Undirected Communication Topology Research Articles

Global Consensus-Based Formation Control of Nonholonomic Mobile Robots With Time-Varying Delays and Without Velocity Measurements

We propose a solution to the full consensus-based formation problem for torque-controlled nonholonomic mobile robots under time-varying communication delays and without velocity measurements. Under the assumptions of static and undirected communication topologies, and smooth and bounded delays, we propose a distributed smooth, time-varying control law which achieves the goal of acquiring a global formation pattern in a common consensus point for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">both</i> position and orientation. The controller is a combination of a simple Proportional-Plus-Damping scheme and a simple globally exponentially convergent velocity observer. Consensus is reached independently of all initial conditions. Realistic simulations in the Gazebo-ROS environment illustrate the effectiveness of the proposed algorithm and the robustness with respect to measurement noise, non-smooth delays and uncertain dynamics.

Leader–follower consensus control for a class of nonlinear multi-agent systems using dynamical neural networks

This paper addresses the formation consensus tracking control problem of uncertain dynamical multi-agent system with nonlinear dynamics based on a leader–follower configuration based on a undirected communication topology. The control design is based on a novel combination of consensus protocols and dynamical neural networks, known as differential neural networks, to approximate the modeling uncertainties and external disturbances of the follower agents. The proposed controller-identifier structure forces the state of each agent to maintain a formation with respect to the leader ensuring limited residual errors. The stability proof supports the control design and guarantees the multi-agent system states to be ultimately bounded. In order to show the effectiveness of the proposed tracking controller and the superior performance against the static RBFNNs approach, some simulation results are presented considering a multi-robotic system with five agents following a helical three-dimensional reference signal of a virtual leader.

Adaptive super-twisting sliding mode attitude coordination control for spacecraft formation flying with actuator saturation

This paper investigates the attitude coordination control issue for spacecraft formation flying in the presence of actuator saturation and external disturbances with unknown boundaries. Firstly, a super-twisting integral terminal sliding mode surface is developed, which ensures that the sliding mode surface and its first-time derivative converge to zero in finite time. Then, based on the developed sliding mode surface and adaptive technique, a robust anti-saturation distributed attitude coordination controller that enables the attitude and angular velocity to precisely track the desired time-varying command in finite time is devised under the undirected communication topology. Finally, stability analysis and numerical simulations validate the effectiveness and feasibility of the devised control approach.

Dynamic Event-Triggered Consensus for Linear Multi-Agent Systems With Hybrid Intelligence

In this brief, consensus control is investigated for general linear multi-agent systems (MASs) over undirected communication topologies. Considering that the agents in MASs may have nonidentical intelligence characteristics, the concept of intelligent level is introduced to characterize the intelligence characteristics of agents. A novel dynamic event-triggered communication mechanism is developed based on periodic sampled data and the intelligent levels of agents, in which the threshold parameter of the event-triggered condition updates periodically in accordance with a prescribed dynamic law. By making use of a delayed system method and Lyapunov stability theory, some sufficient conditions are derived to guarantee the desired consensus under a novel delicately designed control protocol. Finally, the effectiveness of the proposed approach is validated by a simulation example.

An Adaptive Continuous Approach to Consensus Tracking of Nonlinear Multiagent Systems With a Nonautonomous Leader

It is challenging and critical to achieve zero error consensus tracking in multiagent systems (MASs) with nonautonomous leaders (i.e., leaders with nonzero inputs). The traditional approach is to use discontinuous controllers which may cause a chattering phenomenon. How to achieve zero error consensus tracking via a chattering-free controller is still open. We propose a class of adaptive continuous controllers to achieve zero error consensus tracking for Lipschitz nonlinear MASs with a nonautonomous leader and directed communication topology. Unlike existing works that use discontinuous functions to eliminate the impacts of leaders’ inputs, we use a continuous function by introducing an exponential decay function into the denominator. First, we design a continuous controller with fixed coupling strengths and prove that zero error consensus tracking can be achieved if the coupling strengths are greater than some positive constants. Second, we design a continuous controller with dynamic coupling strengths under which fully distributed zero error consensus tracking can be achieved. Moreover, the case with undirected communication topology is studied. Finally, three examples are given to verify the theoretical results. Specifically, convergence results between the continuous controller here and that is developed via the boundary layer technique are compared. Compared with existing works, the designed adaptive continuous controllers here can not only achieve zero error consensus tracking but also is chattering free.

