Sequential Observation and Control of Robotic Systems Subjected to Measurement Delay and Disturbance

Affiliation(s)

Department of Production Engineering and Mechanical Design, Faculty of Engineering, Menoufiya Unicersity, Minoufia, Egypt.

Department of Production Engineering and Mechanical Design, Faculty of Engineering, Menoufiya Unicersity, Minoufia, Egypt.

ABSTRACT

An approach for motion control and observation of robotic manipulators is presented in this article. It links the design of a joint acceleration controller to the design of a variable structure observer including Luenberger-like observation term. Both the joint acceleration controller and the observer that are introduced in this paper are very likely to use either large or moderate or small gains. Thus the time delay issue of the output measurements is highly taken into consideration in the design of the intended observers. The observer design is therefore based on two different generalized forms of nonlinear systems with/without undelayed outputs. A study to investigate the effects of the gains of the joint acceleration controller on the performance capabilities of the observer is introduced. Also, the effects of the time delay factor on the operation of both the controller and the observer and their own interaction are studied. Then a chain observer design is presented for circumventing the time delay effects. The time delay constant is found to be of vital importance to the robot performance capabilities. Moreover, the results show that the gains of the joint acceleration controller are of significant influence on the operation of the proposed observers.

An approach for motion control and observation of robotic manipulators is presented in this article. It links the design of a joint acceleration controller to the design of a variable structure observer including Luenberger-like observation term. Both the joint acceleration controller and the observer that are introduced in this paper are very likely to use either large or moderate or small gains. Thus the time delay issue of the output measurements is highly taken into consideration in the design of the intended observers. The observer design is therefore based on two different generalized forms of nonlinear systems with/without undelayed outputs. A study to investigate the effects of the gains of the joint acceleration controller on the performance capabilities of the observer is introduced. Also, the effects of the time delay factor on the operation of both the controller and the observer and their own interaction are studied. Then a chain observer design is presented for circumventing the time delay effects. The time delay constant is found to be of vital importance to the robot performance capabilities. Moreover, the results show that the gains of the joint acceleration controller are of significant influence on the operation of the proposed observers.

Cite this paper

E. ElBeheiry, "Sequential Observation and Control of Robotic Systems Subjected to Measurement Delay and Disturbance,"*Intelligent Control and Automation*, Vol. 3 No. 4, 2012, pp. 291-302. doi: 10.4236/ica.2012.34034.

E. ElBeheiry, "Sequential Observation and Control of Robotic Systems Subjected to Measurement Delay and Disturbance,"

References

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[2] S. Ibrir, “Observer-Based Control of a Class of Time Delay Nonlinear Systems Having Triangular Structure,” Automatica, Vol. 47, 2011, pp. 388-394. doi:10.1016/j.automatica.2010.10.052

[3] S. J. Yoo and J. B. Park, “Decentralized Adaptive OutputFeedback Control for a Class of Nonlinear Large-Scale Systems with Unknown Time-Varying Delayed Interactions,” Information Sciences, Vol. 186, 2012, pp. 222-238. doi:10.1016/j.ins.2011.10.004

[4] T. Ahmed-Ali, E. Cherrier and M. M’Saad, “Cascade High Gain Observers for Nonlinear Systems with Delayed Output Measurement,” Proceeding of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, 16-18 December 2009, pp. 8226-8231.

[5] V. Van Assache, T. Ahmed-Ali and C. A. B. Hann, “High Gain Observer for Nonlinear Systems with Time Varying Delayed Measurements,” Proceeding of the 18th IFAC World Congress, Milano, 28 August-2 September 2011, pp. 692-696.

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[7] F. Cacace, A. Germanib and C. Manesb, “An Observer for a Class of Nonlinear Systems with Time Varying Observation Delay,” Systems & Control Letters, Vol. 59, 2010, pp. 305-312 doi:10.1016/j.sysconle.2010.03.005

[8] A. Germani, C. Manes and P. Pepe, “An Asymptotic State Observer for a Class of Nonlinear Delay Systems,” Kybernetika, Vol. 37, No. 4, 2001, pp. 459-478.

