کنترل مد لغزشی سیستم ربات دوچرخ تعادلی در حضور عدم قطعیت‌های ساختاری و غیر ساختاری موجود در معادلات دینامیکی و بدون نیاز به معادلات سینماتیکی
محورهای موضوعی : مهندسی برق و کامپیوترمحمدرضا سلطانپور 1 , رضا غلامي 2
1 - دانشگاه علوم و فنون هوایی شهید ستاری
2 - دانشگاه علوم و فنون هوایی شهید ستاری
کلید واژه: ربات دوچرخ تعادلی کنترل مد لغزشیعدم قطعیت‌های ساختاری و غیر ساختاری معادلات سینماتیک,
چکیده مقاله :
در این مقاله، راهکارهایی برای کنترل سیستم ربات دوچرخ تعادلی در حضور عدم قطعیت‌های موجود در معادلات دینامیکی و بدون نیاز به معادلات سینماتیکی پیشنهاد می‌گردد. بدین منظور در ابتدا معادلات دینامیکی این سیستم به حوزه خطا انتقال داده می‌شود و سپس این معادلات به دو زیرسیستم فروتحریک و تمام‌تحریک کاملاً مستقل تقسیم‌بندی می‌گردند. در ادامه برای کنترل زیرسیستم فروتحریک، دو کنترل‌کننده مد لغزشی کاملاً متفاوت ارائه می‌گردد که قادرند این زیرسیستم را در حضور عدم قطعیت‌های ساختاری و غیر ساختاری دارای پایداری مجانبی سراسری نمایند. پس از آن برای کنترل زیرسیستم تمام تحریک نیز کنترل مد لغزشی پیشنهاد می‌شود که این زیرسیستم را در حضور عدم قطعیت‌های موجود دارای پایداری مجانبی سراسری می‌کند. از آنجا که این دو زیرسیستم کاملاً از یکدیگر مستقل می‌باشند، بنابراین اثبات پایداری مجانبی سراسری آنها، اثبات پایداری مجانبی سراسری سیستم حلقه بسته را مهیا می‌سازد. جداسازی زیرسیستم‌های ربات دوچرخ تعادلی، نیاز به استفاده از معادلات سینماتیک را مرتفع نموده و این امر باعث می‌شود تا حضور عدم قطعیت‌های ساختاری تأثیری بر دقت ردگیری متغیرهای حالت سیستم حلقه بسته نداشته باشند. نهایتاً برای بررسی عملکرد کنترل‌کننده‌های پیشنهادی و مقایسه نتایج عملکرد آنها، شبیه‌سازی‌هایی در 3 مرحله بر روی سیستم ربات دوچرخ تعادلی پیاده‌سازی می‌شود. اثبات ریاضی و نتایج شبیه‌سازی‌ها عملکرد مطلوب راهکارهای پیشنهادی را نشان می‌دهند.
In this paper, we proposed solutions for controlling the two-wheel self-balancing robot system in the presence of uncertainties in dynamical equation and without the need for kinematic equations. For this purpose, the dynamical equations of this system are initially transmitted to the domain of error, then these equations are divided into two independent subsystems, one of which is an under-actuated system and the other is fully actuated system. In order to control the under-actuated subsystem, two completely different sliding mode controllers are proposed that are able to provide this subsystem in the presence of structured and un-structured uncertainties with global asymptotic stability. Subsequently, in order to control the fully under-actuated subsystem, a sliding mode control is proposed to provide this subsystem in the presence of existing uncertainties with global asymptotic stability. Since these two subsystems are completely independent of each other, their global asymptotic stability proofs prove the global asymptotic stability of the closed-loop system. The separation of two-wheeled self-balancing robot sub-systems eliminates the need to use the kinematic equations, and this causes the presence of structured uncertainties to have no effect on the accuracy of tracing the closed-loop system state variables. Finally, to evaluate the performance of the proposed controllers and compare their performance results, three-stage simulations are implemented on the two-wheeled self-balancing robot system. Mathematical proofs and simulation results show the desired performance of the proposed solutions.
[1] O. Mohareri, R. Dhaouadi, and A. B. Rad, "Indirect adaptive tracking control of a nonholonomic mobile robot via neural networks," Neurocomput, vol. 88, no. 13, pp. 54-66, Jul. 2012.
[2] M. G. Villarreal-Cervantes, J. F. Guerrero-Castellanos, S. Ramirez-Martinez, and J. P. Sanchez-Santana, "Stabilization of a (3,0) mobile robot by means of an event-triggered control," ISA Trans., vol. 58, pp. 605-613, Sept. 2015.
