Dynamic modeling and optimal control of stone-carving robotic manipulators

Document Type : Article

Authors

- National & Local Joint Engineering Research Center for Intelligent Manufacturing Technology of Brittle Material Products, Huaqiao University, Xiamen 361021, China - Institute of Manufacturing Engineering, Huaqiao University, Xiamen 361021, China

Abstract

The stone-carving robotic manipulators (SCRM) find a broad range of applications due to their high efficiency, wide range of processing and strong flexibility. However, the features of strong disturbance, uncertainty and variation in the parameters make the design of SCRM control systems more complicated. This paper introduced the inverse linear quadratic (ILQ) theory into the SCRM control system. First, we deduced the dynamic equation and state-space equation of the SCRM system with the Lagrange method. Then, the ILQ theory was used to achieve the desired closed-loop poles assignment of the system. To simplify the design process and meet the requirement of practical use, the state feedback optimal control law was determined by an improved ILQ design method. The proposed control scheme has the explicit capacity to achieve the desired joint angle and joint torque control performances, with fewer external disturbances and no sensitivity to changing model parameters. The effectiveness of the proposed control scheme compared with the traditional control strategies is shown in the simulation results. Thus, the vibration of the joint torque during the manufacturing process can be greatly reduced.

Keywords


References:

[1] Lu, L., Zhang, J., Han, J. and Wang, H. “Time-optimal tool motion planning with tool-tip kinematic constraints for robotic machining of sculptured surfaces”, Robotics and Computer-Integrated Manufacturing,65, pp.101969 (2020).
[2] Andersson, J.E. and Johansson, G. “Robot control for wood carving operations”, Mechatronics, 11, pp.475-490 (2001).
[3] Yin, F.C., Ji, Q.Z. and Wang, C.Z. “Research on machining error prediction and compensation technology for a stone-carving robotic manipulator”, International Journal of Advanced Manufacturing Technology, 115, pp.1683-1700 (2021).
[4] Yin, F.C., Ji, Q.Z. and Jin, C.W. “An improved QPSO-SVM-based approach for predicting the milling force for white marble in robot stone machining”, Journal of Intelligent& Fuzzy Systems, 41, pp.1589-1609 (2021).
[5] Wen, S.H., Zheng, W., Jia, S.D., Ji, Z. X., Han, P. C. and Lam, H. K. “Unactuated force control of 5-DOF parallel robot based on fuzzy PI”, International Journal of Control, Automation and Systems, 18(6), pp.1629-1640 (2020).
[6] Garrido, R. and Trujano, M.A. “Stability analysis of a visual PID controller applied to a planar robot”, International Journal of Control, Automation and Systems, 17(6), pp.1589-1598 (2019).
[7] Su, Y. X., Sun, D. and Duan, B. Y. “Design of an enhanced nonlinear PID controller”, Mechatronics, 15(8), pp.1005-1024 (2005).
[8] Van, M., Do, X.P, and Mavrovouniotis, M. “Self-tuning PID-nonsingular fast terminal sliding mode control for robust fault tolerant control of robot manipulators”, ISA Transactions, 96, pp.60-68 (2020).
[9] Nohooji, H.R. “Constrained neural adaptive PID control for robot manipulators”, Journal of the Franklin Institute, 357(7), pp.3907-3923 (2020).
[10] Huang, H., Zhang, T, and Yang, C. “Motor learning and generalization using broad learning adaptive neural control”, IEEE Transactions on Industrial Electronics, 67, pp.8608-8617 (2020).
[11] Liu, C.X., Wen, G.L., Zhao, Z.J, and Sedaghtai, R. “Modeling, control, and simulation of a SCARA PRR-type robot manipulator”, IEEE Transactions on Cybernetics, 99, pp.1-8. (2020).
[12] He, W, and Dong, Y.T. “Adaptive fuzzy neural network control for a constrained robot using impedance learning”, EEE Transactions on Neural Networks and Learning Systems, 29(4), pp.1174-1186. (2018).
[13] Zhang, T., Wang, X., Xu, X, and Chen, L.P. “GCB-Net: Graph convolutional broad network and its application in emotion recognition”, IEEE Transactions on Affective Computing, 99, pp.1-1. (2019).
[14] Li, C.G., Cui, W., Yan, D. D., Wang, Y. and Wang, C.M. “Adaptive dynamic surface control of a flexible-joint robot with parametric uncertainties”, Scientia Iranica, 26(5), pp.2749-2759. (2019).
[15] He, W., Dong, Y. and Sun, C. “Adaptive neural impedance control of a robotic manipulator with input saturation”, IEEE Transactions on Systems Man Cybernetics-Systems, 46, pp. 334-344 (2016).
[16] Chen, W. and Jiao, L. “Adaptive  tracking  for  periodically  time-varying  and  nonlinearly parameterized  systems  using  multilayer  neural  networks”, IEEE Transactions on Neural Networks and Learning Systems, 21(2), pp. 345-351(2010).
[17] Talole, S. E., Kolhe, J. P. and Phadke, S. B. “Extended-state-observer-based control of flexible-joint system with experimental validation”, IEEE Transactions on Industrial Electronics, 57(4), pp. 1411-1419, (2010).
[18] Liu, Y., Liu, H. and Meng, Y.N. “Active disturbance rejection control for a multiple-flexible-link manipulator”, Journal of Harbin Institute of Technology, 25(1), pp. 18-28, (2018).
[19] Saeed, A. and Barjuei, E.S. “Linear quadratic optimal controller for cable-driven parallel robots”, Frontiers of Mechanical Engineering, 10, pp. 344-351, (2014).
[20] Pan, H. J. and Xin, M. “Nonlinear robust and optimal control of robot manipulators”, Nonlinear Dynamics, 76, pp. 237-254, (2014).
[21] Zhang, H., Umenberger, J. and Hu, X.M. “Inverse optimal control for discrete-time finite-horizon linear quadratic regulators”, Automatica, 110, pp.108593, (2019).
[22] Li, Y.B., Yao, Y. and Hu, X.M. “Continuous-time inverse quadratic optimal control problem”, Automatica, 117, pp.108977, (2020).
[23] Xu, J.Y., Liu, H.P. and Zhou, J. H. “Tracking robustness of model-reference inverse linear quadratic (MR-ILQ) optimal current-control for permanent magnet synchronous motor”, Control Theory & Applications, 25(6), pp. 1081-1084, (2008).
[24] Hu, Y.J., Sun, J., Wang, Q.L. and Yin, F.C. “Characteristic analysis and optimal control of the thickness and tension system on tandem cold rolling”, International Journal of Advanced Manufacturing Technology, 101, pp. 2297-2312, (2019).
[25] Liu, C.X., Zhao, Z.J., and Wen, G.L. “Adaptive neural network control with optimal number of hidden nodes for trajectory tracking of robot manipulators”, Neurocomputing, 350, pp.60-68 (2019).
[26] Van, M., Do, X.P., and Mavrovouniotis, M. “Self-tuning PID-nonsingular fast terminal sliding mode control for robust fault tolerant control of robot manipulators”, ISA Transactions, 96, pp.60-68 (2019).
[27] Wang, G.C., Wang, W.C., and Yan, Z.G. “Linear quadratic control of backward stochastic differential equation with partial information”, Applied Mathematics and Computation, 403, pp.126164 (2021).
[28] Yu, C.P., Li, Y., and Fang, H. “System identification approach for inverse optimal control of finite-horizon linear quadratic regulators”, Automatica, 129, pp.109636 (2021).