Time-varying Formation Tracking Research Articles

Formation tracking control with disturbance rejection in leader-follower multi-agent systems under dynamic event-triggered mechanism

This paper investigates the problem of time-varying formation tracking (TVFT) in a linear multi-agent systems (MASs) with external disturbance in a type of directed network topology, and proposes a formation control strategy in a leader-follower control framework with disturbance rejection under a dynamic event-triggering mechanism (DETM). Firstly, in order to improve the overall performance of the system, an extended state observer is used to estimate the status of the follower and the presence of external disturbance in real time. Secondly, a DETM is designed to avoid continuous communication between adjacent intelligent agents. And the formation tracking error between adjacent multi-agents is used to formulate a distributed TVFT control strategy. Furthermore, a compensation function is designed to actively offset the impact of time-varying disturbances on system. A Lyapunov function is then established for stability analysis, verifying the absence of Zeno behavior with this DETM. Finally, a comparative numerical simulation was conducted using an unmanned aerial vehicle (UAV) cluster case to verify that the proposed method can save communication resources to a greater extent and has good control performance.

Dynamic Self-Triggered Fuzzy Bipartite Time-Varying Formation Tracking for Nonlinear Multiagent Systems With Deferred Asymmetric Output Constraints

Dynamic Self-Triggered Fuzzy Bipartite Time-Varying Formation Tracking for Nonlinear Multiagent Systems With Deferred Asymmetric Output Constraints

Finite-Time Time-Varying Formation Tracking for Heterogeneous Nonlinear Multiagent Systems Using Adaptive Output Regulation.

The finite-time output time-varying formation tracking (TVFT) problem for heterogeneous nonlinear multiagent system (MAS) is investigated in this article, where the dynamics of the agents can be nonidentical, and leader's input is unknown. The target of this article is that the outputs of followers need to track leader's output and realize the desired formation in finite time. First, for removing the assumption that all agents are required to know the information of leader's system matrices and the upper boundary of its unknown control input in previous studies, a kind of finite-time observer is constructed by exploiting the neighboring information, which can estimate not only the leader's state and system matrices but also can compensate for the effects of unknown input. On the basis of the developed finite-time observers and adaptive output regulation method, a novel finite-time distributed output TVFT controller is proposed with the help of the technique of coordinate transformation by introducing an extra variable, which removes the assumption that the generalized inverse matrix of follows' input matrix needs to be found in the existing results. By means of the Lyapunov and finite-time stability theory, it is proven that the expected finite-time output TVFT can be realized by the considered heterogeneous nonlinear MASs within a finite time. Finally, simulation results demonstrate the efficacy of the proposed approach.

Resilient Output Formation-Tracking of Heterogeneous Multiagent Systems Against General Byzantine Attacks: A Twin-Layer Approach.

This work solves the countermeasure design problems of distributed resilient output time-varying formation-tracking (TVFT) of heterogeneous multiagent systems (MASs) against general Byzantine attacks (GBAs). Inspired by the concept of Digital Twin, a hierarchical protocol equipped with a twin layer (TL) is proposed, which decouples the above problem into the defense against Byzantine edge attacks (BEAs) on the TL and the defense against Byzantine node attacks (BNAs) on the cyber-physical layer (CPL). First, a secure TL with respect to (w.r.t.) the high-order leader dynamics is designed, which achieves resilient estimation against BEAs. A trusted-node strategy against BEAs is proposed, which promotes network resilience by protecting almost the smallest fraction of crucial nodes on the TL. It is proven that strongly (2f+1) -robustness w.r.t. the above trusted nodes is sufficient for the resilient estimation performance of the TL. Second, a decentralized adaptive and chattering-free controller against potentially unbounded BNAs is designed on the CPL. This controller has the merit of uniformly ultimately bounded (UUB) convergence and an assignable exponential decay rate when converging into the above UUB bound. To the best of our knowledge, this article is the first to achieve resilient output TVFT against GBAs, rather than under GBAs. Finally, the practicability and validity of this new hierarchical protocol are illustrated via a simulation example.

