A Robust Fuzzy Tracking Control Scheme for Robotic Manipulators with Experimental Verification

ABSTRACT

The performance of any fuzzy logic controller (FLC) is greatly dependent on its inference rules. In most cases, the closed-loop control performance and stability are enhanced if more rules are added to the rule base of the FLC. However, a large set of rules requires more on-line computational time and more parameters need to be adjusted. In this paper, a robust PD-type FLC is driven for a class of MIMO second order nonlin- ear systems with application to robotic manipulators. The rule base consists of only four rules per each de- gree of freedom (DOF). The approach implements fuzzy partition to the state variables based on Lyapunov synthesis. The resulting control law is stable and able to exploit the dynamic variables of the system in a lin- guistic manner. The presented methodology enables the designer to systematically derive the rule base of the control. Furthermore, the controller is decoupled and the procedure is simplified leading to a computationally efficient FLC. The methodology is model free approach and does not require any information about the sys- tem nonlinearities, uncertainties, time varying parameters, etc. Here, we present experimental results for the following controllers: the conventional PD controller, computed torque controller (CTC), sliding mode con- troller (SMC) and the proposed FLC. The four controllers are tested and compared with respect to ease of design, implementation, and performance of the closed-loop system. Results show that the proposed FLC has outperformed the other controllers.

The performance of any fuzzy logic controller (FLC) is greatly dependent on its inference rules. In most cases, the closed-loop control performance and stability are enhanced if more rules are added to the rule base of the FLC. However, a large set of rules requires more on-line computational time and more parameters need to be adjusted. In this paper, a robust PD-type FLC is driven for a class of MIMO second order nonlin- ear systems with application to robotic manipulators. The rule base consists of only four rules per each de- gree of freedom (DOF). The approach implements fuzzy partition to the state variables based on Lyapunov synthesis. The resulting control law is stable and able to exploit the dynamic variables of the system in a lin- guistic manner. The presented methodology enables the designer to systematically derive the rule base of the control. Furthermore, the controller is decoupled and the procedure is simplified leading to a computationally efficient FLC. The methodology is model free approach and does not require any information about the sys- tem nonlinearities, uncertainties, time varying parameters, etc. Here, we present experimental results for the following controllers: the conventional PD controller, computed torque controller (CTC), sliding mode con- troller (SMC) and the proposed FLC. The four controllers are tested and compared with respect to ease of design, implementation, and performance of the closed-loop system. Results show that the proposed FLC has outperformed the other controllers.

KEYWORDS

Fuzzy Logic Control (FLC), PD Control, Computed-Torque Control (CTC), Sliding Mode Control (SMC), Lyapunov Synthesis, Test Rig

Fuzzy Logic Control (FLC), PD Control, Computed-Torque Control (CTC), Sliding Mode Control (SMC), Lyapunov Synthesis, Test Rig

Cite this paper

nullA. Sharkawy, M. Othman and A. Khalil, "A Robust Fuzzy Tracking Control Scheme for Robotic Manipulators with Experimental Verification,"*Intelligent Control and Automation*, Vol. 2 No. 2, 2011, pp. 100-111. doi: 10.4236/ica.2011.22012.

nullA. Sharkawy, M. Othman and A. Khalil, "A Robust Fuzzy Tracking Control Scheme for Robotic Manipulators with Experimental Verification,"

References

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[2] T.-H. S. Li and Y.-C. Huang, “MIMO Adaptive Fuzzy Terminal Sliding-Mode Controller for Robotic Manipulators,” Information Sciences, Vol. 180, No. 23, 2010, pp. 4641-4660. doi:10.1016/j.ins.2010.08.009

[3] L. Tian and C. Collins, “Optimal Placement of a Two-Link Planar Manipulator Using a Genetic Algorithm,” Robotica, Cambridge University Press, Cambridge, Vol. 23, No. 2, 2005, pp. 169-176.

[4] M. W. Spong, S. Hutchinson and M. Vidyasagar, “Robot Modeling and Control,” John Wiley & Sons Inc., New York, 2006.

[5] F. Reyes and R. Kelly, “Experimental Evaluation of Model-Based Controllers on a Direct-Drive Robot Arm,” Mechatronics, Vol. 11, No. 3, 2001, pp. 267-282. doi:10.1016/S0957-4158(00)00008-8

[6] J. Slotine and W. Li, “Applied Nonlinear Control,” Prentice-Hall Inc., New Jersey, 1991.