[9] A. Germani, C. Manes and P. Pepe, “A New Approach to State Observation of Nonlinear Systems with Delayed Outputs,” IEEE Transactions on Automatic Control, Vol. 47, 2002, pp. 96-101. doi:10.1109/9.981726

[10] M. D. Mora, A. Germani and C. Manes, “A State Observer for Nonlinear Dynamical Systems,” Nonlinear Analysis, Theory, Methods & Applications, Vol. 30, 1997, pp. 4485-4496.

[11] M. D. Mora, A. Germani and C. Manes, “Design of State Observers from a Drift-Observability Property,” IEEE Transactions on Automatic Control, Vol. 45, 2000, pp. 1536-1540. doi:10.1109/9.871767

[12] G. Ciccarella, M. D. Mora and A. Germani, “A Luenberger-Like Observer for Nonlinear Systems,” International Journal of Control, Vol. 57, 1993, pp. 537-556. doi:10.1080/00207179308934406

[13] A. S. Zaki, E. M. ElBeheiry and W. H. ElMaraghy, “Variable Structure Observers Design for Flexible-Link Manipulator Control,” Transaction of the CSME/de la SCGM, Vol. 27, No. 1-2, 2003, pp. 107-129.

[14] E. M. ElBeheiry, A. Zaki and W. H. ElMaraghy, “A Unified Approach for Independent Manipulator Joint Acceleration Control and Observation,” ASME Dynamic Systems and Control Division—DSC, Vol. 72, No. 1, 2003, pp. 659-666.

[15] W. L. Xu and J. D. Han, “Joint Acceleration Feedback Control for Robots: Analysis, Sensing and Experiments,” Robotics and Computer Integrated Manufacturing, Vol. 16, 2000, pp. 307-320. doi:10.1016/S0736-5845(00)00010-7

[16] J. D. Han, Y. Q. He and W. L. Xu, “Angular Acceleration Estimation and Feedback Control: An Experimental Investigation,” Mechatronics, Vol. 17, 2007, pp. 524-532 doi:10.1016/j.mechatronics.2007.05.006

[17] G. L. Luo and G. N. Saridis, “LQ Design of PID Controllers for Robot Arms,” IEEE Journal of Robotics and Automation, Vol. l, 1985, pp. 152-159.

[18] S. J. Ovaska and S. Valiviita, “Angular Acceleration Measurement: A Review,” Proceedings of the IEEE Conference on Instrumentation and Measurement Technology, St. Paul, 18-21 May 1998, pp. 875-880.

[19] J. Studenny, P. R. Belanger and L. K. Daneshmend, “A Digital Implementation of the Acceleration Feedback Law on A PUMA 560 Manipulator,” Proceedings of 30th IEEE Conference on Decision and Control, Brighton, 11-13 December 1991, pp. 2639-2648. doi:10.1109/CDC.1991.261831

[20] P. Chiacchi, L. Sciavicco and B. Siciliano, “Practical Design of Independent Joint Controllers for Industrial Robots,” Proceedings of the American Control Conference, Chicago, 24-26 June 1992, pp. 1239-1240.

[21] P. B. Schmidt and R. D. Lorenz, “Design Principles and Implementation of Acceleration Feedback to Improve Performance of DC Drives,” Proceeding of the Industry Applications Society Annual Meeting, Seatle, 7-12 October 1990, pp. 422-427.