[3] M. S. Miah and W. Gueaieb, "Mobile robot trajectory tracking using noisy RSS measurements: an RFID approach," ISA Trans., vol. 53, no. 21, pp. 433-443, Mar. 2014.
[4] G. Scaglia, E. Serrano, A. Rosales, and P. Albertos, "Linear interpolation based controller design for trajectory tracking under uncertainties: application to mobile robots," Control Eng. Pract., vol. 45, no. 9, pp. 123-132, Nov. 2015.
[5] M. Baloh and M. Parent, "Modeling and model verification of an intelligence self-balancing two-wheeled vehicle for an autonomous urban transportation system," in Proc. Conf. on Computational Intelligence, Robotics, and Autonomous Systems, 7 pp., Singapore, Singapore, 15-15 Dec. 2003.
[6] A. Salerno and J. Angeles, "A new family of two wheeled mobile robots: modeling and controllability," IEEE Trans. Robotics, vol. 23, no. 1, pp. 169-173, Feb. 2007.
[7] Y. Kim, S. Lee, and D. H. Kim, "Dynamic equations of a wheeled inverted pendulum with changing its center of gravity," in Proc. Int. Conf. on Control, Automation and Systems, pp. 853-854, Gyeonggi-do, South Korea, 26-29 Oct. 2011.
[8] T. Takei, R. Imamura, and S. Yuta, "Baggage transportation and navigation by a wheeled inverted pendulum mobile robot," IEEE Trans. Ind. Electron., vol. 56, no. 10, pp. 3989-3994, Jul. 2009.
[9] W. Junfeng and Z. H. Wanying, "Research on control method of two-wheeled self-balancing robot," in Proc. Int. Conf. on Intelligent Computation Technology and Automation, vol. 1, pp. 476-479, Shenzhen, Guangdong, China, 28-29 Mar. 2011.
[10] K. Pathak, J. Franch, and S. K. Agrawal, "Velocity and position control of a wheeled inverted pendulum by partial feedback linearization," IEEE Trans. Robot. Autom., vol. 21, no. 3, pp. 505-513, May 2005.
[11] C. H. Chiu, "The design and implementation of a wheeled inverted pendulum using an adaptive output recurrent cerebellar model articulation controller," IEEE Trans. Ind. Electron., vol. 57, no. 5, pp. 1814-1822, Sept. 2010.
[12] H. T. Yau, C. C. Wang, N. S. Pai, and M. J. Jang, "Robust control method applied in self-balancing two-wheeled robot," in Proc. Int. Symp. on Knowledge Acquisition and Modeling, pp. 268-271, Wuhan, China, 30 Nov.-1 Dec. 2009.
[13] S. C. Lin, C. C. Tsai, and H. C. Huang, "Nonlinear adaptive sliding-mode control design for two-wheeled human transportation vehicle," in Proc. IEEE Int. Conf. on Systems, Man, and Cybernetics, pp. 1965-1970, San Antonio, TX, USA, 11-14 Oct. 2009.
[14] J. Wu, Y. Liang, and Z. Wang, "A robust control method of two-wheeled self-balancing robot," in Proc. Int. Forum on Strategic Technology, pp. 1031-1035, Harbin, Heilongjiang, Harbin, 22-24 Aug. 2011.
[15] A. Wasif, D. Raza, W. Rasheed, Z. Farooq, and S. Q. Ali, "Design and implementation of a two wheel self balancing robot with a two level adaptive control," in Proc. IEEE Int. Conf. on Digital Information Management System, Man, and Cybernetics, pp. 187-193, Islamabad, Pakistan, 10-12 Sept. 2013.
[16] R. D. Pinzon-Morales and Y. Hirata, "A portable stand-alone bi-hemispherical neuronal network model of the cerebellum for adaptive robot control," in Proc. IEEE Int. Conf. on Robotics and Biomimetics, pp. 1148-1151, Bali, Indonesia, 5-10 Sept. 2014.
[17] K. H. Su and Y. Y. Chen, "Balance control for two-wheeled robot via neural-fuzzy technique," in Proc. SICE Annual Conf., pp. 1838-2842, Taipei, Taiwan, 18-21 Aug. 2010.