[7] H. B. Guo, Y. G. Liu, G. R. Liu and H. R. Li, “Cascade Control of a Hydraulically Driven 6-DOF Parallel Robot Manipulator Based on a Sliding Mode,” Control Engineering Practice, Vol. 16, No. 9, 2008, pp. 1055-1068. doi:10.1016/j.conengprac.2007.11.005

[8] W. Gueaieb, S. Al-Sharhan and M. Bolic, “Robust Com- Putationally Efficient Control of Cooperative Closed- Chain Manipulators with Uncertain Dynamics,” Automatica, Vol. 43, 2007, pp. 842-851. doi:10.1016/j.automatica.2006.10.025

[9] P. Herman, “Sliding Mode Control of Manipulators Using First-Order Equations of Motion with Diagonal Mass Matrix,” Journal of the Franklin Institute, Vol. 342, No. 4, 2005, pp. 353-363. doi:10.1016/j.jfranklin.2004.12.001

[10] P. Herman, “Strict Lyapunov Function for Sliding Mode Control of Manipulator Using Quasi-Velocities,” Mechanics Research Communications, Vol. 36, No. 2, 2009, pp. 169-174. doi:10.1016/j.mechrescom.2008.09.010

[11] D. Brambilla, L. M. Capisani, A. Ferrara and P. Pisu, “Fault Detection for Robot Manipulators via Second-Order Sliding Modes,” IEEE Transactions on Industrial Electronics, Vol. 55, No. 11, 2008, pp. 3954-3963. doi:10.1109/TIE.2008.2005932

[12] M. Jin, J. Lee, P. H. Chang and C. Choi, “Practical Non- Singular Terminal Sliding-Mode Control of Robot Manipulators for High-Accuracy Tracking Control,” IEEE Transactions on Industrial Electronics, Vol. 56, No. 9, 2009, pp. 3593-3601. doi:10.1109/TIE.2009.2024097

[13] B. Brogliato, D. Rey, A. Pastore and J. Barnier, “Experi- mental Comparison of Nonlinear Controllers for Flexible Joint Manipulators,” The International Journal of Robotics Research, Vol. 17, No. 3, 1998, pp. 260-281. doi:10.1177/027836499801700304

[14] F. Alonge, F. D’Ippolito and F. M. Raimondo, “Globally Convergent Adaptive and Robust Control of Robotic Ma- nipulators for Trajectory Tracking,” Control Engineering Practice, Vol. 12, No. 9, 2004, pp. 1091-1100. doi:10.1016/j.conengprac.2003.11.007

[15] M. K. Ciliz and M. O. Tuncay, “Comparative Experi- ments with a Multiple Model Based Adaptive Controller for a SCARA Type Direct Drive Manipulator,” Robotica, Vol. 23, No. 6, 2005, pp. 721-729. doi:10.1017/S026357470500158X

[16] M. Margaloit and G. Langholz, “Fuzzy Control of a Benchmark Problem: Computing with Words Approach,” IEEE Transactions on Fuzzy Systems, Vol. 12, No. 2, 2004, pp. 230-235. doi:10.1109/TFUZZ.2004.825083

[17] V. Giordano, D. Naso. and B. Turchiano, “Combining Genetic Algorithms and Lyapunov-Based Adaptation for Online Design of Fuzzy Controllers,” IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, Vol. 36, No. 5, 2006, pp. 1118-1127. doi:10.1109/TSMCB.2006.873187

[18] O. Cordon, F. Herrera, F. Hoffmann and L. Magdalena, “Genetic Fuzzy Systems: Evolutionary Tuning and Learning of Fuzzy Knowledge Bases,” World Scientific, Singapore, July 2001.

[19] A. B. Sharkawy, “Genetic Fuzzy Self-Tuning PID Controllers for Antilock Braking Systems,” Engineering Applications of Artificial Intelligence, Vol. 23, No. 7, 2010, pp. 1041-1052. doi:10.1016/j.engappai.2010.06.011

[20] M. A. Llama, R. Kelly and V. Santibanez, “A Stable Motion Control System for Manipulators via Fuzzy Self-Tuning,” Fuzzy Sets and Systems, Vol. 124, No. 2, 2001, pp. 133-154. doi:10.1016/S0165-0114(00)00061-0

[21] T. L. Seng, M. Khalid and R. Yusof, “Tuning of a Neuro-Fuzzy Controller by Genetic Algorithm,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol. 29, No. 2, 1999, pp. 226-239. doi:10.1109/3477.752795

[22] A. B. Sharkawy, “A Computationally Efficient Fuzzy Logic Controller for Robotic Systems,” Proceedings of the 9th International Conference on Production Engineering, Design and Control (PEDAC’9), Alexandria, 10-12 February 2009.

