Comparison of Two Approaches to Count Derivations for Continuous-Time Adaptive Control

The control of continuous-time systems can be realized by adaptive controllers. Self-tuning controllers are adaptive controllers which call on-line identification and controllers parameters tuning in one step of computation. Supervision enlarges the area of usage of controllers. It is necessary to count derivations of action and output signals during control, which is usually realized by filters. Settings of filters are directly connected with the model of the system. Another approach allows us to use the regression polynomials instead of filters, because the general form of derivations is known before the control. Without filters, this approach keeps the signal unchanged, but the choice of inappropriate length of time interval for polynomial regression increases the amplitude of noise. The chapter shows two examples of control and suggests the appropriate length of time interval for polynomial regression.

Track trajectories with model uncertainty using a robust differentiator

[EN] In this article, we present the Levant’s Robust Differentiator applied to robot manipulators whose objective is to follow a desired trajectory. The robots’ dynamic model is unknown. The velocity obtained using the Robust Differentiator is applied in the control structure in order to fulfill the tracking task. A comparative study is made between the Levant’s Robust Differentiator and the most-used techniques to calculate the velocity. Experimental results are presented.[ES] En este artículo se presenta el uso de un diferenciador robusto de Levant aplicado a robots manipuladores cuyo objetivo es realizar el seguimiento de una trayectoria deseada. El modelo dinámico de los robots es desconocido. La velocidad obtenida empleando el diferenciador robusto se aplica en la estructura de control con la finalidad de cumplir con la tarea de seguimiento. Se realiza un estudio comparativo entre el diferenciador robusto de Levant y las técnicas más usadas para calcular la velocidad. Son presentados resultados experimentales.Los autores agradecen a PRODEP (PROMEP) con el número de Folio BUAP–811 y los proyectos PAPIIT 116314 y 114617 por el apoyo recibido, a CONACYT por la Cátedra CONACYT–CICESE 2017 y al Laboratorio de Robótica de la Facultad de Ciencias de la Electrónica de la Benemérita Universidad Autónoma de Puebla.Sánchez-Sánchez, P.; Gutiérrez–giles, A.; Pliego–jiménez, J.; Arteaga–pérez, M. (2019). Seguimiento de trayectorias con incertidumbre del modelo usando un diferenciador robusto. Revista Iberoamericana de Automática e Informática. 16(4):423-434. https://doi.org/10.4995/riai.2019.10265SWORD423434164Alcocer, A. and Robertsson, A. and Valera, A. and Johansson, R., 2003. Force Estimation and Control in Robot Manipulators. Proceedings of 7th Symposium on Robot Control (SYROCO'03) 55-60. Wroclaw, Poland https://doi.org/10.1016/S1474-6670(17)33369-4Atassi, A. N. and Khalil, H. K., 2000. Separation results for the stabilization of nonlinear systems using di_erent high-gain observer designs. Systems and Control Letters, 39(15), 183-191. https://doi.org/10.1016/S0167-6911(99)00085-7Berghuis, H. and Nijmeijer, H., 1994. Robust control of robots via linear estimated state feedback. IEEE Transactions on Automatic Control, 39(10), 2159-2162.https://doi.org/10.1109/9.328807Calafiore, G. and Indri, M. and Bona, B., 1997. Robot dynamic calibration: Optimal excitation trajectories and experimental parameter estimation. Journal of Robotic Systems 18(2), 55-68. https://doi.org/10.1002/1097-4563(200102)18:23.3.CO;2-FCruz-Zavala, E. and Moreno, J. A. and Fridman, L. M., 2010. Diferenciador Robusto Exacto y Uniforme. Proceedings of AMCA 2010, 1-6.Dabroom, A. M. and Khalil, H. K., 1994. Numerical differentiation using high gain observers. Proceedings of of the IEEE Conference on Decision and Control, 4790-4795. https://doi.org/10.1109/CDC.1997.649776Diop, S. and Grizzle, J. and Moraal, P. and Stefanopoulou, A., 