Abstract
This chapter considers cooperative kinematic control of multiple robot arms with a full distributed control topology by using distributed recurrent neural networks. The problem is formulated as a constrained game, where energy consumptions for each robot arm, saturations of control input, and the topological constraints imposed by the communication graph are taken into account. An implicit form of the Nash equilibrium for the game is obtained by converting the problem into its dual space. Then, a distributed dynamic controller based on recurrent neural networks is devised to drive the system towards the desired Nash equilibrium to seek the optimal solution of the cooperative control. Global stability and solution optimality of the neural networks are proved in theory. Simulations demonstrate the effectiveness of the method presented in this chapter.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Liu G, Xu J, Wang X, Li Z (2004) On quality functions for grasp synthesis, fixture planning, and coordinated manipulation. IEEE Trans Autom Sci Eng 1(2):146–162
Wu L, Cui K, Chen S (2000) Redundancy coordination of multiple robotic devices for welding through genetic algorithm. Robotica 18(6):669–676
Jin L, Li S, Xiao L, Liao B (2017) Cooperative motion generation in a distributed network of redundant robot manipulators with noises. IEEE Trans Syst Man Cybern: Syst. https://doi.org/10.1109/TSMC.2017.2693400
Jin L, Li S (2017) Distributed task allocation of multiple robots: A control perspective. IEEE Trans Syst Man Cybern: Syst. https://doi.org/10.1109/TSMC.2016.2627579
Fraile J, Paredis C, Wang C, Khosla P (1999) Agent-based planning and control of a multi-manipulator assembly system. In: Proceedings of IEEE International conference on robotics and automation, pp 1219–1225
Montemayor G, Wen J (2005) Decentralized collaborative load transport by multiple robots. In: Proceedings of IEEE International conference on robotics and automation, pp 372–377
Wang Z, Zhou T, Mao Y, Chen Q (2014) Adaptive recurrent neural network control of uncertain constrained nonholonomic mobile manipulators. Int J Syst Sci 45(2):133–144
Zhang Y, Ge SS, Lee HT (2004) A unified quadratic-programming-based dynamical system approach to joint torque optimization of physically constrained redundant manipulators. IEEE Trans Syst Man Cybern Part B: Cybern 34(5):2126–2132
Xiao L, Zhang Y (2014) A new performance index for the repetitive motion of mobile manipulators. IEEE Trans Cybern 44(2):280–292
Zhang Y, Wang J, Xia Y (2003) A dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limits. IEEE Trans Neural Netw 14(3):658–667
Zhang Z, Zhang Y (2013) Variable joint-velocity limits of redundant robot manipulators handled by quadratic programming. IEEE/ASME Trans Mechatron 18(2):674–686
Ding H, Wang J (1999) Recurrent neural networks for minimum infinity-norm kinematic control of redundant manipulators. IEEE Trans Syst Man Cybern Part A: Syst Hum 29(3):269–276
Tang W, Wang J (2001) A recurrent neural network for minimum infinity-norm kinematic control of redundant manipulators with an improved problem formulation and reduced architecture complexity. IEEE Trans Syst Man Cybern Part B: Cybern 31(1):98–105
Xia Y, Feng G, Wang J (2005) A primal-dual neural network for online resolving constrained kinematic redundancy in robot motion control. IEEE Trans Syst Man Cybern Part B: Cybern 35(1):54–64
Cai B, Zhang Y (2012) Different-level redundancy-resolution and its equivalent relationship analysis for robot manipulators using gradient-descent and Zhang’s neural-dynamic methods. IEEE Trans Ind Electron 59(8):3146–3155
Mohammed A, Li S (2015) Dynamic neural networks for kinematic redundancy resolution of parallel stewart platforms. IEEE Trans Cybern 17(3):1400–1410
Guo D, Zhang Y (2014) Acceleration-level inequality-based MAN scheme for obstacle avoidance of redundant robot manipulators. IEEE Trans Ind Electron 61(12):6903–6914
Wen U, Lan K, Shih H (2009) A review of Hopfield neural networks for solving mathematical programming problems. Eur J Oper Res 198(3):675–687
Xia Y, Wang J (2005) A recurrent neural network for solving nonlinear convex programs subject to linear constraints. IEEE Trans Neural Netw 16(2):379–386
Xiao L (2015) A finite-time convergent neural dynamics for online solution of time-varying linear complex matrix equation. Neurocomputing 167:254–259
Xiao L, Lu R (2015) Finite-time solution to nonlinear equation using recurrent neural dynamics with a specially-constructed activation function. Neurocomputing 151:246–251
Liu Q, Wang J (2011) A one-layer recurrent neural network for constrained nonsmooth optimization. IEEE Trans Syst Man Cybern Part B: Cybern 41(5):1323–1333
Zhang H, Wang Z, Liu D (2014) A comprehensive review of stability analysis of continuous-time recurrent neural networks. IEEE Trans Neural Netw Learn Syst 25(7):1229–1262
