Linear/Nonlinear PID Control of Cooperative Multiple Robot Manipulators: A Robust Approach

Document Type : Research Article

Authors

1 Department of Electrical Engineering, Garmsar Branch, Islamic Azad University, Garmsar, Iran.

2 Department of Electrical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran.

3 The Center of Excellence on Control and Robotics, Department of Electrical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran.

Abstract

The issue of position/force control of collaborative robotic systems moving a payload is proposed in this paper. The proposed approach must be able to maintain the orientation/position of the payload on the reference trajectory while applying a limited force to the object through the robot's end-effector. With this in mind, linear/nonlinear PID control schemes have been proposed to achieve accurate and robust tracking performance. Lyapunov's stability analysis is utilized to confirm the stability of the controlled system. It proves that the controlled system is stable, while the object’s orientation/position tracking errors are uniformly ultimately bounded (UUB) in any bounded region of state space. It also presents some conditions for proper selection of the linear/nonlinear PID controllers’ gains in the form of two theorems. The proposed controllers apply to two coordinated 3DOF robotic arms that carry a payload. The simulation results tested two types of trajectories, including simple and complex paths. The results are also compared to those of a strong state-of-the-art approximator, the Chebyshev Neural Network (CNN).

Keywords

Main Subjects


[1] Kallu, K. D. , Jie, W., and Lee, M. C., 2018, “Sensorless reaction force estimation of the end effector of a dual-arm robot manipulator using sliding mode control with a sliding perturbation observer”. International Journal of Control, Automation and Systems, 16(3), pp. 1367-1378.
[2] Kim, H. H., Lee, M. C., Kyung, J. H., and Do, H. M., 2021, “Evaluation of Force Estimation Method Based on Sliding Perturbation Observer for Dual-arm Robot System”. International Journal of Control, Automation and Systems, 19(1), pp. 1-10.
[3] Eid, J. J., and Oleynikov, D., 2021, “Cooperative and Miniature Robotics: Potential Applications in Surgery”. In Digital Surgery, pp. 269-273, Springer, Cham. https://doi.org/10.1007/978-3-030-49100-0_20
[4] Poudel, L., Zhou, W., and Sha, Z. 2021, “Resource-Constrained Scheduling for Multi-Robot Cooperative 3D Printing”. Journal of Mechanical Design, pp. 1-29. https://doi.org/10.1115/1.4050380
[5] Makris, S., 2021, Cooperative Manipulation-The Case of Dual Arm Robots”. In Cooperating Robots for Flexible Manufacturing, Springer, Cham, pp. 123-132. https://doi.org/10.1007/978-3-030-51591-1_5
[6] Azizzadeh, H., Menhaj, M.B., and Talebi, H.A., 2019, “Model-based force/position control of cooperative manipulation systems”. Automatica, 60 (1), pp. 113-123.
[7] Pizetta, I.H.B., Brandão, A.S., and Sarcinelli-Filho, M., 2019, ”Avoiding obstacles in cooperative load transportation”. ISA Transactions, 91, pp.  253-261.
[8] Chen, Y., and Lin, Y., 2020, “Combining model-based and model-free methods for stochastic control of distributed energy resources”. Appl. Energy. 283: 116204 (2020)
[9] Hu, B., Guan, Z.H., Lewis, F.L., and Chen, C.P., 2020, “Adaptive tracking control of cooperative robot manipulators with markovian switched couplings”. IEEE Transactions on Industrial  Electronics, 68(3), pp. 2427-2436.
[10] Khan, A.T., Li, S., and Cao, X., 2021, “Control framework for cooperative robots in smart home using bio-inspired neural network”. Measurement, 167, 108253.
[11] Wu, J., Jin, Z., Liu, A., and Yu, L., 2020, “Vision-based neural predictive tracking control for multi-manipulator systems with parametric uncertainty”. ISA Transactions, 110, pp. 247-257