[18] J. Wu and S. Jia, "T-S adaptive neural network fuzzy control applied in two-wheeled self-balancing robot," in Proc. Int. Forum on Strategic Technology, pp. 1023-1026, Harbin, Heilongjiang, Harbin, 22-24 Aug. 2011. [19] C. H. Chiu, Y. W. Lin, and C. H. Lin, "Real-time control of a wheeled inverted pendulum based on an intelligent model free controller," Mechatronics, vol. 21, no. 3, pp. 523-533, Apr. 2011.
[20] W. Zeng, Q. Wang, F. Liu, and Y. Wang, "Learning from adaptive neural network output feedback control of a unicycle-type mobile robot," ISA Trans., vol. 61, no. 2, pp. 337-347, Mar. 2016.
[21] Y. Dai, Y. Kim, S. G. Wee, D. H. Lee, and S. G. Lee, "Symmetric caging formation for convex polygonal object transportation by multiple mobile robots based on fuzzy sliding mode control," ISA Trans., vol. 60, no. 4, pp. 321-332, Jan. 2016.
[22] M. H. Khooban, A. Alfi, and D. N. Maryam Abadi, "Teaching-learning-based optimal interval type-2 fuzzy PID controller design: a nonholonomic wheeled mobile robots," Robotica, vol. 31, no. 7, pp. 1059-1071, Oct. 2013.
[23] J. Huang, Z. H. Guan, and T. Matsuno, "Sliding-mode velocity control of mobile-wheeled inverted-pendulum systems," IEEE Trans. Robotics, vol. 26, no. 4, pp. 750-758, Aug. 2010.
[24] H. T. Yau, C. C. Wang, N. S. Paid, and M. J. Jang, "Robust control method applied in self-balancing two-wheeled robot," in Proc. Int. Symp. on Knowledge Acquisition and Modeling, pp. 268-271, Wuhan, China, 30 Nov.-1 Dec. 2009.
[25] N. M. A. Ghani, N. I. M. Yatim, and N. A. Azmi, "Comparative assessment for two wheels inverted pendulum mobile robot using robust control," in Proc. Int. Conf. on Control, Automation and System, pp. 562-567, Gyeonggi-Do, South Korea, 27-30 Oct. 2010.
[26] J. Wu, Y. Liang, and Z. Wang, "A robust control method of two-wheeled self-balancing robot," in Proc. Int. Forum on Strategic Technology, pp. 1031-1035, Harbin, Heilongjiang, Harbin, 22-24 Aug. 2011.
[27] S. C. Lin, C. C. Tsai, and H. C. Huang, "Nonlinear adaptive sliding-mode control design for two-wheeled human transportation vehicle," in Proc. IEEE Int. Conf. on Systems, Man, and Cybernetics, pp. 1965-1970, San Antonio, TX, USA, 11-14 Oct. 2009.
[28] F. Dai, F. Li, Y. Bai, W. Guo, C. Zong, and X. Gao, "Development of a coaxial self-balancing robot based on sliding mode control," in Proc. IEEE Int. Conf. on Mechatronics and Automation, pp. 1241-1246, Chengdu, China, 5-8 Aug. 2012.
[29] A. Filipescu, V. Minzu, B. Dumitrascu, A. Filipescu, and E. Minca, "Trajectory-tracking and discrete-time sliding-mode control of wheeled mobile robots," in Proc. IEEE Int.l Conf. on Information and Automation, pp. 27-32, Shenzhen, China, 6-8 Jun. 2011.
[30] M. Yue, W. Sun, and P. Hu, "Sliding mode robust control for two-wheeled mobile robot with lower center of gravity," International J. of Innovative Computing, Information and Control, vol. 7, no. 7, pp. 637-646, Jan. 2011.
[31] M. Cui, W. Liu, H. Liu, H. Jiang, and Z. Wang, "Extended state observer-based adaptive sliding mode control of differential-driving mobile robot with uncertainties," Nonlinear Dyn., vol. 83, no. 4, pp. 667-683, Aug. 2016.
[32] W. Wang, J. Yi, D. Zhao, and X. Liu, "Double layer sliding mode control for second-order underactuated mechanical system," in Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp. 295-300, Edmonton, Canada, 2-6 Aug. 2005.
[33] T. R. Kane and D. A. Levinson, Dynamics, Theory and Applications, McGraw-Hill, 1985.
[34] Y. Kim, S. H. Kim, and Y. K. Kwak, "Dynamic analysis of a nonholonomic two-wheeled inverted pendulum robot," J. of Intelligent and Robotic Systems, J. of Intelligent and Robotic Systems, vol. 44, no. 3, pp. 25-46, Jan. 2005. [35] H. K. Khalil, Nonlinear Systems, Prentice-Hall, 2002.
