Chattering Eliminated and Stable Motion of Biped Robots using a Fuzzy Sliding Mode Controller

Majlesi Journal of Electrical Engineering

مقاله 5، دوره 7، شماره 1، خرداد 2013   

نوع مقاله: Review Article

نویسندگان

Amir Takhmar¹؛ Mansoor Alghooneh^{* 2}؛ S. Ali A. Moosavian³

¹Electrical and Computer Department, University of Western Ontario, London, ON, CAN

²Mechanical and Manufacturing Department, University of Manitoba, Winnipeg, MB, CAN

³Mechanical and Manufacturing Department, K. N. Toosi Univ. of Tech., Tehran

چکیده

Control of biped walking robots based on designated smooth and stable trajectories is a challenging problem that is the focus of this article. Because of highly nonlinear dynamics of biped robots, minor uncertainties in systems parameters may drastically affect the system performance, leading to chattering phenomenon. To tackle this, a new Sliding Mode Control (SMC) approach is proposed privileging a chattering elimination method based on Fuzzy logic to regulate the switching gain. To this end, first a desired trajectory for the lower body will be designed to alleviate the impacts due to contact with the ground. This is obtained by fitting proper polynomials at appropriate break points. Then, the upper body motion is planned based on the Zero Moment Point (ZMP) criterion to provide a stable motion for the biped robot. Next, dynamics equations will be obtained for both single support phase (SSP) and double support phase (DSP). Finally, the SMC approach is applied for both the SSP and the DSP, while a new chattering elimination method using Fuzzy logic will be proposed based on regulating constant switching gain. Obtained simulation results show that the performance of the system is properly accurate in terms of the tracking errors even in the presence of considerable uncertainties and exerted disturbances. Also, the new proposed method substantially reduces chattering effects and avoids the instability of the biped robot due to this phenomenon, resulting in stable smooth motion control of this complicated system.

کلیدواژه‌ها

Biped Robots؛ Khaje Nasir University of technology (K. N. Toosi Univ. of Tech.)؛ en؛ fuzzy systems؛ sliding mode control؛ Stability؛ Gait Planning

مراجع

[1] M. Vukobratovic, A. A. Frank, and D. Jricic, “On The Stability of Biped Locomotion”, IEEE Trans. On Biomedical Engineering, BME 17-1, pages 25-36, 1970.

[2] M. Vukobratovic, and B. Brovac, “Zero-Moment Point-Thirty five years of its life”, Int. Journal of Humanoid Robotics, Vol.1, No. 1, pages 157-173, 2004.

[3] A. Goswami, “Foot-Rotation indicator (FRI) point: A New Gait Planning Tool to Evaluate Postural Stability of Biped Robots”, Proc. IEEE ICRA, Detroit, pages 47-52, 1999.

[4] A. Goswami, and V. Kallem, ”Rate of Change of Angular Momentum and Balance Maintenance of Biped Robots”, Proc. IEEE ICRA, New Orleans, pages 3785-3790, 2004.

[5] H. O. Lim and A. Takanishi, “Compensatory Motion Control for a Biped Walking Robot”, Robotica, Vol. 23, Pages 1-11, 2005.

[6] M. Vukobratovic et al, Biped Locomotion Dynamic, Stability, Control and Application, springer-verlag 1990.

[7] S. Tzafestas, M. Raibert and C. Tzafestas, “Robust sliding-mode control applied to a 5-link biped robot”, Int. Journal of Intelligent and Robotic Systems, Vol.15, pages 67–133, 1996.

[8] H. K. Lum, M.Zribi and Y. C. Soh, “Planing and Control of a Biped Robot”, Int. Journal of Engineering Science, Vol.37, pages 1319-1349, 1999.

[9] K. Mitobe, G. Capi and Y. Nasu, “Control of walking robots based on manipulation of the zero moment point”, Robotica, Vol.18, pages 651–657, 2000.

[10] K. Mitobe, N. Mori, K. Aida and Y. Nasu, “Nonlinear feedback control of a biped walking robot”, Proc of IEEE Int. Conf. on Robotics and Automation, Nagoya, pages 2865–2870, 1995.

[11] C. Chevallereau, “Time-scaling control of an underactuated biped robot”, IEEE Trans. on Robotics and Automation, Vol.19, Issue.2, pages 362–368, 2003.

[12] C. M. Chew and Gl. A. Pratt, “A Minimum Model Adaptive Control approach for a Planner Biped “, Int. Conf. on Intelligent Robotics and System, Vol.3, pages 1469-1474, 1999.

[13] X. Mu and Q. Wuy, “Development of a complete dynamic model of a planar five-link biped and sliding mode control of its locomotion during the double support phase”, Int. Journal of Control, Vol.77, No.8, pages 789–799, 2004.

[14] S. Ali A. Moosavian, Amir Takhmar, and Mansoor Alghoneh, “Regulated Sliding Mode Control of a Biped Robot”, Proc. of the IEEE International Conference on Mechatronics and Automation (ICMA 2007), Harbin, China, August, 2007.

[15] J.E. Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, New Jersey, 1991.

[16] M. R. Rafimanzelat and M. J. Yazdanpanah, “A novel low chattering sliding mode controller”, Proc. of Asian Control Conference, Vol.3, pages 1958-1963, 2004.

[17] I. G. Park and J. G. Kim, “Robust Control for Dynamic Walking of a Biped Robot with Ground Contacting Condition”, Proc. ISIE, Pusan, Vol.3, pages 2067-2072, 2001.

[18] S. Ali. A. Moosavian, and M. Reza Homaeinejad, “Control of Space Free-Flying Robots Using Regulated Sliding Mode Controller,” Proc. Of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2006), Oct. 9-15, 2006, Beijing, China.

[19] S. Ali. A. Moosavian, and M. Reza Homaeinejad, “Regulated Sliding Mode Control of Satellite Rotation,” Proc. Of the IFAC Workshop on Generalized Solutions in Control Problems (GSCP-2004), Russia, 22-26 Sept. 2004.

[20] R. Guclu, “Sliding Mode and PID Control of a structural system against earthquake”, Mathematical and Computer Modelling, Vol.44, pages 210-217, 2006.

[21] J. X. Xu, Y. J. Pan and T. H. Lee, “Sliding Mode Control with closed loop filtering architecture for a class of nonlinear system”, IEEE Trans. On Circuits and system II, Vol.51, Issue 4, pages 168-173, 2004.

[22] S. J. Huang and K. C. Chiou, “An Adaptive Neural Sliding Mode Controller for MIMO Systems”, Int. Journal of Intelligent and Robotic Systems, Vol.46, pages 285–301, 2006.

[23] Qi. Zhen, J.E. McInroy and F. Jafari, “Trajectory Tracking with Parallel Robots Using Low Chattering, Fuzzy Sliding Mode Controller”, Int. Journal of Intelligent and Robotic Systems, Vol.48, pages 333–356, 2007.

[24] J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB, Third Editon, Prentice Hall 1999.

[25] S. K. Saha, and J. Angeles, “Dynamics of Nonholonomic Mechanical Systems Using a Natural Orthogonal Complement”, Trans. of the ASME, Vol. 58, pp. 238-244, March 1991.

[26] K. M. Passino and S. Yurkovich, Fuzzy Control, Aaddison Wesley Longman, 1998.