Distributed Adaptive Time-Varying Formation Tracking for Input Saturated Multi-Agent Systems With Multiple Leaders

Distributed Adaptive Time-Varying Formation Tracking for Input Saturated Multi-Agent Systems With Multiple Leaders

Resilient Time-Varying Formation Tracking for Heterogeneous High-Order Multiagent Systems With Multiple Dynamic Leaders

This paper investigates time-varying output formation tracking problems for heterogeneous multiagent systems in an adversarial environment, where both leaders and followers are vulnerable to cyber-attacks. Despite the presence of adversarial agents, the normal followers not suffering from cyber-attacks seek to achieve a desired for-mation configuration and track a safe trajectory generated by normal leaders' outputs simultaneously. To this end, a resilient time-varying output formation (RTVOF) tracking scheme is presented in this work. Firstly, to counteract the effect of adversarial agents, a safety strategy is proposed for general linear heterogeneous systems, which is a syn-thesis of the mean-subsequence-reduced family algorithms and an attack detection procedure. Secondly, using the neighboring interaction, a resilient distributed observer and a local formation controller are designed for each normal follower to estimate the state and track the output of the safe formation reference. Then, it is proved that the hetero-geneous multiagent system with multiple dynamic leaders and time-varying topologies can accomplish the RTVOF tracking if specific graph-theoretic properties and forma-tion feasibility conditions are satisfied. Finally, simulation examples are given to demonstrate the effectiveness of obtained results.

Energy-Constraint Adaptive Time-Varying Formation Tracking for Multi-Agent Systems With Multiple Leaders and Bounded Unknown Inputs

Energy-Constraint Adaptive Time-Varying Formation Tracking for Multi-Agent Systems With Multiple Leaders and Bounded Unknown Inputs

Predictive State Observer-Based Aircraft Distributed Formation Tracking Considering Input Delay and Saturations

This paper investigates a fully distributed time-varying formation tracking problem for a group of fixed-wing aircraft. The fixed-wing aircraft formation control system consists of an outer-loop trajectory control subsystem and an inner-loop attitude control subsystem. For fixed-wing aircraft, it is crucial to consider the time delay of the engine response, the model uncertainties, the tracking capability of the attitude commands in the inner loop, and other agility performances of the aircraft. To address the problems related to the input time delay and model uncertainties, a predictive extended state observer-based fully distributed time-varying formation tracking control (PESO-TVFTC) protocol is proposed. To satisfy the constraints set by the attitude tracking quickness and the trajectory tracking smoothness, the low gain feedback technique is introduced in the protocol to keep the control inputs for the outer loop within the desired saturation constraints. Through theoretical analysis, it is proved that the multiple aircraft systems can achieve time-varying formation tracking consensus under specific initial conditions and feasibility conditions, and it is shown that the upper bounds of the PESO gains are restricted by the time delay. Numerical simulations are used to demonstrate the effectiveness of and the improvements in the proposed method.

Time-varying formation tracking control for multi-agent systems using distributed multi-sensor multi-target filtering

Time-varying formation tracking control issues for multi-agent systems are investigated based on the distributed multi-sensor multi-target filtering algorithm. In order to estimate the states of targets, a distributed multi-sensor multi-target filtering algorithm based on cubature Kalman filtering is investigated. Subsequently, the state estimations calculated by the filtering algorithm are used to design a time-varying formation tracking protocol for multi-agent systems, enabling the agents to form a time-varying formation and track the convex combination of uncooperative targets. The estimation errors of the filtering algorithm are proved to be bounded in mean square by introducing a stochastic process and the boundedness of the formation tracking errors is further proved. Simulation results illustrates the effectiveness of the proposed algorithm and protocol.

Robust Decentralized Formation Tracking Control of Complex Multiagent Systems

This article investigates the decentralized formation tracking problem for complex multiagent systems in finite settling time, subjected to output constraints and external disturbances. The barrier Lyapunov function is used to constrain the output of each agent. Therefore, starting inside a closed boundary, the agents are guaranteed to remain inside it for all future time. Under directed communication topology, decentralized time-varying formation tracking is achieved in finite time. Furthermore, in the proposed work, the linear sliding manifold is employed to mitigate the singularity problem that occurs in the conventional robust finite-time methods, i.e., terminal sliding mode-based control schemes. The stability properties of the proposed framework are established through the Lyapunov method which not only ensures the finite-time formation tracking of nonlinear multiagent systems under directed communication but also guarantees that for all time the agents remain inside a closed boundary if they are initially inside it. Consequently, the uniqueness of this article is that it presents a novel formation tracking control framework for multiagent systems that simultaneously considers three performance metrics of robustness, finite-time convergence, and output constraints while mitigating the singularity problem. The proposed topology is validated by implementing the numerical examples in MATLAB/SIMULINK.