Consensus of discrete-time multi-agent systems with consecutive packet losses in directed communication topology

In this paper, consensus analysis and design are investigated for discrete-time multi-agent systems (MASs) with consecutive packet losses in communication links of directed communication topology. It is assumed that at each transmitted instant, the packet loss is stochastic and described by Bernoulli distribution, but during a given time window, the data could be successfully transmitted to the agent from each of its neighbors. First, we utilize the incidence matrix of a directed spanning tree of the communication topology to construct a linear transformation matrix so that the consensus problem is equivalently transformed into a mean square asymptotic stability problem of a reduced-order system. Second, by using Lyapunov–Krasovskii functional approach, we derive some sufficient conditions of consensus criterion in terms of linear matrix inequalities (LMIs). These conditions express the relationship among the control gain matrix, packet loss rate, and the number of consecutive packet losses. Based on the conditions, gain matrix in the consensus protocol is designed to guarantee the MAS with stochastic packet losses to achieve mean square asymptotic consensus. Moreover, for the special case of undirected communication topology, by using the matrix decomposition method, the variables of LMIs are transformed into the low-order conditions independent of the network size. Finally, some numerical examples are given to show the effectiveness of the proposed method.

Identification of Malicious Activity in Distributed Average Consensus via Non-Concurrent Checking

We consider the problem of average consensus in a network system under a fixed, undirected communication topology, when there are malicious nodes present that may try to influence the average calculation. In the setting considered, the average consensus is performed by the nodes in a distributed fashion using a linear iterative algorithm. We assume malicious nodes can manipulate, in an arbitrary manner, the value of their state in the aforementioned algorithm; the problem is then to check whether or not each node is correctly performing the updates of its state. To address this problem, we propose a distributed algorithm whereby each node is in charge of checking the updates performed by its neighboring nodes based on information that it receives from them and also from the neighbors of its neighbors. The algorithm leverages ideas from non-concurrent error detection schemes and its main advantage is that information from two-hop neighbors is only needed infrequently—a relaxation that significantly reduces the communication overhead associated with the requirement to make such information available

Fully distributed consensus control for second-order multi-agent systems based on adaptive dynamic clock communication

This paper proposes a novel event-triggered control strategy based on an adaptive dynamic clock to address the consensus problem of second-order multi-agent systems with undirected communication topology. The agent determines the triggering time according to its dynamic clock, adaptively resets the clock, and broadcasts its state information to neighbors at the triggering time. Each agent only obtains the status information of its neighbors at the triggering time and updates the clock and control signals based on its own state and the status of its neighbors at the triggering time. It does not require real-time status information from neighbors and does not rely on any global communication topology information. The designed control strategy is completely distributed and effectively avoids continuous communication. Using the Lyapunov stability analysis method and algebraic graph theory, it is proved that the proposed control strategy can ensure that the system is asymptotically stable and does not exhibit Zeno behavior. Finally, the effectiveness of the proposed dynamic event-triggered control strategy is demonstrated by a simulation example.

Consensus of multi-agent systems with heterogeneous unknown nonlinear switching dynamics: A dwelling time approach

This paper investigates the consensus problem of multi-agent systems with unknown heterogeneous nonlinear switching dynamics. First, an extended model-free adaptive controller is proposed to mitigate the effect of unknown switching dynamics. Then, an average dwelling time is provided to guarantee the stability of the multi-agent system and ensure consensus with both directed and undirected communication topologies. Finally, numerical examples are provided to show the impact of switching dynamics on the standard model-free adaptive controller. Then, the average dwelling time is calculated and added to ensure consensus in the presence of switching dynamics.

Distributed fixed-time time-varying formation-containment control for networked underactuated quadrotor UAVs with unknown disturbances

This paper focuses on the fixed-time time-varying formation-containment (TVFC) control problem for multiple underactuated quadrotor unmanned aerial vehicles (QUAVs) with unknown disturbances. A two-layer control framework comprising reference trajectory generators and trajectory tracking controllers is proposed. Under undirected communication topology, the first layer includes two fixed-time distributed reference trajectory generators for leaders and followers. The generated trajectories can be in accordance with the TVFC control requirements. In the second layer, two fixed-time tracking controllers are proposed, and a fixed-time disturbance observer (FTDO) is developed to ensure the robustness and timeliness of the control system. Meanwhile, the intermediary control input developed in the translational controller can be used to obtain the desired attitude by the attitude extraction algorithm. To handle the derivative calculations of variables in the rotational controller, an exact tracking differentiator is adopted, and the closed-loop stability of the control system is proved mathematically. In the end, the proposed control methods are verified through simulations and two comparison simulations are presented to show the superiority.