[23] A. Visioli and G. Legnani, “On the Trajectory Tracking Control of Industrial SCARA Robot Manipulators,” IEEE Transactions on Industrial Electronics, Vol. 49, No. 1, February 2002, pp. 224-232. doi:10.1109/41.982266

[24] F.-J. Lin and R.-J. Wai, “A Hybrid Computed Torque Controller Using Fuzzy Neural Network for Motor- Quick-Return Servo Mechanism,” IEEE/ASME Trans- actions on Mechatronics, Vol. 6, No. 1, March 2001, pp. 75-89. doi:10.1109/3516.914394

[25] L. A Zadeh, “Fuzzy Logic = Computing with Words,” IEEE Transactions on Fuzzy Systems, Vol. 4, No. 2, 1996, pp. 103-111. doi:10.1109/91.493904

[26] L. X. Wang, “Fuzzy Systems Are Universal Approxima- tions,” Proceedings of IEEE International Conference on Fuzzy Systems, San Diago, 8 March 1992. doi:10.1109/FUZZY.1992.258721

[27] M. Margaloit and G. Langholz, “Fuzzy Lyapunov-Based Approach to the Design of Fuzzy Controllers”, Fuzzy Sets and Systems, Vol. 106, No. 1, 1999, pp. 49-59. doi:10.1016/S0165-0114(98)00356-X

[28] L. X. Wang, “A Course in Fuzzy Systems and Control,” Prentice-Hall, Upper Saddle River, 1997.

[29] M. M. Othman, “Fuzzy Control of Two Degrees of Free- dom Robotic Arm,” M.Sc Dissertation, Mechanical Engi- neering Department, Assiut University, Assiut, 2010.

[1] Z. Bingul and O. Karahan, “A Fuzzy Logic Controller Tuned with PSO for 2 DOF Robot Trajectory Control,” Expert Systems with Applications, Vol. 38, No. 1, 2011, pp. 1017-1031. doi:10.1016/j.eswa.2010.07.131

[2] T.-H. S. Li and Y.-C. Huang, “MIMO Adaptive Fuzzy Terminal Sliding-Mode Controller for Robotic Manipulators,” Information Sciences, Vol. 180, No. 23, 2010, pp. 4641-4660. doi:10.1016/j.ins.2010.08.009

[3] L. Tian and C. Collins, “Optimal Placement of a Two-Link Planar Manipulator Using a Genetic Algorithm,” Robotica, Cambridge University Press, Cambridge, Vol. 23, No. 2, 2005, pp. 169-176.

[4] M. W. Spong, S. Hutchinson and M. Vidyasagar, “Robot Modeling and Control,” John Wiley & Sons Inc., New York, 2006.

[5] F. Reyes and R. Kelly, “Experimental Evaluation of Model-Based Controllers on a Direct-Drive Robot Arm,” Mechatronics, Vol. 11, No. 3, 2001, pp. 267-282. doi:10.1016/S0957-4158(00)00008-8

[6] J. Slotine and W. Li, “Applied Nonlinear Control,” Prentice-Hall Inc., New Jersey, 1991.

[7] H. B. Guo, Y. G. Liu, G. R. Liu and H. R. Li, “Cascade Control of a Hydraulically Driven 6-DOF Parallel Robot Manipulator Based on a Sliding Mode,” Control Engineering Practice, Vol. 16, No. 9, 2008, pp. 1055-1068. doi:10.1016/j.conengprac.2007.11.005

[8] W. Gueaieb, S. Al-Sharhan and M. Bolic, “Robust Com- Putationally Efficient Control of Cooperative Closed- Chain Manipulators with Uncertain Dynamics,” Automatica, Vol. 43, 2007, pp. 842-851. doi:10.1016/j.automatica.2006.10.025

[9] P. Herman, “Sliding Mode Control of Manipulators Using First-Order Equations of Motion with Diagonal Mass Matrix,” Journal of the Franklin Institute, Vol. 342, No. 4, 2005, pp. 353-363. doi:10.1016/j.jfranklin.2004.12.001

[10] P. Herman, “Strict Lyapunov Function for Sliding Mode Control of Manipulator Using Quasi-Velocities,” Mechanics Research Communications, Vol. 36, No. 2, 2009, pp. 169-174. doi:10.1016/j.mechrescom.2008.09.010

[11] D. Brambilla, L. M. Capisani, A. Ferrara and P. Pisu, “Fault Detection for Robot Manipulators via Second-Order Sliding Modes,” IEEE Transactions on Industrial Electronics, Vol. 55, No. 11, 2008, pp. 3954-3963. doi:10.1109/TIE.2008.2005932

[12] M. Jin, J. Lee, P. H. Chang and C. Choi, “Practical Non- Singular Terminal Sliding-Mode Control of Robot Manipulators for High-Accuracy Tracking Control,” IEEE Transactions on Industrial Electronics, Vol. 56, No. 9, 2009, pp. 3593-3601. doi:10.1109/TIE.2009.2024097