[22] A. De Luca, D. Schroder and M. Thummel, “An Acceleration-Based State Observer for Robot Manipulators with Elastic Joints,” Proceedings of the IEEE International Conference on Robotics and Automation, Roma, 10-14 April 2007, pp. 3817-3823. doi:10.1109/ROBOT.2007.364064

[23] C. J. Tsaprounis and N. A. Aspragathos, “Adaptive Tracking Controller for Rigid-Link Elastic-Joint Robots with Link Acceleration Estimation,” Journal of Intelligent and Robotic Systems, Vol. 27, 2000, pp. 67-83. doi:10.1023/A:1008198029642

[24] J.-J. E. Slotine, J. K. Hedrick and E. A. Misawa, “On Sliding Observers for Nonlinear Systems,” ASME Transactions, Journal of Dynamic Systems, Measurement and Control, Vol. 109, 1987, pp. 245-252 doi:10.1115/1.3143852

[25] E. M. El Beheiry and H. A. El Maraghy, “Robotic Manipulator State Observation via One Time Gain Switching,” Journal of Intelligent & Robotic Systems, Vol. 38, No. 3-4, 2003, pp. 313-344. doi:10.1023/B:JINT.0000004972.84871.b5

[26] K. Jezernik, B. Curk and J. Harnik, “Observer Based Sliding Model Control of Robotic Manipulator,” Robotica, Vol. 12, 1994, pp. 443-448. doi:10.1017/S0263574700017999

[27] B. Bona and M. Indri, “Analysis and Implementation of Observers for Robotic Manipulators,” Proceedings of the IEEE Conference on Robotic & Automation, Leuven, 16-20 May 1998, pp. 3006-3011.

[28] J. P. Gauthier, H. Hammouri and S. Othman, “A Simple Observer for Nonlinear Systems: Applications to Bioreactors,” IEEE Transactions on Automatic Control, Vol. 37, 1992, pp. 875-880. doi:10.1109/9.256352

[29] R. A. Garcia and C. E. D’Attellis, “Nonlinear Observers in Closed Loop Trajectory Tracking,” Proceeding of the 20th IECON International Conference on Industrial Electronics, Control and Instrumentation, Vol. 3, 1994, pp. 1767-1772.

[30] B. L. Walcott and S. H. Zak, “State Observation of Nonlinear Uncertain Dynamical Systems,” IEEE Transactions on Automatic Control, Vol. 32, 1987, pp. 166-170. doi:10.1109/TAC.1987.1104530

[31] A. J. Koshkouei and A. S. I. Zinober, “Sliding Mode Observers for a Class of Nonlinear Systems,” Proceeding of the American Control Conference, Anchorage, 7-12 May 2002, pp. 2106-2111.

[32] A. Isidori, “Nonlinear Control Systems,” 3rd Edition, Springer-Verlag, London, 1995.

[33] T.-J. Tarn, A. K. Bejczy, X. Yun and Z. Li, “Effect of Motor Dynamics on Nonlinear Feedback Robot Arm Control,” IEEE Transactions on Robotics and Automation, Vol. 7, No. 1, 1991, pp. 114-122. doi:10.1109/70.68075

[1] J.-P. Richard, “Time-Delay Systems: An Overview of Some Recent Advances and Open Problems,” Automatica, Vol. 39, 2003, pp. 1667-1694. doi:10.1016/S0005-1098(03)00167-5

[2] S. Ibrir, “Observer-Based Control of a Class of Time Delay Nonlinear Systems Having Triangular Structure,” Automatica, Vol. 47, 2011, pp. 388-394. doi:10.1016/j.automatica.2010.10.052

[3] S. J. Yoo and J. B. Park, “Decentralized Adaptive OutputFeedback Control for a Class of Nonlinear Large-Scale Systems with Unknown Time-Varying Delayed Interactions,” Information Sciences, Vol. 186, 2012, pp. 222-238. doi:10.1016/j.ins.2011.10.004

[4] T. Ahmed-Ali, E. Cherrier and M. M’Saad, “Cascade High Gain Observers for Nonlinear Systems with Delayed Output Measurement,” Proceeding of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, 16-18 December 2009, pp. 8226-8231.

