Nonlinear Control and Synchronization with Time Delays of Multiagent Robotic Systems

Hindawi Publishing Corporation Journal of Control Science and Engineering Volume 2011, Article ID 632374, 9 pages doi:10.1155/2011/632374 Research Article Nonlinear Control and Synchronization with Time Delays of Multiagent Robotic Systems Yassine Bouteraa,1, 2 Jawhar Ghommam,1 Nabil Derbel,1 and Gérard Poisson2 1 Research Unit on Intelligent Control, Design and Optimization of Complex Systems, National Engineering School of Sfax, University of Sfax, BP W, Sfax 3038, Tunisia 2 Laboratoire Prisme - Pôle IRAuS, Université d’ Orléans, 63 avenue de Lattre de Tassigny 18020 Bourges Cedex, France Correspondence should be addressed to Yassine Bouteraa, Received 3 January 2011; Accepted 20 April 2011 Academic Editor: Weizhou Su Copyright © 2011 Yassine Bouteraa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We investigate the cooperative control and global asymptotic synchronization Lagrangian system groups, such as industrial robots. The proposed control approach works to accomplish multirobot systems synchronization under an undirected connected communication topology. The control strategy is to synchronize each robot in position and velocity to others robots in the network with respect to the common desired trajectory. The cooperative robot network only requires local neighbor-to-neighbor information exchange between manipulators and does not assume the existence of an explicit leader in the team. It is assumed that network robots have the same number of joints and equivalent joint work spaces. A combination of the lyapunov-based technique and the cross-coupling method has been used to establish the multirobot system asymptotic stability. The developed control combines trajectory tracking and coordination algorithms. To address the time-delay problem in the cooperative network communication, the suggested synchronization control law is shown to synchronize multiple robots as well as to track given trajectory, taking into account the presence of the time delay. To this end, Krasovskii functional method has been used to deal with the delay-dependent stability problem. 1. Introduction Nowadays, much research has been focusing on group coordination, cooperative control, and synchronization problems. In fact, motivated by the profit acquired by using multiple inexpensive systems working together to achieve complex tasks exceeding the abilities of a single agent, cooperative synchronization control has received significant attention. Distributed coordination and decentralized synchronization of multiagent systems have recently been studies extensively in the context of cooperative control [1–5], to name a few. In particular, design based on graph theory and Laplacian matrix produce interesting results [6–9]. Agreement, consensus problems in the area of cooperative control of multiagent systems have been studied in [7, 8, 10–12]. The coordination control strategies are closely related to the synchronization problem in which control laws are coupled and each agent robot control is updated using local rule based on its own sensors and the states of its neighbors. In this context, one recent representative work [13] shows that we can synchronize the multicomposed system in the case of partial knowledge, that is, only position measuring. A decentralized tracking control law globally exponentially synchronizes an arbitrary number of robots and represents a generalization of the average consensus problem. This has been presented in [5]. A synchronization approach to trajectory tracking of multiple mobile robots while maintaining time-varying formations has been presented in [14]. Adaptive control strategy to position synchronization of multiple motion axes using cross-coupling technology has been developed in [15]. In many engineering applications, communication delays between subsystems cannot be neglected. Therefore, the problem of time-delayed communication in control of multirobot systems is important in numerous practical applications. Indeed, without control measures of time delays in cooperative task may even cause instability. The 2 Journal of Control Science and Engineering problem of time-delayed communication in control of multiagent systems has been studied in several references [7, 16– 18]. The consideration of time-delayed communication in control of multirobot systems is a mainly practical necessity. In particular, this need occurs when addressing areas which require real-time applications such as operations in unsafe environments and robotic surgery. The objective of this paper is to design a control approach that can achieve both synchronization of the robot movements and asymptotic stable tracking of a common desired trajectory. The proposed controller relies principally on a consensus algorithm for systems modeled by nonlinear second-order dynamics and applies the algorithm to the synchronization control problem by choosing appropriately information states on which consensus is reached. The concept key of the new synchronizing controller is the introduction of a state vector that quantifies the coordination degree between a robot manipulator positions and different positions of its neighbors. In the literature, most of earlier works on multiagent coordination and consensus [3, 4, 7, 19] mainly deal with very simple dynamic models such as linear systems and focuses on an algorithm taking the form of first-order dynamics [11, 20, 21]. In particular, most previous works on consensus and coordination of multiagent systems using the graph theory and laplacian [3, 4, 7–9] have presented a synchronization to the weighted average of initial conditions but they do not consider multiagent systems where there is a desired path to follow. Therefore, the aforementioned algorithms cannot give solutions for robot networks, where a desired trajectory is required. In contrast, the present work deals with highly nonlinear systems. Moreover, the developed approach achieves not only global asymptotic synchronization of the configuration variables, but also global asymptotic convergence to the desired trajectory. Notable works have focused on highly nonlinear systems. Their developed strategy requires the coupling feedback of the most adjacent robots [5] or axis [15] for the algorithm. However, the proposed strategy is based in partial mesh topology in which there are interconnections between all robots, such that all robots have direct influence in the combined dynamics. We provide by the use of partial mesh topology a high degree of reliability due to the presence of multiple paths for data between robots. On the other hand, it is not a fully connected mesh topology and consequently we avoid the expense and the complexity required for a connection between every robot in the network. In this paper, we (...truncated)