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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.

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 [

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 [

The

Since we based on our coordination algorithm conception on consensus strategy and concepts of graph theory, we present several basic properties of these technology. Let

The graph laplacian of

Undirected graph topology structure.

In this paper, we consider the synchronization of multiple robots following a common time-varying trajectory. We will design decentralized control laws for

The objective of this paper is to design individual tracking controller for

Substituting (

The synchronized error dynamics (

Referring to the expression of the global error (

Referring to (

In this section, we study the coordination control problem taking into account time delays of communication channels. As a first assumption, we suppose that these delays can be justified by the fact that data information sent by the neighboring vehicles

Substituting (

To analyze the stability of the global system, we consider the following Lyapunov-Krasovskii functional (LKF):

This results in

The proof pursued the same line reasoning as the proof of Section 3.3. Consequently, we obtain the following equation derived from the global error expression:

To show the effectiveness of the proposed synchronizing controller we provide some simulation results. These simulations were proposed for a network of 3 identical robot manipulators interconnected under a cooperative scheme as shown in Figure

Robot network using bidirectional communication.

Let the communication structure among the robots described by an undirected strongly connected graph topology as shown in Figure

Control gains.

Control Gains and JIC | Robot 1 | Robot 2 | Robot 3 |
---|---|---|---|

(2.5, 2.5) | (−2, −2) | (1.5, 1.5) |

The topology model of the robots in simulation.

Robots synchronization and trajectory tracking.

Figures

Position errors.

Synchronization errors.

Robots synchronization without communication delay.

Robots synchronization in presence of time delay (0.5 s).

Robots synchronization in presence of time delay (1 s).

Robots synchronization without time delay.

Robots synchronization in presence of time delay.

This paper has considered the synchronization problem in distributed multi-Lagrangian systems. The aim of this work was to find out a decentralized controller, which individually applied to each lagrangian system, the synchronization in position and velocity is therefore met. Reaching synchronization stability of highly nonlinear robot dynamics constitutes one of the main contributions of this paper. The proposed control law ensures the robots’ states synchronization while tracking a common desired trajectory. Another aspect of robots coordination and trajectory tracking control was investigated. In the coordination strategy there are practically interconnections between all the systems, such that all systems have influence on the overall dynamics. The proposed algorithm works under cooperative scheme in the sense that it does not require any explicit leaders in the team. The studied topology is connected under an undirected interaction graph. To deal with time-delay problem in communication between robots, the proposed decentralized control guarantees that the information variables of each robot reach agreement even in the presence of communication delay. Illustrative examples have shown the effectiveness of the described strategy. Future work will address the coordination control of under actuated lagrangian systems.