Abstract
In this paper, a new hybrid position/force control scheme is proposed for coordinated multiple mobile manipulators holding a rigid object. The problem of the controller design for multiple mobile manipulators is much complicated as compared to single mobile manipulator. Many of the position/force control schemes for coordinated multiple mobile manipulators assume exact knowledge of the dynamical model. But the dynamic model of the coordinated multiple mobile manipulators is highly uncertain and faces external disturbances, uncertain environment intervention, etc. Therefore, model-based controller is inadequate to deal with such uncertain systems. In the proposed scheme, the inefficiency of the model-based controller is recovered by combining with RBF neural network-based mode-free controller along with a compensation controller. RBF neural network is utilized to estimate the unmodeled dynamics of the system without requiring the offline learning. The compensation controller is utilized to neutralize the effects of the friction terms, external disturbances, and the network reconstruction error. The online adaptation of the weights and the parameter updates are utilized in the Lyapunov function to make the system to be stable. Furthermore, the proposed control scheme assures that both the position and the internal force trajectory errors converge asymptotically. To depict the adequacy of the proposed control scheme, simulation results are provided with different existing controllers in a comparative manner.
Similar content being viewed by others
Abbreviations
- h :
-
Number of mobile manipulators
- \(q_{bi}\in R^{p_{bi}}\) :
-
Generalized coordinate vector for mobile base
- \(q_{mi}\in R^{p_{mi}}\) :
-
Generalized coordinate vector for mobile arm
- \(\lambda _{i}\in R^{p}\) :
-
Lagrangian multiplier associated with the mobile base and the manipulator’s arm
- \(\tau _i \in R^{t}\) :
-
Torque input vector for ith manipulator
- \(\mu _{i}\) :
-
Joint position vector for the ith manipulator
- \(f_i\in R^{p}\) :
-
Interacting force between the end-effector of the ith manipulator and the object
- \({\varTheta _i}(q_{bi})\in R^{p_{bi}\times (p_{bi}-k)}\) :
-
A smooth and linearly independent set of vector fields
- \(y_{o}\) :
-
Coordinate vector of the object frame
- \(p_{o}\) :
-
Dimension of the operational coordinate of the object
- \(F_{1}\in R^{p_o}\) :
-
Resultant force vector acting at the center of mass of the object
- \(F_{I}\in R^{h(p-k)}\) :
-
Internal force vector
- \(J_o(y_o)\in R^{h(p-k)\times {p_o}}\) :
-
Jacobian matrix from the object’s frame to the manipulator’s end-effector frame
- \(y_{ei}\in R^{p-k}\) :
-
Position and the orientation vector of the ith manipulator
- \(s_i>0\) \((1\leqslant {i}\leqslant 3)\) :
-
Finite constants
- \(K_{o}\), \(K_{f}\), \(K_{d}\) :
-
Positive definite gain matrices
- \(y \in R^{5l}\) :
-
Input vector
- N :
-
Number of nodes of the neural network
- \(\varepsilon _N\) :
-
An arbitrary small positive constant
- \(\varepsilon (y)\) :
-
Neural network reconstruction error
- \(\varPsi (y)\) :
-
Gaussian activation function
- \(\gamma , \delta \) :
-
Positive constants
- \(\varphi \in R^{s}\) :
-
Parameter vector
- \(\varGamma _\varPi \), \(\varGamma _\varphi \) :
-
Positive definite symmetric matrices
- \(L ^2\) :
-
Performance index
References
Yamamoto, Y.; Yun, X.: Coordinating locomotion and manipulation of a mobile manipulator. In: General Robotics and Active Sensory Perception (GRASP) Laboratory, pp. 1–13. (1992)
Yamamoto, Y.; Yun, X.: Unified analysis on mobility and manipulability of mobile manipulators. In: Proceedings of the International Conference on Robotics and Automation, pp. 1200–1206 (1999)
Hirata, Y.; Kume, Y.; Sawada, T.; Wang, Z.; Kosuge, K.: Handling of an object by multiple mobile manipulators in coordination based on caster-like dynamics. In: Proceedings of the 2004 IEEE International Conference on Robotics and Automation, pp. 807–812. (2004)
Tanner, H.G.; Loizou, S.G.; Kyrakopoulos, K.J.: Nonholonomic navigation and control of cooperating mobile manipulators. IEEE Trans. Robot. Autom. 19(1), 53–64 (2003)
Yamamoto, Y.; Fukuda, S.: Trajectory planning of multiple mobile manipulators with collision avoidance capability. In: Proceedings of IEEE International Conference on Robotics and Automation, pp. 3565–3570. (2002)
Sugar, T.G.; Kumar, V.: Control of cooperating mobile manipulators. IEEE Trans. Robot. Autom. 18(1), 94–103 (2002)
Mohajerpoor, R.; Rezaei, M.; Talebi, A.; Noorhosseini, M.; Monfaredi, R.: A robust adaptive hybrid force/position control scheme of two planar manipulators handling an unknown object interacting with an environment. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 226(4), 509–522 (2012)
Gueaieba, W.; Al-Sharhanb, S.; Bolica, M.: Robust computationally efficient control of cooperative closed-chain manipulators with uncertain dynamics. Automatica 43, 842–851 (2007)