[12] Farahmandrad, M., Ganjefar, S., Talebi, H.A., and Bayati, M., 2019, “Fuzzy sliding mode controller design for a cooperative robotic system with uncertainty for handling an object”. Journal of Dynamic Systems Measurements and Control, 141(6), pp. 1-8.
[13] Li, Y., Yang, C., Yan, W., Cui, R., and Annamalai, A., 2019, “Admittance-based adaptive cooperative control for multiple manipulators with output constraints”. IEEE Transactions on Neural Networks Learning Systems, 30(12), pp. 3621-3632
[14] Hwang, C. L., Abebe, H. B., Chen, B. S., and Wu, F., 2020, “Fuzzy adaptive finite-time cooperative control with input saturation for nonlinear multiagent systems and its application”. IEEE Access, 8, pp.105507-105520.
[15] Ngo, V. T., and Liu, Y. C., 2020, “Object transportation with force-sensorless control and event-triggered synchronization for networked uncertain manipulators”. IEEE Transactions on Industrial Electronics, 68(1), pp. 902-912.
[16] Zhang, L., Sun, Y., Barth, A., and Ma, O., 2020, “Decentralized control of multi-robot system in cooperative object transportation using deep reinforcement learning”. IEEE Access, 8, pp. 184109-184119.
[17] Izadbakhsh, A., Kalat, A. A. and Nikdel, N., 2022, “FAT-based robust adaptive controller ‎design for electrically direct driven robots ‎using Phillips q-Bernstein operators”. Robotica, 40(10), pp. 3415–3434
[18] Izadbakhsh, A., Zamani, I., and Khorashadizadeh, S., 2021, “Szász–Mirakyan‐based adaptive controller design for chaotic synchronization”. International Journal of Robust and Nonlinear Control, 31(5), pp.1689-1703, https://doi.org/10.1002/rnc.5380
[19] Nasiri, N., Fakharian A., and Menhaj M.B., 2020, “Observer-based robust control for flexible-joint robot manipulators: A state-dependent Riccati equation-based approach”. Transactions of the institute of measurement and control, 42(16), pp. 3135-3155.
[20] Nasiri, N., Fakharian, A., and Menhaj, M.B., 2021, “A novel controller for nonlinear uncertain systems using a combination of SDRE and function approximation technique: Regulation and tracking of flexible-joint manipulators”. Journal of the Franklin Institute, 358 (10), pp. 5185-5212.
[21] Nasiri, N., and Lademakhi, N. Y.,  2021, “Nonlinear combined SMC-SDRE control versus SMC and SDRE approaches for electrical flexible-joint robots based on optimal observer”. 9th RSI International Conference on Robotics and Mechatronics (ICRoM), pp. 568-573, doi: 10.1109/ICRoM54204.2021.9663514.
[22] Nasiri, N., Fakharian A., and Menhaj, M. B., 2022, “An Uncertain Optimal Factorization of Cooperative Manipulators for Robust Optimal Control Schemes”. 30th International Conference on Electrical Engineering (ICEE), pp. 582-586, doi: 10.1109/ICEE55646.2022.9827024.
[23] Azar, A.T., Serrano, F.E., Hameed, I.A., and Kamal, N.A., 2020, “Vaidyanathan, S., Robust H-Infinity Decentralized Control for Industrial Cooperative Robots”. In: Hassanien, A., Shaalan, K., Tolba, M. (eds) Proceedings of the International Conference on Advanced Intelligent Systems and Informatics 2019.. Advances in Intelligent Systems and Computing, 1058, Springer, Cham, https://doi.org/10.1007/978-3-030-31129-2_24
[24] Jose Guadalupe Romero, Emmanuel Nuño., and Carlos I. Aldana, 2021, “Robust PID consensus-based formation control of nonholonomic mobile robots affected by disturbances”. International Journal of Control, DOI: 10.1080/00207179.2021.2015541.
[25] Ammar, H.H., and Azar, A.T., 2019,” Robust Path Tracking of Mobile Robot Using Fractional Order PID Controller”. In: Hassanien, A., Azar, A., Gaber, T., Bhatnagar, R., F. Tolba, M. (eds) The International Conference on Advanced Machine Learning Technologies and Applications (AMLTA2019). Advances in Intelligent Systems and Computing, 921. Springer, Cham. https://doi.org/10.1007/978-3-030-14118-9_37