1994. Interpolation and numerical differentiation for observer design. Proceedings of the American Control Conference, 1329-1333. https://doi.org/10.1109/ACC.1994.752275Hacksel, P. J. and Salcudean, S. E., 1994. Estimation of Environment Forces and Rigid-Body Velocities using Observers. Proc. IEEE International Conference on Robotics and Automation, 931-936. San Diego, CA, USA https://doi.org/10.1109/ROBOT.1994.351233Kelly, R. and Ortega, R. and Ailon, A. and Loria, A., 1994. Global regulation of flexible joint robots using approximate differentiation. IEEE Transactions on Automatic Control 39(6), 1222-1224. https://doi.org/10.1109/9.293181Kelly, R. and Santibáñez, V., 2003. Control de Movimiento de Robots Manipuladores. Prentice-HallKhalil, H. K., 1996. Nonlinear Systems. Prentice-HallKhatib, O., 1987. A Unified Approach for Motion and Force Control of Robot Manipulators: The Operational Space Formulation. IEEE Journal of Robotics and Automation 3(1), 43-53. https://doi.org/10.1109/JRA.1987.1087068Kumar, B. and Dutta-Roy, S. C., 1988. Design of digital differentiators for low frequencies. Proceedings of the IEEE, 76(3), 287-289. https://doi.org/10.1109/5.4408Levant, A., 1998. Sliding order and sliding accuracy in sliding mode control. International Journal of Control, 58(6), 1247-1263. https://doi.org/10.1080/00207179308923053Levant, A., 1998. Robust exact diferentiation via sliding mode technique. Automatica, 34(3), 379-384. https://doi.org/10.1016/S0005-1098(97)00209-4Levant, A., 2003. Higher-order sliding modes, diferentiation and output-feedback control. International Journal of Control, 76(9), 924-941. https://doi.org/10.1080/0020717031000099029Loria, A., 2016. Observers are Unnecessary for Output-Feedback Control of Lagrangian Systems. IEEE Transactions on Automatic Control, 61(4), 905- 920. https://doi.org/10.1109/TAC.2015.2446831Martínez-Rosas, J. C. and Arteaga-Pérez, M. A. and Castillo-Sánchez, A., 2006. Decentralized Control of Cooperative Robots without Velocity-Force Measurements. Automatica 42, 329-336. https://doi.org/10.1016/j.automatica.2005.10.007Martínez-Rosas, J. C. and Arteaga-Pérez, M. A., 2008. Force and Velocity Observers for the Control of Cooperative Robots. Robotica 26, 85-92. https://doi.org/10.1017/S026357470700361XMoreno, J. and Kelly, R., 2002. On motor velocity control by using only position measurements: two case studies. International Journal of Electrical Engineering Education 39(2), 118-127. https://doi.org/10.7227/IJEEE.39.2.4Nicosia, S. and Tornambe, A. and Valigi, P., 1990. Experimental results in state estimation of industrial robots. Proceedings of 29th IEEE Conference on Decision and Control, 360-365. https://doi.org/10.1109/CDC.1990.203613Parsa, K. and Aghili, F., 2006. Adaptive Observer for the Calibration of the Force-Moment Sensor of a Space Robot. Proceedings of the 2006 IEEE International Conference on Robotics and Automation, 1667-1673. Orlando, Florida. https://doi.org/10.1109/ROBOT.2006.1641946Rabiner, L. R. and Steiglitz, K., 1970. The design of wide-band recursive and nonrecursive digital differentiators. IEEE Transactions on Audio and Electroacoustics, 18(2), 204-209. https://doi.org/10.1109/TAU.1970.1162090Radkhah, K. and Kulic, D. and Croft, E., 2007. Dynamic parameter identification for the CRS A460 robot. Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 1-6. San Diego, CA, USA. https://doi.org/10.1109/IROS.2007.4399314Sira-Ramírez, H., 2005. Control de sistemas no lineales linealización aproximada, extendida, exacta. Pearson Prentice-HallStotsky, A. and Hedrick, J. K. and Yip, P. P., 1994. The use of sliding modes to simplify the backstepping control method. 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Generalized Proportional Integral observer–based force control in robot manipulators