Hu X, Wang J (2008) An improved dual neural network for solving a class of quadratic programming problems and its-winners-take-all application. IEEE Trans Neural Netw 19(12):2022–2031
Hu X, Zhang B (2009) A new recurrent neural network for solving convex quadratic programming problems with an application to the-winners-take-all problem. IEEE Trans Neural Netw 20(4):654–664
Li S, Li Y, Wang Z (2013) A class of finite-time dual neural networks for solving quadratic programming problems and its \(k\)-winners-take-all application. Neural Netw 39:27–39
Liu S, Wang J (2006) A simplified dual neural network for quadratic programming with its \(k\)-WTA application. IEEE Trans Neural Netw 17(6):1500–1510
Yan Z, Wang J (2012) Model predictive control of nonlinear systems with unmodeled dynamics based on feedforward and recurrent neural networks. IEEE Trans Ind Inform 8(4):746–756
Jin L, Zhang Y, Li S, Zhang Y (2016) Modified ZNN for time-varying quadratic programming with inherent tolerance to noises and its application to kinematic redundancy resolution of robot manipulators. IEEE Trans Ind Electron 63(11):6978–6988
Jin L, Zhang Y (2014) G2-Type SRMPC scheme for synchronous manipulation of two redundant robot arms. IEEE Trans Cybern 45(2):153–164
Jin L, Zhang Y (2014) Discrete-time Zhang neural network for online time-varying nonlinear optimization with application to manipulator motion generation. IEEE Trans Neural Netw Learn Syst 26(7):1525–1531
Jin L, Li S (2017) Nonconvex function activated zeroing neural network models for dynamic quadratic programming subject to equality and inequality constraints. https://doi.org/10.1016/j.neucom.2017.05.017
Jin L, Li S, La HM, Luo X (2017) Manipulability optimization of redundant manipulators using dynamic neural networks 64(6):4710–4720
Jin L, Zhang Y (2015) G2-type SRMPC scheme for synchronous manipulation of two redundant robot arms. IEEE Trans Cybern 45(2):153–164
Li S, Chen S, Liu B, Li Y, Liang Y (2012) Decentralized kinematic control of a class of collaborative redundant manipulators via recurrent neural networks. Neurocomputing 91(15):1–9
Li S, Cui H, Li Y, Liu B, Lou Y (2012) Decentralized control of collaborative redundant manipulators with partial command coverage via locally connected recurrent neural networks. Neural Comput Appl 23(3):1051–1060
Li S, He J, Rafique U, Li Y (2016) Distributed recurrent neural networks for cooperative control of manipulators: a game-theoretic perspective. IEEE Trans Neural Netw Learn Syst 28(2):415–426
Li S, Zhou M, Luo X, You Z (2017) Distributed winner-take-all in dynamic networks. IEEE Trans Autom Control 62(2):577–589
Li S, Zhang Y, Jin L (2016) Kinematic control of redundant manipulators using neural networks. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2016.2574363
Jin L, Zhang Y, Li S, Zhang Y (2017) Noise-tolerant ZNN models for solving time-varying zero-finding problems: a control-theoretic approach. IEEE Trans Autom Control 62(2):992–997
Jin L, Zhang Y, Li S (2016) Integration-enhanced Zhang neural network for real-time varying matrix inversion in the presence of various kinds of noises. IEEE Trans Neural Netw Learn Syst 27(12):2615–2627
Mao M, Li J, Jin L, Li S, Zhang Y (2016) Enhanced discrete-time Zhang neural network for time-variant matrix inversion in the presence of bias noises. Neurocomputing 207:220–230
Khan M, Lin S, Wang Q, Shao Z (2016) Distributed multi-robot formation and tracking control in cluttered environment. ACM Trans Auton Adapt Syst 11(2):12
Wang H, Liu X, Liu P, Li S (2016) Robust adaptive fuzzy fault-tolerant control for a class of non-lower-triangular nonlinear systems with actuator failures. Inf Sci 336:60–74
Khan M, Li S, Wang Q, Shao Z (2016) CPS oriented control design for networked surveillance robots with multiple physical constraints. IEEE Trans Comput-Aided Design Integr Circuits Syst 35(5):778–791
Khan M, Li S, Wang Q, Shao Z (2016) Formation control and tracking for co-operative robots with non-holonomic constraints. J Intell Robot Syst 82(1):163–174
Wang H, Yang H, Liu X, Liu L, Li S (2016) Direct adaptive neural control of nonlinear strict-feedback systems with un-modeled dynamics using small-gain approach. Int J Adapt Control Signal Process 30(6):906–927
Li S, You Z, Guo H, Luo X, Zhao Z (2015) Inverse-free extreme learning machine with optimal information updating. IEEE Trans Cybern 46(5):1229–1241
Wang Z, Liu X, Liu K, Li S, Wang H (2016) Backstepping-based lyapunov function construction using approximate dynamic programming and sum of square techniques. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2016.2574747
Muhammad A, Li S (2016) Dynamic neural networks for kinematic redundancy resolution of parallel stewart platforms. IEEE Trans Cybern 46(7):1538–1550
