Practical consensus tracking control of multiple nonholonomic wheeled mobile robots in polar coordinates

This paper proposes a sliding‐mode control (SMC) method to achieve practical cooperative consensus tracking for a network of multiple nonholonomic wheeled mobile robots (MNWMRs) with input disturbances. A novel SMC surface under the nonholonomic constraints is first formulated to characterize the network communication interactions among the networked robots under the framework of polar coordinates. A unified distributed consensus tracking strategy is then proposed by systematically combining a position controller and a direction controller. Furthermore, a simple yet general criterion is derived to achieve the desired practical consensus of trajectory tracking and posture stabilization for MNWMRs. In particular, for a specific common consensus trajectory, the complete asymptotic tracking in heading direction can be fully guaranteed when the perfect asymptotic position‐tracking errors are realized. Accordingly, the developed consensus tracking strategy for MNWMRs demonstrates some advantages of control performance including stability, robustness, and effectiveness over the existing control method proposed for their single‐robot counterparts. Some comparative simulation results are given to confirm the effectiveness of the proposed cooperative consensus control method.     

Leader‐following control for multiple inertial agents

This paper investigates distributed controller design problem for a leader‐follower network in the presence of communication delays. Two main contributions are made in this work. First, the second‐order controlled consensus scheme for the weakly connected communication graph topology is proposed. A necessary and sufficient condition is given under which the exponential consensus is achieved. Meanwhile, the relationship among the agents' inertias, the allowable delay bound, the communication topology, the consensus convergence rate, and the control gains is unveiled. Second, the robustness performances of the distributed control scheme with respect to the communication failures and delays are provided. It is shown that if the communication failure rate and the topology switching frequency, respectively, satisfy the given bounds, the exponential second‐order controlled consensus can be achieved under a bounded delay. Numerical examples are given to illustrate the theoretical results. Copyright © 2010 John Wiley & Sons, Ltd.     

Distributed model‐independent consensus of Euler–Lagrange agents on directed networks

This paper proposes a distributed model‐independent algorithm to achieve leaderless consensus on a directed network where each fully‐actuated agent has self‐dynamics described by Euler–Lagrange equations of motion. Specifically, we aim to achieve consensus of the generalised coordinates with zero generalised velocity. We show that on a strongly connected graph, a model‐independent algorithm can achieve the consensus objective at an exponential rate if an upper bound on the initial conditions is known a priori. By model‐independent, we mean that each agent can execute the algorithm with no knowledge of the equations describing the self‐dynamics of any agent. For design of the control laws which achieve consensus, a control gain scalar and a control gain matrix are required to satisfy several inequalities involving bounds on the matrices of the agent dynamic model, bounds on the Laplacian matrix describing the network topology and the set of initial conditions; design of the algorithm therefore requires some knowledge on the bounds of the agent dynamical parameters. Because only bounds are required, the proposed algorithm offers robustness to uncertainty in the parameters of the multiagent system. We systematically show that additional relative velocity information improves the performance of the controller. Numerical simulations are provided to show the effectiveness of the algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Consensus of multi‐agent systems with time‐varying topology: An event‐based dynamic feedback scheme

The event‐based control strategy is an effective methodology for reducing the controller update and communication over the network. In this paper, the event‐based consensus of multi‐agent systems with linear dynamics and time‐varying topology is studied. For each agent, a state‐dependent threshold with an exponentially decaying bound is presented to determine the event times, and a new event‐based dynamic feedback scheme is proposed. It is shown that the controller update for each agent is only dependent on its own event times, which reduces significantly the controller update or computation for each agent. Moreover, based on the event‐based dynamic feedback scheme and the event triggering function presented in this paper, the continuous communication among neighboring agents is avoided, and the Zeno‐behavior of the closed‐loop systems is excluded. A numerical example is given to illustrate the effectiveness of theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

基于能量整形方案实现具有通讯时滞欠驱动Euler-Lagrange网络的一致性

本文主要基于能量整形方案研究具有通讯时滞网络化欠驱动Euler-Lagrange (EL)系统的一致性问题,通过利用阻尼注入和互连分配的无源控制(PBC)技术,在有向连通网络拓扑下提出了一个简单的分布式协议,来实现在无引导者和有引导者-跟随者两种情形下欠驱动EL网络的一致性. 本文提出的一致性能量整形方案的主要特点是有机地整合了系统欠驱动和驱动部分以及控制器三部分能量作为整个系统的总能量,这个总能量被利用作为一个合适的Lyapunov函数,它能够充分确保网络化欠驱动EL系统达到所期望的分布式一致性. 最后,通过由欠驱动EL网络所描述柔性关节机械臂系统的数值模拟,来分析通讯时滞对一致性的效应和验证所提出控制算法的正确性.     

