabilization of an underactuated two-wheeled mobile pendulum system. The proposed fuzzy control strategy applies three fuzzy logic controllers to both provide the planar motion of the plant and reduce the inner body oscillations. Among these controllers, one is a special PI-type fuzzy logic controller designed to simultaneously ensure the linear speed and prevent high current peaks in the motor drive system. The input-output ranges and membership functions of the controllers are initially selected based on earlier studies. A complex fitness function is formulated for the quantification of the overall control performance. In this fitness function, the quality of reference tracking related to the planar motion, the efficiency of the suppression of inner body oscillations as well as the magnitude of the resulting current peaks in the driving mechanism are considered. Using the defined fitness function, the optimization of the parameters of fuzzy logic controllers is realized with the aid of particle swarm optimization, yielding the optimal possible control performance. Results demonstrate that the optimized fuzzy control strategy provides satisfying overall control quality with both fast closed loop behavior and small current peaks in the driving mechanism of the plant. The flexibility of the proposed fuzzy control strategy allows to protect the plant’s electro-mechanical parts against jerks and vibrations along with smaller energy consumption. At the end of the paper, a look-up table based implementation technique of fuzzy logic controllers is described, which requires small computational time and is suitable for small embedded processors.

KEYWORDS: fuzzy tuning, particle swarm optimization, inverted pendulum robot, robot control

REFERENCES:

[1] L.-X. Wang, A course in fuzzy systems. Prentice-Hall press, USA, 1999.

[2] Á. Odry, J. Fodor, and P. Odry, “Stabilization of a two-wheeled mobile pendulum system using LQG and fuzzy control techniques,” International Journal On Advances in Intelligent Systems, vol. 9, no. 1,2, pp. 223–232, 2016.

[3] Á. Odry, E. Burkus, and P. Odry, “LQG control of a two-wheeled mobile pendulum system,” The Fourth International Conference on Intelligent Systems and Applications (INTELLI 2015), pp. 105–112, 2015.

[4] I. Kecskés and P. Odry, “Optimization of PI and fuzzy-PI controllers on simulation model of Szabad(ka)-ii walking robot,” International Journal of Advanced Robotic Systems, vol. 11, no. 11, p. 186, 2014.

[5] J.-X. Xu, Z.-Q. Guo, and T. H. Lee, “Design and implementation of a takagi–sugeno-type fuzzy logic controller on a two-wheeled mobile robot,” IEEE Transactions on Industrial Electronics, vol. 60, no. 12, pp. 5717–5728, 2013.

[6] C.-H. Huang, W.-J. Wang, and C.-H. Chiu, “Design and implementation of fuzzy control on a two-wheel inverted pendulum,” IEEE Transactions on Industrial Electronics, vol. 58, no. 7, pp. 2988–3001, 2011.

[7] A. Salerno and J. Angeles, “A new family of two-wheeled mobile robots: Modeling and controllability,” IEEE Transactions on Robotics, vol. 23, no. 1, pp. 169–173, 2007.

[8] J. Angeles, Fundamentals of robotic mechanical systems: theory, methods, and algorithms. Springer Science & Business Media, 2013.

[9] A. Salerno and J. Angeles, “The control of semi-autonomous two wheeled robots undergoing large payload-variations,” IEEE International Conference on Robotics and Fig. 8. Flowchart of the embedded software. START Peripherals initialization Timer ISR Ts = 10 ms Search for 𝑢𝑢𝜈, 𝑢𝑢𝜃3 and 𝑢𝑢𝜉 in the look-up table using the measurements Update the PWM duty cycle Return UART2 ISR (Bluetooth) Select the control method, desired values Variables declaration and initialization while (1) Return Send the measurements to the Bluetooth module (UART2) Calculate 𝜃𝜃3,𝜔𝜔3 based on the IMU measurements Calculate 𝜈𝜈, 𝜉𝜉 based on the incremental encoder measurements Calculate 𝑅𝑅 𝐴 based on the ADC results Automation (ICRA’04), vol. 2, pp. 1740–1745, 2004.

[10] P. Oryschuk, A. Salerno, A. M. AlHusseini, and J. Angeles, “Experimental validation of an underactuated two-wheeled mobile robot,” IEEE/ASME Transactions on Mechatronics, vol. 14, no. 2, pp. 252–257, 2009.

[11] B. Cazzolato, J. Harvey, C. Dyer, K. Fulton, E. Schumann, T. Zhu, Z. Prime, B. Davis, S. Hart, E. Pearce et al., “Modeling, simulation and control of an electric diwheel,” in Australasian Conference on Robotics and Automation, pp. 1–10, 2011.

[12] Á. Odry, I. Harmati, Z. Király, and P. Odry, “Design, realization and modeling of a twowheeled mobile pendulum system,” 14th International Conference on Instrumentation, Measurement, Circuits and Systems (IMCAS ’15), pp. 75–79, 2015.

[13] Á. Odry, E. Burkus, I. Kecskés, J. Fodor, and P. Odry, “Fuzzy control of a two-wheeled mobile pendulum system,” IEEE 11th International Symposium on Applied Computational Intelligence and Informatics (SACI), pp. 99–104, 2016.

[14] AppL-DSP.com: Video demonstration of the system dynamics, http://appldsp.com/lqgand-fuzzy-control-of-a-mobile-wheeledpendulum/, accessed 4 June 2017.

[15] Á. Odry, I. Kecskés, E. Burkus, Z. Király, and P. Odry, “Optimized Fuzzy Control of a Two-Wheeled Mobile Pendulum System,” International Journal of Control Systems and Robotics, vol. 2, pp. 73-79, 2017.

[16] G. Carbone, “Stiffness analysis and experimental validation of robotic systems,” Frontiers of Mechanical Engineering, vol. 6, no. 2, pp. 182-196, 2011.

[17] I. Kecskés, E. Burkus, Z. Király, Á. Odry, and P. Odry, “Competition of Motor Controllers Using a Simplified Robot Leg: PID vs Fuzzy Logic,” 4th International Conference on Mathematics and Computers in Sciences and Industry (MCSI), 2017, in press.

[18] A. Odry, D. Toth, and T. Szakall, “Two independent front-wheel driven robot model,” IEEE 6th International Symposium on Intelligent Systems and Informatics (SISY), pp. 1-3, 2008.

[19] J. Basilio and S. Matos, “Design of PI and PID controllers with transient performance specification,” IEEE Transactions on education, vol. 45, no. 4, pp. 364-370, 2002.

[20] J. F. Kennedy, J. Kennedy, R. C. Eberhart, and Y. Shi, Swarm intelligence. Morgan Kaufmann, 2001.

[21] psomatlab: Particle swarm toolbox for matlab, https://code.google.com/p/psomatlab/, accessed 4 June 2017.

[22] K. J. Åström and T. Hägglung, Advanced PID control. ISA-The Instrumentation, Systems and Automation Society, 2006.