[5] V. Van Assache, T. Ahmed-Ali and C. A. B. Hann, “High Gain Observer for Nonlinear Systems with Time Varying Delayed Measurements,” Proceeding of the 18th IFAC World Congress, Milano, 28 August-2 September 2011, pp. 692-696.

[6] A. Seuret, T. Floquet, J.-P. Richard and S. Spurgeon, “Observer Design for Systems with Non Small and Unknown Time-Varying Delay,” In: J. J. Loiseau, W. Michiels, S.-I. Niculescu and R. Sipahi, Eds., Topics in Time-Delay Systems: Analysis, Algorithms and Control, Springer Verlag Series in Lecture Notes in Control and Information Sciences, Vol. 388, 2009, pp. 233-242.

[7] F. Cacace, A. Germanib and C. Manesb, “An Observer for a Class of Nonlinear Systems with Time Varying Observation Delay,” Systems & Control Letters, Vol. 59, 2010, pp. 305-312 doi:10.1016/j.sysconle.2010.03.005

[8] A. Germani, C. Manes and P. Pepe, “An Asymptotic State Observer for a Class of Nonlinear Delay Systems,” Kybernetika, Vol. 37, No. 4, 2001, pp. 459-478.

[9] A. Germani, C. Manes and P. Pepe, “A New Approach to State Observation of Nonlinear Systems with Delayed Outputs,” IEEE Transactions on Automatic Control, Vol. 47, 2002, pp. 96-101. doi:10.1109/9.981726

[10] M. D. Mora, A. Germani and C. Manes, “A State Observer for Nonlinear Dynamical Systems,” Nonlinear Analysis, Theory, Methods & Applications, Vol. 30, 1997, pp. 4485-4496.

[11] M. D. Mora, A. Germani and C. Manes, “Design of State Observers from a Drift-Observability Property,” IEEE Transactions on Automatic Control, Vol. 45, 2000, pp. 1536-1540. doi:10.1109/9.871767

[12] G. Ciccarella, M. D. Mora and A. Germani, “A Luenberger-Like Observer for Nonlinear Systems,” International Journal of Control, Vol. 57, 1993, pp. 537-556. doi:10.1080/00207179308934406

[13] A. S. Zaki, E. M. ElBeheiry and W. H. ElMaraghy, “Variable Structure Observers Design for Flexible-Link Manipulator Control,” Transaction of the CSME/de la SCGM, Vol. 27, No. 1-2, 2003, pp. 107-129.

[14] E. M. ElBeheiry, A. Zaki and W. H. ElMaraghy, “A Unified Approach for Independent Manipulator Joint Acceleration Control and Observation,” ASME Dynamic Systems and Control Division—DSC, Vol. 72, No. 1, 2003, pp. 659-666.

[15] W. L. Xu and J. D. Han, “Joint Acceleration Feedback Control for Robots: Analysis, Sensing and Experiments,” Robotics and Computer Integrated Manufacturing, Vol. 16, 2000, pp. 307-320. doi:10.1016/S0736-5845(00)00010-7

[16] J. D. Han, Y. Q. He and W. L. Xu, “Angular Acceleration Estimation and Feedback Control: An Experimental Investigation,” Mechatronics, Vol. 17, 2007, pp. 524-532 doi:10.1016/j.mechatronics.2007.05.006

[17] G. L. Luo and G. N. Saridis, “LQ Design of PID Controllers for Robot Arms,” IEEE Journal of Robotics and Automation, Vol. l, 1985, pp. 152-159.

[18] S. J. Ovaska and S. Valiviita, “Angular Acceleration Measurement: A Review,” Proceedings of the IEEE Conference on Instrumentation and Measurement Technology, St. Paul, 18-21 May 1998, pp. 875-880.