Distributed consensus control for multi‐agent systems using terminal sliding mode and Chebyshev neural networks

This paper investigates the problem of consensus tracking control for second‐order multi‐agent systems in the presence of uncertain dynamics and bounded external disturbances. The communication ?ow among neighbor agents is described by an undirected connected graph. A fast terminal sliding manifold based on lumped state errors that include absolute and relative state errors is proposed, and then a distributed finite‐time consensus tracking controller is developed by using terminal sliding mode and Chebyshev neural networks. In the proposed control scheme, Chebyshev neural networks are used as universal approximators to learn unknown nonlinear functions in the agent dynamics online, and a robust control term using the hyperbolic tangent function is applied to counteract neural‐network approximation errors and external disturbances, which makes the proposed controller be continuous and hence chattering‐free. Meanwhile, a smooth projection algorithm is employed to guarantee that estimated parameters remain within some known bounded sets. Furthermore, the proposed control scheme for each agent only employs the information of its neighbor agents and guarantees a group of agents to track a time‐varying reference trajectory even when the reference signals are available to only a subset of the group members. Most importantly, finite‐time stability in both the reaching phase and the sliding phase is guaranteed by a Lyapunov‐based approach. Finally, numerical simulations are presented to demonstrate the performance of the proposed controller and show that the proposed controller exceeds to a linear hyperplane‐based sliding mode controller. Copyright © 2011 John Wiley & Sons, Ltd.     

Distributed reliable H∞ consensus control for a class of multi‐agent systems under switching networks: A topology‐based average dwell time approach

This paper investigates the problem of distributed reliable H_∞ consensus control for high‐order networked agent systems with actuator faults and switching undirected topologies. The Lipschitz nonlinearities, several types of actuator faults, and exogenous disturbances are considered in subsystems. Suppose the communication network of the multi‐agent systems may switch among finite connected graphs. By utilizing the relative state information of neighbors, a new distributed adaptive reliable consensus protocol is presented for actuator failure compensations in individual nodes. Note that the Lyapunov function for error systems may not decrease as the communication network is time‐varying; as a result, the existing distributed adaptive control technique cannot be applied directly. To overcome this difficulty, the topology‐based average dwell time approach is introduced to deal with switching jumps. By applying topology‐based average dwell time approach and Lyapunov theory, the distributed controller design condition is given in terms of LMIs. It is shown that the proposed scheme can guarantee that the reliable H_∞ consensus problem is solvable in the presence actuator faults and external disturbance. Finally, two numerical examples are given the effectiveness of the proposed theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Distributed Consensus of Multi‐Agent Networks Via Event‐Triggered Pinning Control

This paper is concerned with distributed consensus between two multi‐agent networks with the same topology structure. Considering one network as the leaders' network and the other one as the followers' network, a new event‐triggered pinning control scheme is proposed to realize distributed consensus between these two networks. By utilizing the graph theory and Lyapunov functional method, consensus criteria are derived in the form of linear matrix inequalities. Moreover, distributed consensus of multi‐agent networks with Lipschitz nonlinear dynamics is also discussed. Numerical simulations are provided to demonstrate the effectiveness of the theoretical analysis.     

Finite‐time consensus of Euler‐Lagrange agents without velocity measurements via energy shaping

Motivated by the energy‐shaping framework and the properties of homogeneous systems, this paper deals with the problem of achieving consensus of multiple Euler‐Lagrange (EL) systems using the energy shaping plus damping injection principles of passivity‐based control. We propose a method to derive a novel family of decentralized controllers that is capable of solving the leaderless and the leader‐follower consensus problems in finite‐time in networks of fully actuated EL systems without employing velocity measurements. As in the energy‐shaping methodology, the controller is another EL system and the plant‐controller interconnection is the gradient of a suitable defined potential function. The potential energy and dissipation functions, of the controller, are provided with some homogeneous properties in order to achieve finite‐time convergence. This paper provides several simulations that corroborate the performance of different controllers.     