Li S, Kong R, Guo Y (2014) Cooperative distributed source seeking by multiple robots: algorithms and experiments. IEEE/ASME Trans Mechatron 19(6):1810–1820
Li S, Guo Y (2014) Distributed consensus filtering on directed switching graphs. Int J Robust Nonlinear Control 25:2019–2040
Li S, Lou Y, Liu B (2014) Bluetooth aided mobile phone localization: a nonlinear neural circuit approach. ACM Trans Embedded Comput Syst 13(4):78
Li S, Li Y (2013) Nonlinearly activated neural network for solving time-varying complex Sylvester equation. IEEE Trans Cybern 44(8):1397–1407
Li S, Liu B, Li Y (2013) Selective positive-negative feedback produces the winner-take-all competition in recurrent neural networks. IEEE Trans Neural Netw Learn Syst 24(2):301–309
Li S, Li Y, Wang Z (2013) A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application. Neural Netw 39:27–39
Li S, Guo Y (2013) Dynamic consensus estimation of weighted average on directed graphs. Int J Syst Sci 46(10):1839–1853
Li S, Qin F (2013) A dynamic neural network approach for solving nonlinear inequalities defined on a graph and its application to distributed, routing-free, range-free localization of WSNs. Neurocomputing 117:72–80
Li S, Guo Y, Fang J, Li H (2013) Average consensus with weighting matrix design for quantized communication on directed switching graphs. Int J Adapt Control Signal Process 27:519–540
Li S, Li Y, Liu B (2012) Model-free control of Lorenz chaos using an approximate optimal control strategy. Commun Nonlinear Sci Numer Simul 17:4891–4900
Li S, Wang Y, Yu J, Liu B (2013) A nonlinear model to generate the winner-take-all competition. Commun Nonlinear Sci Numer Simul 18:435–442
Li S, Wang Z, Li Y (2013) Using Laplacian eigenmap as heuristic information to solve nonlinear constraints defined on a graph and its application in distributed range-free localization of wireless sensor networks. Neural Process Lett 37:411–424
Li S, Chen S, Liu B (2013) Accelerating a recurrent neural network to finite-time convergence for solving time-varying Sylvester equation by using a sign-bi-power activation function. Neural Process Lett 37:189–205
Li S, Yu J, Pan M, Chen S (2012) Winner-take-all based on discrete-time dynamic feedback. Appl Math Comput 219:1569–1575
Li Y, Li S (2013) A biologically inspired solution to simultaneous localization and consistent mapping in dynamic environments. Neurocomputing 104:170–179
Chen S, Li S, Liu B, Lou Y, Liang Y (2012) Self-learning variable structure control for a class of sensor-actuator systems. Sensors 12:6117–6128
Armstrong B, Khatib O, Burdick J (1986) The explicit dynamic model and inertial parameters of the PUMA 560 arm. In: Proceedings of IEEE International conference on robotics and automation, pp 510–518
Spong M, Hutchinson S, Vidyasagar M (2006) Robot modeling and control. Wiley, New York
Szabó G, Fáth G (2007) Evolutionary games on graphs. Phys Rep 446(5):97–216
Basar T, Olsder G (1999) Dynamic noncooperative game theory. Academic Press
Mohar B (1991) Graph theory. Wiley, Combinatorics and Applications
Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press
Raafat R, Chater N, Frith C (2009) Herding in humans. Trends Cognit Sci 13(10):420–428
Toner J, Tu Y (1998) Flocks, herds, and schools: a quantitative theory of flocking. Phys Rev E 58(4):4828
Karsenti E (2008) Self-organization in cell biology: A brief history. Nat Rev Mol Cell Biol 9(3):255–262
Slotine J, Li W (1991) Applied nonlinear control. Prentice Hall
Dattorro J (2006) Convex optimization and Euclidean distance geometry. Meboo Publishing
Mastroeni G (2005) Gap functions and descent methods for minty variational inequality. Springer, Optimization and Control with Applications
Marescaux J, Leroy J, Rubino F, Smith M, Vix M, Simone M, Mutter D (2002) Transcontinental robot-assisted remote telesurgery: feasibility and potential applications. Ann Surg 235(4):487–493
Kypson A, Nifong L, Chitwood W (2003) Robotic cardiac surgery. J Long Term Effects Med Implants 13(6):451–464
Aiyama Y, Hara M, Yabuki T, Ota J, Arai T (1999) Cooperative transportation by two four-legged robots with implicit communication. Robot Auton Syst 29(1):13–19
Welch J, Backer D (2009) The Allen Telescope array: the first Widefield, panchromatic, snapshot radio camera for radio astronomy and SETI. Proc IEEE 97(8):1438–1447
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 The Author(s)
About this chapter
Cite this chapter
Li, S., Zhang, Y. (2018). Neural Networks for Robot Arm Cooperation with a Full Distributed Control Topology. In: Neural Networks for Cooperative Control of Multiple Robot Arms. SpringerBriefs in Applied Sciences and Technology(). Springer, Singapore. https://doi.org/10.1007/978-981-10-7037-2_4
Download citation
DOI: https://doi.org/10.1007/978-981-10-7037-2_4
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-7036-5
Online ISBN: 978-981-10-7037-2
eBook Packages: EngineeringEngineering (R0)