Directed Interaction Topologies Research Articles

Fully Distributed Cooperative Circumnavigation of Networked Unmanned Aerial Vehicles

In this article, cooperative circumnavigation (CCN) is studied for groups of networked unmanned aerial vehicles (UAVs) under a directed interaction topology. The CCN drives UAVs to given planar ellipses with desired spatial formation. A first contribution is that based on affine transformations, CCN control design is structured, which can deploy UAVs on spatial orbits with different radii concerning a moving target in 3-D space. Second, no global information, such as the formation center, the desired radius, the angular velocity of circumnavigation, etc., is needed for any follower UAVs since they are completely maneuvered by the leader UAVs.

Fully distributed time-varying formation tracking control for multiple quadrotor vehicles via finite-time convergent extended state observer

This paper investigates a time-varying anti-disturbance formation problem for a group of quadrotor aircrafts with time-varying uncertainties and a directed interaction topology. A novel Finite-Time Convergent Extended State Observer (FTCESO) based fully-distributed formation control scheme is proposed to enhance the disturbance rejection and the formation tracking performances for networked quadrotors. By adopting the hierarchical control strategy, the multi-quadrotor system is separated into two subsystems: the outer-loop cooperative subsystem and the inner-loop attitude subsystem. In the outer-loop subsystem, with the estimation of disturbing forces and uncertain dynamics from FTCESOs, an adaptive consensus theory based cooperative controller is exploited to ensure the multiple quadrotors form and maintain a time-varying pattern relying only on the positions of the neighboring aircrafts. In the inner-loop subsystem, the desired attitude generated by the cooperative control law is stably tracked under a FTCESO-based attitude controller in a finite time. Based on a detailed algorithm to specify the cooperative control protocol, the feasibility condition to achieve the time-varying anti-disturbance formation tracking is derived and the rigorous analysis of the whole closed-loop multi-quadrotor system is given. Some numerical examples are conducted to intuitively demonstrate the effectiveness and the improvements of the proposed control framework.

Time-varying formation control for UAV swarm with directed interaction topology and communication delay

Time-varying formation control for UAV swarm with directed interaction topology and communication delay

Layered Affine Formation Control of Networked Uncertain Systems: A Fully Distributed Approach Over Directed Graphs.

Distributed formation control is presented for networked Euler-Lagrange systems (ELSs) over a directed interaction topology. This problem is defined by a layered framework in which information flow both among the leaders and among the followers is described by different layers. To empower the formation to make a variety of geometric transformations, we present the necessary and sufficient conditions for affine maneuverability under a directed graph. Unlike most existing results using a diagonal stabilizing matrix to achieve the stabilizability of affine formation, this fully distributed approach is feasible without any global information. Next, we propose an adaptive control law for agents in each layer, where the closed-loop errors are driven to a neighborhood of the origin in finite time. Adaptive neural networks are integrated to tackle the model uncertainties in ELSs by updating the norm of the weight matrix, which can simplify the control design and alleviate the computational burden compared with traditional ones. The simulation results are given to show the effectiveness of the proposed approach.

Distributed containment control of singular heterogeneous multi-agent systems

This paper investigates the containment control problem of singular heterogeneous multi-agent systems under directed interaction topology. Firstly, a distributed observer, in which the eigenvalue information of the leaders is not needed, is proposed to estimate the convex hull spanned by the states of the leaders. Secondly, state feedback control and reduced-order normal observer based output feedback control are presented, respectively. Finally, some numerical simulation examples are performed to demonstrate the efficiency of the proposed theoretical results.

