Formation Tracking For Multi-agent Systems Research Articles

Time-varying formation tracking for multi-agent systems based on prescribed-time control

In this paper, a time-varying formation tracking method based on prescribed-time control is presented for second-order multi-agent systems. The control objective is that the formation system forms and maintains the desired time-varying configuration within an arbitrarily specified time. Addressing the problem that the existing prescribed-time control theorem may lead to divergence of system caused by infinite control input, a novel prescribed-time control theorem based on a novel time-varying scale function is proposed. Different from the existing prescribed-time control results, the proposed theorem introduces convergence time, lead time and prescribed time to avoid the occurrence of the infinite control input. Meanwhile, it can estimate the actual convergence time and has faster convergence rate. Based on proposed theorem, a distributed prescribed-time observer is designed to estimate leader’s states for each follower (suppose that only a few followers can obtain the states of leader) and a prescribed-time formation tracking controller is designed with the estimations of the observer to track leader. Both the observer and controller achieve the prescribed-time stability. Finally, a simulation example is proposed to verify the efficiency of the main results.

Time-varying formation tracking of multi-agent systems with multiple leaders based on aperiodic time-triggered intermittent control

In this article, the distributed aperiodic time-triggered intermittent control protocol (DATICP) is presented for the time-varying formation tracking of multi-agent systems (MASs) with multiple leaders. Firstly, we present the mathematical description of DATICP. The characteristic of DATICP lies in that for each agent, its control signal is updated at aperiodic sampling instants on work time intervals and disappears on rest time intervals. Secondly, based on a mixed time-dependent Lyapunov functional (MTLF), the exponential stability theorem of the derived system is established. Thirdly, according to the theorem, sufficient conditions are given to achieve time-varying formation tracking for MASs with multiple leaders by DATICP. As a result, a corollary is obtained which compromises conservativeness and complexity. Finally, two simulation examples are offered for illustration.

Time-Varying Group Formation Tracking for Multiagent Systems With Competition and Cooperation via Distributed Nash Equilibrium Seeking

Time-Varying Group Formation Tracking for Multiagent Systems With Competition and Cooperation via Distributed Nash Equilibrium Seeking

Observer-based guaranteed-cost bipartite time-varying formation tracking control for multiagent systems subject to communication delays

The paper centers on the guaranteed-cost bipartite time-varying formation tracking control for multiagent systems with nonuniform time-varying communication delays under the framework of a distributed observer. An integral quadratic cost function is presented, founded on formation tracking and observation error. Firstly, distributed state observers, using the relative measurement output between neighbors, are established so that the leader and follower can accurately estimate each agent's unmeasurable state. Subsequently, a bipartite formation tracking protocol is proposed, incorporating estimation information and nonuniform time-varying communication delays. This protocol aims to achieve bipartite time-varying formation tracking for multiagent systems. Next, a new augmented Lyapunov-Krasovskii functional with delay-product and triple integral terms is constructed. By integrating the second-order Bessel-Legendre inequality technique, the delay-dependent reciprocally convex combination inequality method, and the free weight matrix technique, a new guaranteed-cost bipartite time-varying formation tracking criterion is developed, offering less conservatism. Compared to certain existing delay conditions, the stability conditions assure a greater allowable upper bound of delay. Finally, a numerical example is conducted to confirm the validity and superiority of the theoretical findings.

Distributed weighted centroid formation tracking of multi-agent systems without velocity measurement

Distributed weighted centroid formation tracking of multi-agent systems without velocity measurement

Event-triggered finite-time formation tracking of multi-agent systems with mismatched disturbances under switching topologies

The formation tracking of the leader–follower multi-agent systems (MASs) under switching topologies is investigated. The considered system is exposed to both the mismatched and matched disturbances in the dynamics of the leader and followers, which places higher requirements for the robustness of the control protocol. In the presence of disturbances and leader’s unknown control input, an innovative distributed observer embedded with robust terms is designed firstly to estimate leader’s states in finite time. Taking account of the switching topologies, a novel analysis scheme that divides the convergence process into two stages is proposed to establish the finite-time (FT) convergence of estimation errors. Then, by virtue of a constructed auxiliary variable, a FT controller with an event-triggered mechanism is put forward, in which multiple robust feedback terms are designed wisely to suppress the mismatched and matched disturbances effectively. As a result, the FT formation tracking can be achieved with saved resources, despite perturbed environments and switching topologies. Simulation examples are presented to confirm the effectiveness of the proposed algorithm.