Multiple time-varying formation tracking of multiple heterogeneous Euler–Lagrange systems via prescribed-time hierarchical control algorithms in task space

Multiple time-varying formation tracking of multiple heterogeneous Euler–Lagrange systems via prescribed-time hierarchical control algorithms in task space

Time-Varying Formation Tracking Control of Multi-Leader Multiagent Systems With Sampled-Data

In this paper, the time-varying formation tracking (TVFT) problem of multi-leader multi-agent systems (MASs) under sampled-data control is studied. First, an improved TVFT criterion is derived by employing a general looped-functional and a zero integral functional. Then a new TVFT controller is designed based on our proposed method. Unlike the existing works, the TVFT controller can allow for bigger sampling intervals of multi-leader MASs. The results demonstrate that the states of the followers can form the designated formation and rotate around the convex combination formed by the multiple leaders. In addition, we generalize the results of TVFT to the sampled-data consensus for MASs, a sampled-data consensus controller which can reduce communication consumption is designed. Meanwhile, the values of the allowable maximum sampling intervals (AMSIs) are calculated. Finally, the superiority and availability of the theoretical results are verified by two simulation experiments. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this paper is to address the problem of TVFT for MAS with multiple leaders. It has been applied to several practical engineering systems, e.g., satellite formation control and unmanned air vehicles (UAVs) formation control. Note that information exchange is a prerequisite to ensure safe and stable control of multi-UAV formation. However, continuous-time communication is difficult to be realized in the actual environment, and it will inevitably consume a lot of energy. In addition, sampled-data controller for MAS with a small sampling interval may cause network congestion. Therefore, a sampled-data controller which allows for a bigger sampling interval for MAS is designed to save network resources in this paper. Through simulation experiments, it can be proved that the followers not only track the leaders, but also form the designated formation.

Predefined-Time Bipartite Time-Varying Formation Tracking Control of Networked Autonomous Surface Vehicles Via Hierarchical Control Approach

Predefined-Time Bipartite Time-Varying Formation Tracking Control of Networked Autonomous Surface Vehicles Via Hierarchical Control Approach

Discrete-time adaptive distributed output observer for time-varying formation tracking of heterogeneous multi-agent systems

This paper presents discrete-time distributed algorithms to achieve time-varying output formation tracking of heterogeneous linear multi-agent systems subject to time-varying faults and directed graphs. To overcome the impacts caused by unknown faults and directed graphs, a discrete-time adaptive distributed output observer-based control architecture is established to guarantee time-varying output formation tracking exponentially. In particular, several distributed leader observers are firstly given to estimate and reconstruct the leader’s state over a directed graph. The new discrete-time adaptive distributed output observer is presented to remove the need of having fully access to the leader’s system matrices and to reduce the dimension and information exchange in the developed distributed observers. In terms of this estimated information from the adaptive distributed output observer, a distributed output feedback controller integrated with an observer-based scheme is developed to compensate for the impact of unknown faults such that time-varying output formation tracking is achieved with a global exponential convergence. Two examples and simulation results are provided to validate the effectiveness of the proposed designs.

Adaptive practical prescribed-time formation tracking of networked nonlinear multiagent systems with quantized inter-agent communication

This paper presents an adaptive practical prescribed-time (PPT) control design for distributed time-varying formation tracking of networked uncertain strict-feedback nonlinear systems with quantized inter-agent communication under a directed network. The primary contribution of this study is to develop a time-varying formation tracking strategy to resolve the quantized inter-agent communication problem in the prescribed-time control field. A practical finite-time function is introduced to design an adaptive PPT formation tracker using quantized output information of neighbors, which can be used continuously after a prescribed time. A neural-network-based design methodology that utilizes the quantization-based distributed errors is presented to deal with the unknown virtual and actual control coefficient functions in the command-filtered backstepping design. Distributed adaptive compensating signals are constructed using the practical finite-time function to compensate for command-filter errors, unknown nonlinearities, and quantization errors in the PPT tracking framework. We prove that despite the presence of quantized inter-agent communication, the time-varying formation tracking errors converge to a compact set including the origin within the pre-assigned convergence time, where the compact set can be adjusted by choosing a design parameter of the practical finite-time function, and the prescribed settling time is independent of the initial system conditions and design parameters. The effectiveness of the proposed theoretical approach is confirmed through two simulation examples.

Time-varying formation tracking for multi-agent systems with maneuvering leader under DDoS attacks and actuator faults

Time-varying formation tracking problems for multi-agent systems (MASs) under distributed Denial-of-Service (DDoS) attacks and actuator faults are studied. To deal with the hybrid threats at the cyber and physical layers, an estimator-based fault-tolerant hierarchical control scheme is introduced, which is applicable to channel-wise asynchronous communication. Sufficient conditions for formation tracking of maneuvering leader with ultimately bounded error are obtained, and the particular case of periodic communication and attacks with constrained duration and frequency is further analyzed. Comparative physical simulations based on ROS and Gazebo are first conducted to show the resilience of our scheme against the threats. Finally, an experimental platform containing DJI Tello quadrotors and a self-developed ground control station is built, based on which practical experiments with four quadrotors are carried out to evaluate the effectiveness and engineering practicability of the proposed control framework.