[EN] In this work the design of a linear observer–linear controller robust output feedback scheme is introduced for simultaneous trajectory tracking of position and force in fully actuated robot manipulators. The unknown state–dependent additive nonlinearity influencing the input–output description is modeled as an absolutely bounded “time–varying perturbation”. Generalized Proportional Integral (GPI) observers are shown to naturally estimate the unknown perturbation and a certain number of its time derivatives in an arbitrarily close manner. This information is used to advantage on the linear feedback controller design via a simple cancelation effort. To the best of the authors’ knowledge GPI observers have not been used before for robot force control. A comparison experimental analysis is presented to show the good performance of the proposed approach.[ES] En este trabajo se presenta el diseño de un controlador lineal robusto para el seguimiento simultáneo de posición y fuerza de robots manipuladores completamente actuados. Las no linealidades aditivas, posiblemente dependientes del estado, se modelan como una perturbación variante en el tiempo absolutamente acotada. Los observadores Proporcionales Integrales Generalizados (GPI, por sus siglas en inglés) son capaces de estimar esta perturbación desconocida y un cierto número de sus derivadas temporales de forma aproximada, aunque arbitrariamente cercana. Esta estimacińo del controlador para cancelar los efectos de los términos desconocidos. Hasta donde los autores saben, los observadores GPI no se han utilizado para el control de fuerza de robots manipuladores. Se presenta un análisis comparativo experimental para mostrar el buen desempeño del esquema propuestoEste trabajo se realizo en el marco del proyecto PAPIIT No.IN116314. Alejandro Gutiérrez–Giles agradece al Conacyt bajo la beca doctoral con CVU No. 334785. H. Sira–Ramírez agradece al Cinvestav (México) y al Conacyt bajo el proyecto No. 80777.Gutiérrez Giles, A.; Arteaga Pérez, MA.; Sira Ramírez, H. (2016). Control de Fuerza de Robots Manipuladores Basado en Observadores Proporcionales Integrales Generalizados. Revista Iberoamericana de Automática e Informática industrial. 13(2):238-246. https://doi.org/10.1016/j.riai.2016.01.004OJS238246132Arimoto, S., Liu, Y. H., Naniwa, T., 1993. Principle of orthogonalization for hybrid control of robot arms. En: Proceedings of the 12th IFAC World Congress. Vol. 1. pp. 507-512.Arteaga-Pérez, M. A., & Gutiérrez-Giles, A. (2013). On the GPI approach with unknown inertia matrix in robot manipulators. International Journal of Control, 87(4), 844-860. doi:10.1080/00207179.2013.861080Cheah, C. C., Hou, S. P., Zhao, Y., & Slotine, J.-J. E. (2010). Adaptive Vision and Force Tracking Control for Robots With Constraint Uncertainty. IEEE/ASME Transactions on Mechatronics, 15(3), 389-399. doi:10.1109/tmech.2009.2027115Fliess, M., Marquez, R., Delaleau, E., & Sira–Ramírez, H. (2002). Correcteurs proportionnels-intégraux généralisés. ESAIM: Control, Optimisation and Calculus of Variations, 7, 23-41. doi:10.1051/cocv:2002002Han, J. (2009). From PID to Active Disturbance Rejection Control. IEEE Transactions on Industrial Electronics, 56(3), 900-906. doi:10.1109/tie.2008.2011621Johnson, C. (1971). Accomodation of external disturbances in linear regulator and servomechanism problems. IEEE Transactions on Automatic Control, 16(6), 635-644. doi:10.1109/tac.1971.1099830Katsura, S., Matsumoto, Y., & Ohnishi, K. (2007). Modeling of Force Sensing and Validation of Disturbance Observer for Force Control. IEEE Transactions on Industrial Electronics, 54(1), 530-538. doi:10.1109/tie.2006.885459Martínez-Rosas, J. C., Arteaga, M. A., & Castillo-Sánchez, A. M. (2006). Decentralized control of cooperative robots without velocity–force measurements. Automatica, 42(2), 329-336. doi:10.1016/j.automatica.2005.10.007Ohnishi, K., Shibata, M., & Murakami, T. (1996). Motion control for advanced mechatronics. IEEE/ASME Transactions on Mechatronics, 1(1), 56-67. doi:10.1109/3516.491410Parra-Vega, V., Rodríguez-Angeles, A., Arimoto, S., & Hirzinger, G. (2001). Journal of Intelligent and Robotic Systems, 32(3), 235-254. doi:10.1023/a:101398720954