Nonlinear H control for synchronization of networked manipulators subject to delayed communication

https://doi.org/10.1016/j.jfranklin.2021.11.025Get rights and content

Abstract

In this paper, a distributed synchronization control scheme is proposed for a group of robotic manipulators with non-identical dynamics and model uncertainties subject to time-varying communication delays. By using the nonlinear H control strategy, a dynamic distributed control law is developed to achieve synchronous tracking of networked robots in the joint space. Solving differential inequalities for obtaining controller parameters is a complicated task that is encountered in the nonlinear H control framework, and the main feature of the suggested approach is that the parameters of the controller are found by checking the feasibility of a set of matrix inequalities. The proposed control method is implemented via simulation and its applicability is verified by illustrative results.

Introduction

In the field of robotics and automation, synchronous cooperation of multiple robotic manipulators plays substantial role in accomplishing intricate missions. Synchronization deals with the problem of reaching agreement in a group of agents in some sense [1], [2], [3], [4]. Distributed feedback is an effective networked structure for developing synchronization control, in which team members use the information of their neighbors besides local data to compute the control law [5,6].

There are various studies in the literature addressing the synchronization problem for networked robots. In [7], movement synchronization and trajectory tracking based on an integral sliding-mode control (SMC) was studied for dual arm robotic manipulators. By using the Udwadia–Kalaba approach, the synchronization problem of networked multi-mobile robot systems for the leaderless and the leader-following cases was addressed in [8]. A distributed consensus tracking control for networked nonholonomic wheeled mobile robots was proposed in [9], where a novel unified SMC strategy was used in the presence of input disturbances. Neural network and fuzzy logic-based approaches were also used for synchronization of multiple robots [10,11]. Model uncertainty is an issue that could destructively affect the synchronization task in multi-robot systems and could be addressed using adaptive and robust control techniques. Using the passivity-based control scheme, an adaptive control law was suggested in [12] to achieve synchronization and trajectory tracking for connected robotic manipulators with dynamical uncertainties. Under the leader-follower framework, an adaptive two-layer distributed control scheme was proposed in [13] to synchronize multiple robotic manipulators in the presence of uncertain dynamics. In [14], a cooperative adaptive consensus tracking strategy was proposed for a network of multiple nonholonomic mobile robots by combining a Lyapunov-like analysis with the backstepping and sliding mode approaches. Nonlinear H control was used in [15] to design a distributed synchronization controller for a network of Euler-Lagrange systems, which was based on solving a number of Riccati equations. Based on the nonlinear H control strategy, a simply solvable procedure was developed in [16] to design a static distributed feedback control law for synchronizing a group of robotic manipulators with uncertain dynamics.

Using communication network to transmit data between agents leads to significant advantages such as simple and inexpensive installation and maintenance; however, brings some challenges such as transmission delays to the analysis and design of control system. In [17], a synchronization scheme based on the small-gain strategy was introduced to achieve the synchronous steering of interconnected second order nonlinear systems to a common position. By using the Lyapunov direct method, delay-independent synchronization of networked manipulators for joint space and task space was studied in [12]. In a wireless network environment subject to bounded network-induced delays, a novel network control system (NCS) for the continuous-time Direct-Drive-Wheel (DDW) system via proportional–integral (PI) was established in [18]. In this work, some delay-range-dependent conditions for exponential mean-square stability of NCS with the prescribed H performance were derived based on a new discontinuous Lyapunov–Krasovskii functional. The Synchronization problem of networked heterogeneous robots with kinematic and dynamic uncertainties subject to uniform communication delays was addressed in [19]. In this research work, two classes of adaptive sliding-mode controllers were suggested to solve the synchronization problem of proposed multi-robot system under the directed graph topology with a directed spanning tree. The problem of position synchronization in the presence of time-varying delay and parametric uncertainty for a class of electromechanical systems represented by Euler–Lagrange equations was addressed in [20], where an adaptive control mechanism was proposed to ensures the position synchronization and desired trajectory tracking. By utilizing a decoupling method, a distributed H synchronization control law was presented in [21] for uncertain linear systems with communication delays. In [22], a synchronization strategy based on H control was suggested for motion synchronization in the formation of networked unmanned aircrafts with communication delays.

In this paper, the synchronous trajectory tracking problem of robotic manipulators in joint space is investigated by considering the effects of model uncertainties. Non-identical robotic systems communicate over a balanced and strongly connected communication topology that is subject to time-varying transmission delays. Inspired by diffusive couplings idea from [23], and standard H control framework for nonlinear systems [24,25], a robust dynamic controller is designed in distributed manner to achieve synchronization between robotic manipulators.

The contributions of the proposed method are as follows. First, dynamic controller is used to achieve a high-quality synchronization, especially in transient phase. Second, a suitable Lyapunov-Krasovskii functional is employed to extract the synthesis conditions for distributed dynamic controller, which compensates the effect of data transmission delay in the synchronization problem. Third, the controller parameters are found via solving a set of matrix inequalities that is much more straightforward than finding the solutions of differential inequalities, which is encountered in the nonlinear H control design procedures, like [15]. Finally, simulation results are provided to demonstrate that the performance of the networked manipulators is enhanced by the suggested method.

The remainder of this paper is organized as follows. In Section 2, the proposed problem is formulated. Distributed dynamic H control law for networked uncertain manipulators in the presence of time-varying communication delays is developed in Section 3. In Section 4, simulation results are presented. Finally, Section 5 concludes the paper.

Section snippets

Problem statement and preliminaries

Consider a group of non-identical n-link robotic manipulators consisting of N members, which are interacting over a balanced and strongly connected communication graph [12]. The nominal dynamical model of each manipulator without friction and viscous damping is described by Euler-Lagrange equation as follows:Mi(qi)q¨i+Ci(qi,q˙i)q˙i+gi(qi)=τi,i{1,2,.....,N},where i denotes the index number of robotic manipulators in the team. qin is the vector including the angular positions of joints, which

Synchronizing control law

As mentioned before, dynamical uncertainty could lead to a poor synchronization. and Undesirable effect of the model uncertainty is considered as a disturbance input in the system description Eq. (6). In this section, a distributed control strategy is developed based on the H optimal control for nonlinear systems, which aims at achieving an improved synchronous tracking by reducing the destructive effects of the uncertainties [15]. Moreover, controllers with dynamic structure employed here to

Simulation results

The proposed approach is used in this section to design the synchronization control for a group of two-link robotic manipulators including three members. Dynamical models of the robots considered to be uncertain consist of the mass uncertainties. The communications between manipulators are assumed to be subject to time-varying delays. The efficiency of the developed control strategy is illustrated by simulating the robotic network in Matlab®.

Robotic systems communicate with each other via a

Conclusion

A distributed dynamic control law has been synthesized to achieve the high-quality synchronous tracking of networked robotic manipulators in the joint space. The dynamical models of the robotic systems contain uncertainties, and the corresponding communication network is subject to time-varying data transmission delays. A nonlinear control strategy is employed to attenuate the destructive effects of the uncertainties on the synchronous performance of the robots. Unlike most of the designing

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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