Cooperative Guidance of a Multi-quadrotors System with Switching and Reduced Network Information Exchange: Application to Uncooperative Target Entrapping

In this paper, we investigate the leader–followers Time-Varying Formation Tracking (TVFT) problem of a networked Multi-Agent Systems (MASs) based output feedback. The agents’ behavior is featured by linear dynamics. The interaction topology among the agents is switching over time, directed and only assumed to contain a directed spanning tree. This latter is rooted by a leader-agent whose control input is unknown and bounded. A novel fully distributed TVFT controller is proposed that exhibits a reduced network information exchange property among the agents, thus less communicating-resources are utilized. The proposed controlled design is based on an adaptive observer and disturbance rejection technique, where the unknown leader-input is viewed as an external disturbance. The key feature lies in introducing a local observer in each agent-controller design to observe all the relative neighboring output-measurements and the relative neighboring distributed observer-outputs, all gathered in one signal that we denote the agent’s network information signal. The Lyapunov theory is used to prove that the closed-loop MASs tracking error is stable. An analysis of the effect of the interaction topology structure on the tracking-error convergence rate is further provided, showing the validity of the proposed formation control for switching interaction topologies. Finally, to verify the effectiveness of the obtained results, the proposed controller is extended to a cooperative guidance of a networked quadrotors to track and entrap an uncooperative aerial target that plays the role of a passive leader.

Potential field-based formation tracking control for multi-UGV system with detection behavior and collision avoidance

This paper investigates the time-varying formation tracking and collision avoidance problems for multi-unmanned ground vehicle (UGV) system which consists of omnidirectional vehicles on directed topology. To prevent the failure of collision avoidance caused by the lack of information interaction when the directed graph is not unilaterally connected, partial vehicles are elected as observers and their detection behaviors represented by sectors are realized by potential field and yaw control. Firstly, an improved repulsive potential field force is designed, and two composite potential field forces are proposed for single-to-single detection and single-to-multiple detection situations. Inspired by the equilibrium of forces, it is proven that the reconstructed potential field force which is not affected by the complexity of the collision situation can eradicate the local minima or deadlock states. Secondly, in order to generate detection behaviors according to a basic communication graph, an algorithm is put forward. Then, the protocol of position and velocity control, as well as the protocol of yaw control, are presented respectively. The former ensures the realization of formation tracking, while the latter, together with composite potential field forces, makes the detection behavior continuous. Moreover, according to Lyapunov-based theory, it is proven that the given method can achieve time-varying formation tracking and collision avoidance. Finally, simulations demonstrate the theoretical results.

Predefined-Time Bipartite Time-Varying Formation Tracking of Multiple Euler–Lagrange Systems via Estimator-Based Hierarchical Control Algorithm

This paper investigates the predefined-time bipartite time-varying formation tracking (PTBTVFT) problem of Euler-Lagrange systems (ELSs) with external disturbances under a signed digraph, where the directed topology contains cooperative and antagonistic interactions. Firstly, estimator-based hierarchical control (EBHC) algorithm is proposed to handle the above problem. It is worth noting that the settling time can be randomly predetermined according to practical demands. Then, by Lyapunov stability analysis, some sufficient conditions are derived for the realization of the PTBTVFT. Finally, simulation experiments are performed to confirm the feasibility of the developed control strategy.

Adaptive Time-Varying Formation Tracking Control for Multiagent Systems With Nonzero Leader Input by Intermittent Communications.

The time-varying formation (TVF) tracking problem is studied for linear multiagent systems (MASs), where followers reach a preset TVF when tracking the leader's state. Followers are divided into the informed ones, which directly receive the leader's information, and uninformed ones. To alleviate communication requirements, trigger mechanisms are designed for the leader and all edges. Note that the designed trigger mechanisms enable the leader to send information intermittently and each follower to transmit information asynchronously when the corresponding trigger mechanism is satisfied. To address the TVF tracking problem, the node-event (for the leader) and (dynamic) edge-event triggered adaptive control strategy is proposed, which is fully distributed and has no relation to the system network's scale. Moreover, the MASs do not exhibit the Zeno behavior. Finally, a practice example is introduced to effectively illustrate the theoretical results.