Coordination of networked systems on digraphs with multiple leaders via pinning control

It is well known that achieving consensus among a group of multi-vehicle systems by local distributed control is feasible if and only if all nodes in the communication digraph are reachable from a single (root) node. In this article, we take into account a more general case that the communication digraph of the networked multi-vehicle systems is weakly connected and has two or more zero-in-degree and strongly connected subgraphs, i.e. there are two or more leader groups. Based on the pinning control strategy, the feasibility problem of achieving second-order controlled consensus is studied. At first, a necessary and sufficient condition is given when the topology is fixed. Then the method to design the controller and the rule to choose the pinned vehicles are discussed. The proposed approach allows us to extend several existing results for undirected graphs to directed balanced graphs. A sufficient condition is proposed in the case where the coupling topology is variable. As an illustrative example, a second-order controlled consensus scheme is applied to coordinate the movement of networked multiple mobile robots.     

Predictive Consensus for Networked Multi‐Agent Systems with Switching Topology and Variable Delay

This paper investigates consensus problems of networked linear time invariant (LTI) multi‐agent systems, subject to variable network delays and switching topology. A new protocol is proposed for such systems with matrix B that has full row rank, based on stochastic, indecomposable, aperiodic (SIA) matrix and the predictive control scheme. With the predictive scheme the network delay is compensated. Consensus analysis based on the seminorm is provided. The conditions are obtained for such systems with periodic switching topology to reach consensus. The proposed protocol can deal with time‐varying delays, switching topology, and an unstable mode. The numerical examples demonstrate the effectiveness of the theoretical results.     

Event‐Based Consensus Controller for Linear Multi‐Agent Systems Over Directed Communication Topologies: A Co‐Design Approach

The paper addresses the distributed event‐triggered consensus problem in directed topologies for multi‐agent systems (MAS) with general linear dynamic agents. A co‐design approach is proposed to determine parameters of the consensus controller and its event‐triggered mechanism (ETM), simultaneously. This approach guarantees asymptotic stability along with decreasing data transmission among agents. In the proposed event‐based consensus controller, each agent broadcasts data to the neighbors only at its own triggering instants; this differs from previous studies in which continuous data streams among agents were required. Furthermore, the proposed control law is based on the piecewise constant functions of the measurement values, which are updated at triggering instants. In this case the control scheme decreases the communication network usage, energy consumption, and wear of the actuator. As a result, it facilitates distributed implementation of the proposed consensus controller for real‐world applications. A theorem is proved to outline sufficient conditions to guarantee the asymptotic stability of the closed‐loop system with the event‐based consensus controller. Another theorem is also proved to show the Zeno behavior exclusion. As a case study, the proposed event‐based controller is applied for a diving consensus problem to illustrate the effectiveness of the method.     

Leader‐following consensus of multiple uncertain Euler‐Lagrange systems

A new adaptive distributed controller is developed for the leader‐following consensus problem of multiple uncertain Euler‐Lagrange systems. A distinct feature of our proposed approach as opposed to the existing ones is that it does not need the exchange of controller's state among the communication network. As a consequence, it not only makes the implementation of the controller much easier but also reduces the communication cost. The effectiveness of the main result is demonstrated by some exemplary applications to cooperative control of multiple two‐link robot arms.     

Bounded consensus for multiagent systems by event‐triggered data transmission,time delay,and predictor‐based control

This paper investigates the consensus issue of multiagent systems with data transmission time delay. The state measurement of each local agent is directly sent to a private event‐trigger and further authorized to be broadcasted to its neighbors via communication network only when the threshold of the event‐trigger is violated. Since the controller always receives discrete‐time neighbor information with data transmission time delay, a predictor is employed to estimate the continuous‐time neighbor state. Based on the estimated state, a novel consensus protocol is mainly proposed for achieving the bounded consensus of the multiagent systems. By the proposed method, the asynchronous neighbor information is allowed and the margin of data transmission time delay is also given. Furthermore, it has been proved that the unwanted Zeno phenomena can be naturally excluded. Numerical example is provided to demonstrate the effectiveness of the proposed method.     