Namvar, M.; Aghili, F.: Adaptive force-motion control of coordinated robots interacting with geometrically unknown environments. IEEE Trans. Robot. 21(4), 678–694 (2005)
Tavasoli, A.; Eghtesad, M.; Jafarian, H.: Two-time scale control and observer design for trajectory tracking of two cooperating robot manipulators moving a flexible beam. Robot. Auton. Syst. 57, 212–221 (2009)
Li, Z.; Sam, G.S.; Wang, Z.: Robust adaptive control of coordinated multiple mobile manipulators. Mechatronics 18, 239–250 (2008)
Fang, M.; Chen, W.; Li, Z.: Adaptive tracking control of coordinated nonholonomic mobile manipulators. In: Proceedings of the 17th World Congress the International Federation Automatic Control Seou, pp. 4343–4348. (2008)
Qian, S.; Zi, B.; Ding, H.: Dynamics and trajectory tracking control of cooperative multiple mobile cranes. Nonlinear Dyn 83, 89–108 (2016)
Yi, R.; Chen, Z.; Liu, Y.; Gu, Y.; Jin, M.; Liu, H.: Adaptive hybrid position/force control of dual-arm cooperative manipulators with uncertain dynamics and closed-chain kinematics. J. Frankl. Inst. 354, 7767–7793 (2017)
Huang, D.; Zhai, J.; Ai, W.; Fei, S.: Inertial space tracking for free-floating space robot manipulator using RBFNN based compensating control algorithm. Neurocomputing 89, 198–208 (2016)
Li, Z.; Sam, G.S.; Adams, M.; Wijesoma, W.S.: Robust adaptive control of cooperating mobile manipulators with relative motion. In: 22nd IEEE International Symposium on Intelligent Control Part of IEEE Multi-conference on Systems and Control Singapore, pp. 351–356. (2007)
Jafari, A.; Ryun, J.H.: Independent force and position control for cooperating manipulators handling an unknown object and interacting with an unknown environment. J. Frankl. Inst. 353, 857–875 (2016)
Gierlak, P.; Szuster, M.: Adaptive position/force control for robot manipulator in contact with a flexible environment. Robot. Auton. Syst. 95, 80–101 (2017)
Ge, S.S.; Huang, L.; Lee, T.H.: Model-based and neural-network-based adaptive control of two robotic arms manipulating an object with relative motion. Int. J. Syst. Sci. 32(1), 9–23 (2001)
Li, Z.; Chen, W.: Adaptive neural-fuzzy control of uncertain constrained multiple coordinated nonholonomic mobile manipulators. Eng. Appl. Artif. Intell. 21, 985–1000 (2008)
Zhao, D.; Ni, W.; Zhu, Q.: A framework of neural networks based on consensus control for multiple robotic manipulators. Neurocomputing 140, 8–18 (2014)
Kumar, N.; Panwar, V.; Sukavanam, N.: Neural network control of coordinated multiple manipulator systems. In: Proceedings of the International Conference on Computing: Theory and Applications (ICCTA’07) (2007)
Panwar, V.; Kumar, N.; Sukavanam, N.; Borm, J.H.: Adaptive neural controller for cooperative multiple robot manipulator system manipulating a single rigid object. Appl. Soft Comput. 12, 216–227 (2012)
Singh, H.P.; Sukavanam, N.: Intelligent robust adaptive trajectory and force tracking controller for holonomic constrained nonholonomic mobile manipulators. Adv. Sci. Lett. 16, 313–321 (2012)
Baigzadehnoe, B.; Rahmani, Z.; Khosravi, A.; Rezaie, B.: On position/force tracking control problem of cooperative robot manipulators using adaptive fuzzy backstepping approach. ISA Trans. 70, 432–446 (2017)
Li, Z.; Yang, C.; Tang, Y.: Decentralized adaptive fuzzy control of coordinated multiple mobile manipulators interacting with non-rigid environments. IET Control Theory Appl. 7(3), 397–410 (2012)
Li, Z.; Deng, S.; Su, C.Y.; Li, G.; Yu, Z.; Liu, Y.; Wang, M.: Decentralised adaptive control of cooperating Robotic manipulators with disturbance observers. IET Control Theory Appl. 8(7), 515–521 (2013)
Rao, D.C.; Kabat, M.R.; Das, P.K.; Jena, P.K.: Cooperative navigation planning of multiple mobile robots using improved Krill Herd. Arab. J. Sci. Eng. (2018). https://doi.org/10.1007/s13369-018-3216-0
Li, Z.; Yang, C.; Su, C.Y.; Deng, S.; Sun, F.; Zhang, W.: Decentralized fuzzy control of multiple cooperating robotic manipulators with impedance interaction. IEEE Trans. Fuzzy Syst. 23(4), 1044–1055 (2015)
Rani, M.; Kumar, N.; Singh, H.P.: Efficient position/force control of constrained mobile manipulators. Int. J. Dyn. Control (2018). https://doi.org/10.1007/s40435-018-0401-7
Park, J.; Sandberg, J.W.: Universal approximation using radial basis function networks. Neural Comput. 3, 246–257 (1991)
Slotine, J.J.E.; Li, W.: Applied Nonlinear Control. Prentice-Hall, New Jersey (1991)
Acknowledgements
We are grateful to University Grants Commission (UGC) Sr. No. 2121240927 with Ref No. 23/12/2012 (ii) EU-V, New Delhi, India for their financially support.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rani, M., Kumar, N. A New Hybrid Position/Force Control Scheme for Coordinated Multiple Mobile Manipulators. Arab J Sci Eng 44, 2399–2411 (2019). https://doi.org/10.1007/s13369-018-3544-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13369-018-3544-0