[26] Deylami A., and Izadbakhsh A., 2022, “FAT-based robust adaptive control of cooperative multiple manipulators without velocity measurement”. Robotica, 40 (6), pp.1732-1762, doi:10.1017/S0263574721001338.
[27] Izadbakhsh A, 2022, “An observer-based output tracking controller for electrically driven cooperative multiple manipulators with adaptive Bernstein-type approximator”. Robotica, 40(7), pp. 2295-2319.
[28] Izadbakhsh, A., and Khorashadizadeh, S., 2021, “Polynomial-Based Robust Adaptive Impedance Control of Electrically Driven Robots”. Robotica, 39(7), pp. 1181-1201.
[29] woon, L. C.,  Ge, S. S., Chen, X. Q., and Zhang, C., 1999, “Adaptive neural network control of coordinated manipulators”. Journal of Robotic Systems, 16(4), pp.195-211.
[30] Qu. Z, and Dawson. D. M, 1996, “Robust tracking control of robot manipulators”. IEEE Press, Inc., New York.
[32] Izadbakhsh, A., 2017, “A note on the "nonlinear control of electrical flexible-joint robots”. Nonlinear Dynamics, 89, pp. 2753-2767.
[33] Tang H., and Li, Y., 2015, “Feedforward nonlinear PID control of a novel micromanipulator using Preisach hysteresis compensator”. Robotics and Computer-Integrated Manufacturing, 34, pp. 124-132.
[34] Zhong, J., Fan, J., Zhu, Y., Zhao, J., and Zhai, W., 2014, “One nonlinear PID control to improve the control performance of a manipulator actuated by a pneumatic muscle actuator”. Advances in Mechanical Engineering, 6, pp. 1727-1782.
[35] Diep Cong Thanh TU., and Ahn, K. K., 2006, "Nonlinear PID control to improve the control performance of 2 axes pneumatic artificial muscle manipulator using neural network". Mechatronics, 16, pp. 577–587.
[36] Lee, J., Chang, P. H. , Yu B., and Jin, M., 2020, “An Adaptive PID Control for Robot Manipulators Under Substantial Payload Variations”. IEEE Access, 8, pp. 162261-162270.
[37] Maddi, A., Guessoum, A., and  Berkani D., 2014, “Design of Nonlinear PID Controllers Based on Hyper-Stability Criteria”. 15th international conference on science and techniques of automatic control and computer engineering, pp. 736-741.
[38]  Ghediri, A.,Lamamra, K.,  Ait Kaki, A., and Vaidyanathan, S., 2022, “Adaptive PID computed-torque control of robot manipulators based on DDPG reinforcement learning”. International Journal of Modelling, Identification and Control, 41(3), pp.173-182
[39] Perrusquia, A., Yu, W., and Soria, A., 2019, “Position/Force control of Robot Manipulators Using Reinforcement Learning”. Industrial Robot, 46 (2), pp. 267-280.
[40] Korayem, M. H., and Nekoo, S. R., 2018, “Controller design of Cooperative Manipulators using state-dependent Ricatti equation”. Robotica, 36(4), pp. 484-515.
[41] Kelly, R., Santibanez, V., and Loria, A., 2005, “Control of Robot Manipulators in Joint Space”. Springer-Verlag London Limited.
[42] Izadbakhsh, A., Nikdel, N., and Deylami, A., 2021, “Cooperative and robust object handling by multiple manipulators based on the differential equation approximator”. ISA Transaction, 128, Part B, pp. 68-80.
[43] Izadbakhsh, A., and Nikdel, N., 2022, “Robust adaptive control of cooperative multiple manipulators based on the Stancu-Chlodowsky universal approximator”. Communications in Nonlinear Science and Numerical Simulation, 111, 106471, https://doi.org/10.1016/j.cnsns.2022.106471
[44] Patra, J. C., and Kot, A. C., 2002, “Nonlinear dynamic system identification using chebyshev functional link artificial neural networks”. IEEE Transactions On Systems, man and Cybernetics, Part B, 32, pp. 505-511.
[45] Purwar, S., Kar, I. N., and Jha, A. N., 2008, “Adaptive output feedback tracking control of robot manipulators using position measurements only”. Expert systems with Applications, 34,pp. 2789-2798.