[13] B. Brogliato, D. Rey, A. Pastore and J. Barnier, “Experi- mental Comparison of Nonlinear Controllers for Flexible Joint Manipulators,” The International Journal of Robotics Research, Vol. 17, No. 3, 1998, pp. 260-281. doi:10.1177/027836499801700304

[14] F. Alonge, F. D’Ippolito and F. M. Raimondo, “Globally Convergent Adaptive and Robust Control of Robotic Ma- nipulators for Trajectory Tracking,” Control Engineering Practice, Vol. 12, No. 9, 2004, pp. 1091-1100. doi:10.1016/j.conengprac.2003.11.007

[15] M. K. Ciliz and M. O. Tuncay, “Comparative Experi- ments with a Multiple Model Based Adaptive Controller for a SCARA Type Direct Drive Manipulator,” Robotica, Vol. 23, No. 6, 2005, pp. 721-729. doi:10.1017/S026357470500158X

[16] M. Margaloit and G. Langholz, “Fuzzy Control of a Benchmark Problem: Computing with Words Approach,” IEEE Transactions on Fuzzy Systems, Vol. 12, No. 2, 2004, pp. 230-235. doi:10.1109/TFUZZ.2004.825083

[17] V. Giordano, D. Naso. and B. Turchiano, “Combining Genetic Algorithms and Lyapunov-Based Adaptation for Online Design of Fuzzy Controllers,” IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, Vol. 36, No. 5, 2006, pp. 1118-1127. doi:10.1109/TSMCB.2006.873187

[18] O. Cordon, F. Herrera, F. Hoffmann and L. Magdalena, “Genetic Fuzzy Systems: Evolutionary Tuning and Learning of Fuzzy Knowledge Bases,” World Scientific, Singapore, July 2001.

[19] A. B. Sharkawy, “Genetic Fuzzy Self-Tuning PID Controllers for Antilock Braking Systems,” Engineering Applications of Artificial Intelligence, Vol. 23, No. 7, 2010, pp. 1041-1052. doi:10.1016/j.engappai.2010.06.011

[20] M. A. Llama, R. Kelly and V. Santibanez, “A Stable Motion Control System for Manipulators via Fuzzy Self-Tuning,” Fuzzy Sets and Systems, Vol. 124, No. 2, 2001, pp. 133-154. doi:10.1016/S0165-0114(00)00061-0

[21] T. L. Seng, M. Khalid and R. Yusof, “Tuning of a Neuro-Fuzzy Controller by Genetic Algorithm,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol. 29, No. 2, 1999, pp. 226-239. doi:10.1109/3477.752795

[22] A. B. Sharkawy, “A Computationally Efficient Fuzzy Logic Controller for Robotic Systems,” Proceedings of the 9th International Conference on Production Engineering, Design and Control (PEDAC’9), Alexandria, 10-12 February 2009.

[23] A. Visioli and G. Legnani, “On the Trajectory Tracking Control of Industrial SCARA Robot Manipulators,” IEEE Transactions on Industrial Electronics, Vol. 49, No. 1, February 2002, pp. 224-232. doi:10.1109/41.982266

[24] F.-J. Lin and R.-J. Wai, “A Hybrid Computed Torque Controller Using Fuzzy Neural Network for Motor- Quick-Return Servo Mechanism,” IEEE/ASME Trans- actions on Mechatronics, Vol. 6, No. 1, March 2001, pp. 75-89. doi:10.1109/3516.914394

[25] L. A Zadeh, “Fuzzy Logic = Computing with Words,” IEEE Transactions on Fuzzy Systems, Vol. 4, No. 2, 1996, pp. 103-111. doi:10.1109/91.493904

[26] L. X. Wang, “Fuzzy Systems Are Universal Approxima- tions,” Proceedings of IEEE International Conference on Fuzzy Systems, San Diago, 8 March 1992. doi:10.1109/FUZZY.1992.258721

[27] M. Margaloit and G. Langholz, “Fuzzy Lyapunov-Based Approach to the Design of Fuzzy Controllers”, Fuzzy Sets and Systems, Vol. 106, No. 1, 1999, pp. 49-59. doi:10.1016/S0165-0114(98)00356-X

[28] L. X. Wang, “A Course in Fuzzy Systems and Control,” Prentice-Hall, Upper Saddle River, 1997.

[29] M. M. Othman, “Fuzzy Control of Two Degrees of Free- dom Robotic Arm,” M.Sc Dissertation, Mechanical Engi- neering Department, Assiut University, Assiut, 2010.