Fault-Tolerant Cooperative Bipartite Formation Tracking of Multiagent Systems on Signed Directed Networks With Actuator Faults

Fault-Tolerant Cooperative Bipartite Formation Tracking of Multiagent Systems on Signed Directed Networks With Actuator Faults

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

Leader-Following Formation Tracking of Multiagent Systems Using Adaptive Scaling Mechanism Under Spatial Constraints

Leader-Following Formation Tracking of Multiagent Systems Using Adaptive Scaling Mechanism Under Spatial Constraints

Multiple Transformation Matrix-Based Adaptive Projective Vortex Formation Tracking for Multiagent Systems With a Leader of Completely Unknown Input.

This article systematically studies projective vortex formation tracking (PVFT) of linear multiagent systems (MASs) on directed graphs through multiple transformation matrices, in which the input of leader and its upper bound information are not available to any follower. First, an innovative class of distributed adaptive observer is designed using the projection matrices to capture multiple desired virtual signals of the leader. Next, a novel kind of distributed PVFT protocol based on distributed observer, local observer and coordinates coupling matrices are proposed. Two different adaptive update mechanisms and nonlinear functions are introduced in the observer and controller to override the unknown input of the leader. Then, an algorithm is given, and the protocol under the algorithm is proved from three processes of estimation, aggregation, and rotation to enable linear systems to achieve PVFT. Finally, the effects of parameters on aggregation and rotation are analyzed systematically, and several simulation examples are given to illustrate the reliability of the results.

Fully Distributed Event/Self-Triggered Formation Tracking for Multiagent Systems Under Denial-of-Service Attacks

Fully Distributed Event/Self-Triggered Formation Tracking for Multiagent Systems Under Denial-of-Service Attacks

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.

Bipartite Time-Varying Output Formation Tracking for Multiagent Systems With Multiple Heterogeneous Leaders Under Signed Digraph

This article investigates the bipartite time-varying output formation tracking issue for heterogeneous linear multi-agent systems with multiple leaders under signed digraph. Different from previous related works, the leaders are considered to be heterogeneous, which greatly increases the difficulty of designing distributed control strategies. To address this issue, we develop a novel fully distributed dynamic event-triggered formation tracking control strategy and the Zeno behavior is ruled out. Compared with previous relevant results, in addition to addressing a more meaningful new issue, the developed control strategy also has the following advantages: 1) the control strategy gets rid of this assumption that each given follower must be well-informed or uninformed; 2) the adaptive gains do not increase unboundedly in the presence of external disturbances; 3) the inter-event time is larger. Moreover, a self-triggered realization based on sampled information is also formulated for the developed control strategy. Finally, the theoretical result is demonstrated by a simulation example.

Fully Distributed Dynamic Event-Triggered Bipartite Formation Tracking for Multiagent Systems With Multiple Nonautonomous Leaders.

Considering that cooperative interactions and antagonistic interactions between neighboring agents may exist simultaneously in practice, this article studies the bipartite time-varying output formation tracking (BTVOFT) problems for homogeneous/heterogeneous multiagent systems with multiple nonautonomous leaders under switching communication networks. First, a full-dimensional observer-based nonsmooth distributed dynamic event-triggered (DDET) output feedback control scheme is proposed to ensure that BTVOFT is achieved, and the Zeno behavior is excluded. Note that the nonsmooth distributed control scheme requires global communication network information and may cause unexpected chattering effect, and the design cost of full-dimensional observer is relatively high. Thus, a reduced-dimensional observer-based continuous fully DDET scheme is proposed. Compared with the existing event-triggered schemes, the dynamic event-triggered scheme can ensure larger interevent times by introducing an additional internal dynamic variable. Finally, the effectiveness and performance of the theoretical results are validated by numerical simulations.

Adaptive observer-based event-triggered finite time formation tracking for multi-agent systems with a non-cooperative leader

The event-triggered time-varying formation tracking for a class of second-order multi-agent systems (MASs) subject to a non-cooperative leader is investigated in this paper. First, in the presence of the unknown input of the leader and external disturbances, a distributed observer with adaptive parameters is put forward for followers to estimate the velocity tracking error. Then, based on the estimated tracking error and an auxiliary variable, a finite time formation controller is further constructed, which is updated depending on a pre-designed event-triggered mechanism. As a result, the desired time-varying formation configuration can be realized in finite time with less communication resource consumption. It’s noted that the constructed formation strategy doesn’t rely on any global information and thus is fully distributed. The stability of the controlled multi-agent system is proved rigorously and it’s verified that event-triggered intervals are with a positive lower bound. At last, simulations are carried out to illustrate the effectiveness of the presented algorithm.