Model‐independent consensus control of Euler‐Lagrange agents with interconnecting delays

In this paper, we introduce, for the first time, a proportional‐integral‐derivative controller to solve the consensus problem for networked Euler‐Lagrange agents. The proposed control scheme solves both the leaderless and the leader‐follower consensus problems without requiring the exact knowledge of any part of the agent model. Contrary to the previous studies in the literature, we do not require either to cancel any part of the agent model, which renders robust our approach, nor employ discontinuous controllers. It is proven that both consensus problems are solved globally and asymptotically and the presence of bounded time‐varying communicating delays is considered.     

Robust finite‐time consensus formation control for multiple nonholonomic wheeled mobile robots via output feedback

The finite‐time formation control for multiple nonholonomic wheeled mobile robots with a leader‐following structure is studied. Different from the existing results, the considered mobile robot has the following features: (i) a higher‐order dynamic model, (ii) the robot's velocities cannot be measured, and (iii) there are external disturbances. To solve the problem, a finite‐time consensus formation control algorithm via output feedback is explicitly given. At the first step, some finite‐time convergent observers are skillfully constructed to estimate both the unknown velocity information and the disturbance in finite time by imposing certain assumptions on the disturbances. Then, on the basis of the integral sliding‐mode control method, a disturbance observer‐based finite‐time output feedback controller is developed. Rigorous proof shows that the finite‐time formation can be achieved in finite time. An example is finally given to verify the efficiency of the proposed method.     

Adaptive consensus with a virtual leader of multiple agents governed by locally Lipschitz nonlinearity

This paper is concerned with the second‐order consensus problem of multi‐agent systems with a virtual leader, where all agents and the virtual leader share the same intrinsic dynamics with a locally Lipschitz condition. It is assumed that only a small fraction of agents in the group are informed about the position and velocity of the virtual leader. A connectivity‐preserving adaptive controller is proposed to ensure the consensus of multi‐agent systems, wherein no information about the nonlinear dynamics is needed. Moreover, it is proved that the consensus can be reached globally with the proposed control strategy if the degree of the nonlinear dynamics is smaller than some analytical value. Numerical simulations are further provided to illustrate the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.     

A novel consensus algorithm for second‐order multi‐agent systems without velocity measurements

In this paper, a novel consensus protocol for second‐order multi‐agent systems is elegantly designed, and it relaxes the common requirement of the velocity information of the agents. An interesting consensus criterion is explicitly derived in terms of the proposed cooperation law provided that the dynamical equation for each agent is linear. As an extension, the proposed cooperation rule is further extended to a general scenario, where the coupling weights characterizing the relationships among the neighboring agents are time‐varying. Accordingly, two distributed cooperative algorithms (node/edge‐based scheme) are explicitly designed. Moreover, we study the case of network with switching communication setting. It shows that edge‐based law is capable with the time‐varying topology, while the node‐based scheme is not. In addition, the proposed coordination strategies are applied to the tracking problem as well. Finally, these obtained consensus results are well supported in the light of the pendulum models. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust event‐triggered control of second‐order disturbed leader‐follower MASs: A nonsingular finite‐time consensus approach

This paper addresses the finite‐time and the prescribed finite‐time event‐triggered consensus tracking problems for second‐order multi‐agent systems (MASs) with uncertain disturbances. The prescribed finite‐time event‐triggered consensus of the second‐order disturbed MASs was obtained for the first time and the controller is nonsingular. Furthermore, a new self‐triggered control scheme is presented for the finite‐time consensus tracking, and the continuous communication can be avoided in the triggering condition monitoring. Hence, the finite‐time consensus tracking can be achieved with intermittent communication. Moreover, Zeno behavior is excluded for each follower. The efficiency of the proposed algorithms is verified by numerical simulations.     

Distributed event‐triggered feedback consensus control with state‐dependent threshold for general linear multi‐agent systems

This paper considers the distributed event‐triggered consensus problem for multi‐agent systems with general linear dynamics under undirected graphs. Based on state feedback, we propose a novel distributed event‐triggered consensus controller with state‐dependent threshold for each agent to achieve consensus, without continuous communication in either controller update or triggering condition monitoring. Each agent only needs to monitor its own state continuously to determine if the event is triggered. It is proved that there is no Zeno behavior under the proposed consensus control algorithm. To relax the requirement of the state measurement of each agent, we further propose a novel distributed observer‐based event‐triggered consensus controller to solve the consensus problem in the case with output feedback and prove that there is no Zeno behavior exhibited. Finally, simulation results are given to illustrate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.