Robust dynamic average consensus with prescribed transient and steady state performance

In this paper, we consider the dynamic average consensus problem for a group of multiple agents that cooperate to estimate the average of locally available time-varying reference signals, under an undirected communication topology. More specifically, we develop a novel robust distributed estimation algorithm, capable of achieving practically zero average tracking error even for fast time-varying reference signals. The proposed scheme is purely distributed, since the estimation algorithm is based solely on local computations and local communication among neighboring agents, and guarantees prescribed performance in the sense that any convergence rate and steady state deviation among the agents’ estimates may be achieved via the appropriate selection of certain design parameters. Moreover, the consensus and average tracking performance are fully decoupled, thus allowing easy tuning of the gains. Additionally, intermittent implementation is proposed via appropriately selected event- and self-triggering mechanisms. Finally, the approach is clarified and verified through various simulation paradigms.

Distributed Adaptive Mittag–Leffler Formation Control for Second-Order Fractional Multi-Agent Systems via Event-Triggered Control Strategy

This brief investigates the Mittag–Leffler formation bounded control problem for second-order fractional multi-agent systems (FMASs), where the dynamical nodes of followers are modeled to satisfy quadratic (QUAD) condition. Firstly, under the undirected communication topology, for the considered second-order nonlinear FMASs, a distributed event-triggered control scheme (ETCS) is designed to realize the global Mittag–Leffler bounded formation control goal. Secondly, by introducing adaptive weights into triggering condition and control protocol, an adaptive event-triggered formation protocol is presented to achieve the global Mittag–Leffler bounded formation. Thirdly, a five-step algorithm is provided to describe protocol execution steps. Finally, two simulation examples are given to verify the effectiveness of the proposed schemes.

Solving Specified-Time Distributed Optimization Problem via Sampled-Data-Based Algorithm

Despite significant advances on distributed continuous-time optimization of multi-agent networks, there is still lack of an efficient algorithm to achieve the goal of distributed optimization at a pre-specified time, especially for the case with unbalanced directed topologies. Herein, a new out-degree based design structure is proposed for connected agents with directed topologies to collectively minimize the sum of individual objective functions and keep satisfying an equality constraint. With the designed algorithm, the settling time of distributed optimization can be exactly predefined. The specified selection of such a settling time is independent of not only the initial conditions of agents, but also the algorithm parameters and the communication topologies. Furthermore, the proposed algorithm can realize specified-time optimization by exchanging information among neighbors only at discrete sampling instants and thus reduces the communication burden. In addition, the equality constraint is always satisfied during the whole process, which makes the proposed algorithm applicable to online solving distributed optimization problems such as energy resource allocation. For the special case of undirected communication topologies, a reduced-order algorithm is also designed. Finally, the effectiveness of the theoretical analysis is justified by numerical simulations.

Specified-time group consensus for general linear systems over directed graphs

This paper studies the distributed specified-time group consensus control with hard settling-time constraint and milder communication topology constraint. To this end, we propose two distributed control schemes by employing a motion planning approach for the single- and double-integrator systems. Compared with the most existing works over undirected communication topologies, the underlying topology of each group is required to be directed graphs in our proposed distributed controllers. Furthermore, the root vertex of one group is allowed to belong to the other group. The convergence analysis is performed via the algebraic graph theory and matrix theory. The results show that the agents in the same group can reach consensus within any prespecified settling-time instead of a conservative upper bound of the settling-time. Moreover, the designed specified-time group consensus protocols do not require continuous information exchange. Finally, simulation results are provided to illustrate the effectiveness of the proposed methods.

Leader-following quasi-bipartite synchronization of coupled heterogeneous harmonic oscillators via event-triggered control

This paper investigates the leader-following quasi-bipartite synchronization problem of coupled heterogeneous harmonic oscillators under an undirected communication topology. To save limited resources and alleviate communication burden, two asynchronous event-triggered protocols are proposed. Some sufficient criteria are derived to ensure quasi-bipartite synchronization by utilizing differential equation theory, inequality theory and Lyapunov stability method. Meanwhile, it is shown that there is no Zeno behavior for the proposed event-triggered protocols. Furthermore, an upper bound of quasi-bipartite synchronization errors is explicitly provided. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results.

Pose consensus control of multi‐agent rigid body systems with homogenous and heterogeneous communication delays

AbstractA new strategy for full pose and velocity consensus control of multi‐agent rigid body systems in the presence of communication delays is presented. Specifically, consensus protocols are proposed for a system of N heterogeneous rigid bodies on the Banach manifold associated with the tangent bundle , under a fixed and undirected communication topology, where the attitudes of the rigid bodies are described in terms of rotation matrices. The stability argument is strengthened from that used in prior studies by using an extension of Morse–Lyapunov–Krasovskii approach, and sufficient conditions are derived to achieve almost global asymptotic stability of the consensus subspace. Finally, illustrative examples are given to demonstrate the proposed method where both homogenous and heterogeneous communication delays are considered.