Bipartite hybrid formation tracking control for heterogeneous multi-agent systems in multi-group cooperative-competitive networks

In this paper, the problem of bipartite hybrid formation tracking for multi-agent systems with heterogeneous groups is studied. First, the network structure problem of a cluster of agents with both group relationship and cooperation-competition relationship is discussed. Then, based on the leading-following method, the system model consisting of nonlinear second-order dynamic agents and first-order linear dynamic agents is determined. In this network system, the first group of second-order dynamic individuals needs to track their leader with unknown input and realizes the bipartite time-invariant formation, while the other group tracks its leader to realize the bipartite time-varying formation. To solve this problem, a new control protocol based on neighbor information and leader dynamics is designed. In addition, for first-order dynamic individual, a velocity estimator is introduced to estimate its velocity state. Next, algebraic graph theory and Lyapunov stability theory are used to prove that the formation error can approach arbitrary neighborhood of zero. Finally, the simulation results show the feasibility of the proposed conclusions and the effectiveness of the designed velocity estimator.

Formation Tracking of Multiagent Systems With Time-Varying Actuator Faults and Its Application to Task-Space Cooperative Tracking of Manipulators.

This article is concerned with a fault-tolerant formation tracking problem of nonlinear systems under unknown faults, where the leader's states are only accessible to a small set of followers via a directed graph. Under these faults, not only the amplitudes but also the signs of control coefficients become time-varying and unknown. The current setting will enhance the investigated problem's practical relevance and at the same time, it poses nontrivial design challenges of distributed control algorithms and convergence analysis. To solve this problem, a novel distributed control algorithm is developed by incorporating an estimation-based control framework together with a Nussbaum gain approach to guarantee an asymptotic cooperative formation tracking of nonlinear networked systems under unknown and dynamic actuator faults. Moreover, the proposed control framework is extended to ensure an asymptotic task-space coordination of multiple manipulators under unknown actuator faults, kinematics, and dynamics. Lastly, numerical simulation results are provided to validate the effectiveness of the proposed distributed designs.

Finite-Time Cooperative Control for Bearing-Defined Leader-Following Formation of Multiple Double-Integrators.

In this article, the finite-time cooperative control problem for leader-following bearing-defined formation tracking of multiagent systems with double-integrator dynamics is investigated. Different from the existing works on finite-time containment control, our objective is to make followers track leaders' trajectories and form a shape-preserving formation rather than a convex hull. The target formation is defined by both leaders' motions and bearing constraints among neighboring agents, which enables the formation not only to form and preserve a geometric pattern but also to have the ability to achieve both translational and scaling formation maneuver. To satisfy the bearing constraints, a matrix-weighted estimator/controller is developed. The finite-time stabilization of the target formation is achieved, though the matrix-weighted design makes the stability analysis complicated. Finally, an illustrative example is presented to demonstrate the effectiveness.

Distributed Time-Varying Group Formation Tracking for Multiagent Systems With Switching Interaction Topologies via Adaptive Control Protocols

In this article, time-varying group formation (TVGF) tracking problems for general linear multiagent systems (GLMASs) with switching interaction topologies are investigated. Different from previous studies, a novel TVGF tracking approach is proposed, where all agents are divided into three types: the virtual leader, the group leader, and the follower. The virtual leader is designed to assign the trajectory of GLMASs. Subgroups can be interacted with each other by cooperation among group leaders such that the relative configuration between different groups can be adjusted simultaneously. The followers in each group can achieve time-varying subformations. Moreover, under the influence of external disturbances and switching topologies, based on the distributed observer, two different distributed adaptive control protocols are constructed without using any global information such as the eigenvalue of the Laplacian matrix related to the communication topologies, the upper boundness of the leader’s input, and so on. The algorithms to determine parameters of control protocols are also presented. Furthermore, the closed-loop stability of GLMASs is proven by the Lyapunov theory. Finally, numerical simulations are given to verify the effectiveness of theoretical results.

Adaptive time-varying formation tracking for multi-agent systems with input saturation via low-gain feedback approach

In this paper, the time-varying formation tracking problem is addressed for a class of multi-agent systems, in which the input of followers is saturated and the input of the leader is unknown. Based on detectable state and undetectable state, a novel kind of protocols is proposed for solving time-varying formation tracking problem, without using any global information for the agents. Then, using the low-gain feedback approach and the Lyapunov stability theory, we can prove that the protocols steer the followers to accomplish and maintain the expected formation and track the leader under the appropriate assumptions. A numerical simulation is provided to verify the performance and effectiveness of our obtained main results.