[19] J. Studenny, P. R. Belanger and L. K. Daneshmend, “A Digital Implementation of the Acceleration Feedback Law on A PUMA 560 Manipulator,” Proceedings of 30th IEEE Conference on Decision and Control, Brighton, 11-13 December 1991, pp. 2639-2648. doi:10.1109/CDC.1991.261831

[20] P. Chiacchi, L. Sciavicco and B. Siciliano, “Practical Design of Independent Joint Controllers for Industrial Robots,” Proceedings of the American Control Conference, Chicago, 24-26 June 1992, pp. 1239-1240.

[21] P. B. Schmidt and R. D. Lorenz, “Design Principles and Implementation of Acceleration Feedback to Improve Performance of DC Drives,” Proceeding of the Industry Applications Society Annual Meeting, Seatle, 7-12 October 1990, pp. 422-427.

[22] A. De Luca, D. Schroder and M. Thummel, “An Acceleration-Based State Observer for Robot Manipulators with Elastic Joints,” Proceedings of the IEEE International Conference on Robotics and Automation, Roma, 10-14 April 2007, pp. 3817-3823. doi:10.1109/ROBOT.2007.364064

[23] C. J. Tsaprounis and N. A. Aspragathos, “Adaptive Tracking Controller for Rigid-Link Elastic-Joint Robots with Link Acceleration Estimation,” Journal of Intelligent and Robotic Systems, Vol. 27, 2000, pp. 67-83. doi:10.1023/A:1008198029642

[24] J.-J. E. Slotine, J. K. Hedrick and E. A. Misawa, “On Sliding Observers for Nonlinear Systems,” ASME Transactions, Journal of Dynamic Systems, Measurement and Control, Vol. 109, 1987, pp. 245-252 doi:10.1115/1.3143852

[25] E. M. El Beheiry and H. A. El Maraghy, “Robotic Manipulator State Observation via One Time Gain Switching,” Journal of Intelligent & Robotic Systems, Vol. 38, No. 3-4, 2003, pp. 313-344. doi:10.1023/B:JINT.0000004972.84871.b5

[26] K. Jezernik, B. Curk and J. Harnik, “Observer Based Sliding Model Control of Robotic Manipulator,” Robotica, Vol. 12, 1994, pp. 443-448. doi:10.1017/S0263574700017999

[27] B. Bona and M. Indri, “Analysis and Implementation of Observers for Robotic Manipulators,” Proceedings of the IEEE Conference on Robotic & Automation, Leuven, 16-20 May 1998, pp. 3006-3011.

[28] J. P. Gauthier, H. Hammouri and S. Othman, “A Simple Observer for Nonlinear Systems: Applications to Bioreactors,” IEEE Transactions on Automatic Control, Vol. 37, 1992, pp. 875-880. doi:10.1109/9.256352

[29] R. A. Garcia and C. E. D’Attellis, “Nonlinear Observers in Closed Loop Trajectory Tracking,” Proceeding of the 20th IECON International Conference on Industrial Electronics, Control and Instrumentation, Vol. 3, 1994, pp. 1767-1772.

[30] B. L. Walcott and S. H. Zak, “State Observation of Nonlinear Uncertain Dynamical Systems,” IEEE Transactions on Automatic Control, Vol. 32, 1987, pp. 166-170. doi:10.1109/TAC.1987.1104530

[31] A. J. Koshkouei and A. S. I. Zinober, “Sliding Mode Observers for a Class of Nonlinear Systems,” Proceeding of the American Control Conference, Anchorage, 7-12 May 2002, pp. 2106-2111.

[32] A. Isidori, “Nonlinear Control Systems,” 3rd Edition, Springer-Verlag, London, 1995.

[33] T.-J. Tarn, A. K. Bejczy, X. Yun and Z. Li, “Effect of Motor Dynamics on Nonlinear Feedback Robot Arm Control,” IEEE Transactions on Robotics and Automation, Vol. 7, No. 1, 1991, pp. 114-122. doi:10.1109/70.68075