Distributed Control of 6-DOF Leader-Following Multi-Spacecraft Formation near an Asteroid Based on Scaled Twistors

This paper addresses the distributed six-degree-of-freedom (6-DOF) control problem of translation-rotation coupled spacecraft formation in the vicinity of an asteroid. Due to the complicated gravity field of an asteroid, there exist no circular or elliptic orbits for the spacecraft, which renders the control schemes designed for the spacecraft formation near the Earth inapplicable. In the framework of twistors, a distributed leader-following control scheme is proposed by combining the dynamic surface technique and consensus theory under an undirected communication topology. First, a scaled-twistor-based position-attitude coupled dynamic model of the spacecraft near an asteroid is established to circumvent numerical difficulty. Since the state of the leader can only be accessed by a subset of the followers, an observer is integrated into the control scheme to estimate the state of the leader for each follower. Then, the pose error between each follower and its desired pose is represented by the scaled twistor. Based on the error dynamics, virtual control is designed according to the consensus theory, and a distributed control law is proposed via the dynamic surface method. To eliminate the large control effort and aggressive transient in the initial phase, adaptive gains are introduced into the control scheme. Furthermore, neural networks (NNs) are used to compensate for not only the external disturbances but also the filter errors resulting from the dynamic surface method. By virtue of the Lyapunov theory, it is proved that the pose errors of the followers are ensured to converge to the neighborhood of the origin, and all the adaptive gains and weights of the NNs are bounded. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed control scheme.

Consensusability of discrete-time multi-agent systems under binary encoding with bit errors

This paper is concerned with the consensusability problem for a class of discrete-time multi-agent systems (DT-MASs). A binary encoding scheme (BES) is employed during the data transmission, and only a finite-length binary bit string is transmitted due primarily to the limited network bandwidth in practice. Meanwhile, the binary bit string, transmitted via memoryless binary symmetric channels, might suffer from random bit errors with a certain probability. The purpose of this paper is to derive some consensusability conditions, under which there must exist a distributed controller such that the mean-square bounded consensus is achieved by the considered DT-MASs with BESs subject to random bit errors. To this end, the statistical properties are first revealed for the BES-induced quantization errors and the random bit errors. Then, by resorting to the solvability analysis of a modified Riccati inequality, some sufficient conditions are, respectively, derived to ensure the mean-square bounded consensus under the undirected communication topology in two scenarios: (1) identical bit-error rates (BERs); and (2) non-identical BERs. In particular, a necessary and sufficient condition is established for a single input case with identical BERs. Furthermore, the ultimate upper bound of the consensus errors in the mean-square sense is established to examine the effects of the length of bit string and the BERs. Finally, an illustrative simulation example is provided to validate the effectiveness of the theoretical results.

6-DOF consensus control of multi-agent rigid body systems using rotation matrices

Nonlinear control protocols are proposed for consensus control of a multi-agent system of N heterogeneous rigid bodies in the framework of the tangent bundles TSO(3) and TSE(3) associated with Lie groups SO(3) and SE(3), respectively. The control objective is to stabilise the relative pose configurations with velocity synchronisation of the rigid bodies which share their states according to a static undirected communication topology. The feedback control design is conducted on the dynamic level, and uses the rotation matrix as opposed to various attitude parameterisations. Almost global asymptotic stability of the consensus subspace is demonstrated both analytically using an extension of the Morse–Lyapunov (M–L) approach, and through numerical simulations. Also, the presence of unstable non-consensus equilibria in the closed-loop dynamics is discussed and shown in illustrative examples.

Distributed Event-Triggered Adaptive Coordinated Trajectory Tracking Control of Multi-USVs Based on the Aggregate Tracking Error

Aiming to solving the nonlinear coordinated trajectory tracking control problem of multi-USVs under the influence of slowly changing and uncertain environmental disturbances, reducing energy consumption and ensuring tracking performance and stability, a distributed event-triggered adaptive coordinated trajectory tracking controller (DET-ACTTC) for multiple unmanned surface vessels (multi-USVs) is proposed based on the undirected communication topology. By introducing a virtual leader, a leader-follower formation is used to generate the coordinated tracking errors. Based on the expected formation and states, the aggregate tracking errors are defined, and event-triggered measurement errors are constructed to design the event-triggered conditions. An adaptive term is used to compensate for external environment disturbances, and the DET-ACTTC is deduced for each USV in the group. The tracking errors of the event-triggered coordinated trajectory tracking control (ETCTTC) system gradually converge to zero, and Zeno behavior is avoided. The theoretical results are verified by simulations.