Distributed fixed-time consensus-based formation tracking for multiple nonholonomic wheeled mobile robots under directed topology

This paper investigates the distributed fixed-time consensus-based formation tracking problems for multiple nonholonomic wheeled mobile robots under a directed interaction topology. The distributed fixed-time consensus-based controllers under the directed interaction topology are proposed for the multiple wheeled mobile robots with nonholonomic constraints, which can guarantee the group of robots converge to a predefined formation pattern with its centroid moving along the predefined reference trajectory in a fixed time. The fixed-time formation tracking can be achieved within a fixed settling time, which is independent of the initial states of the whole system. Moreover, the conditions of formation stability control are analysed by utilising graph and Lyapunov stability theories. Finally, the feasibility of the proposed distributed controllers is verified by numerical simulation.

Integral sliding-mode fixed-time consensus tracking for second-order non-linear and time delay multi-agent systems

In this paper, fixed-time consensus tracking problems under directed interaction topologies for second-order non-linear multi-agent systems with disturbance and second-order multi-agent systems with input delay are investigated. Two continuous integral terminal sliding modes are designed, which can effectively eliminate the singularity and chattering. Correspondingly, two fixed-time distributed control protocols are proposed based on the designed continuous ITSM to ensure that the consensus tracking are achieved in fixed-time. It is shown that the upper bounds of settling time are regardless of initial conditions. The rigorous proofs are given by employing Lyapunov stability theory and fixed-time stability theory. Simulations are provided to verify the effectiveness of the theoretical results.

Observer-Based Time-Varying Formation Control of Fractional-Order Multi-Agent Systems With General Linear Dynamics

This brief addresses the time-varying formation control (TVFC) problem for fractional-order multi-agent systems (MASs) with general linear dynamics under fixed and switching directed interaction topologies respectively, where the fractional-order $\alpha $ satisfies a general condition of ${\alpha \in (0,n]}$ . Considering only the output information are available, the observer-based distributed control protocols are proposed to realize TVFC. By a class of linear transformations, the TVFC problem converts into the asymptotical stability problem of a new system. Sufficient conditions for fractional-order MASs are derived by employing the stability theory of fractional-order systems, matrix theory, algebraic graph theory, Laplace transformation, and Mittag–Leffler function. Finally, two numerical simulations are presented to validate the theoretical analysis.

Cluster-Based Cooperative Output Regulation of Linear Multi-Agent Systems

This paper is concerned with the cooperative output regulation problem for multi-agent systems under the directed interaction topology. Comparing with the existing work where the exosystem is common for all the agents, a scenario in which the agents track multiple trajectories with different exogenous signals is considered. The main aim of the study is focused on the design of distributed feedback control laws, such that the agents in diverse clusters track the different reference trajectories exponentially, while rejecting the disturbances asymptotically. Considering that all the agents in each cluster cannot access the exogenous signal, the cooperative output regulation problem of the linear single-integrator agents is solved by devising a distributed state feedback control scheme. Furthermore, it is considered that all the states of the plant cannot be accessed by the agents within each cluster either, the cooperative output regulation problem of linear agents is solved by designing a distributed output feedback controller. Sufficient solvability conditions for those two problems are established, which are shown to be necessary and sufficient under some constraints.

Time-Varying Formation Control for Second-Order Discrete-Time Multi-Agent Systems With Directed Topology and Communication Delay

Time-varying formation control protocol design and analysis problems for the second-order discrete-time multi-agent systems with directed interaction topology and communication delay are investigated. A local information-based distributed protocol is designed by utilizing the delayed state information of neighbors. Through system decomposition and stability analysis, an explicit description of the feasible time-varying formation set is given. Necessary and sufficient conditions for the systems with the directed topology and communication delay to achieve time-varying formation are obtained, which are related to the topology of the interaction graph and the feasibility of the predefined formation. Necessary constraints on the gain parameters and the sampling period are proposed, so as to guide the design of parameters in the protocol. The numerical simulation results indicate that the protocol can steer the agents to accomplish the desired time-varying formation and effectively tolerate the relatively large bounded communication delay. Outdoor experiment with quadrotors is presented to demonstrate the effectiveness of the obtained theoretical results with one sampling period delay.

Sliding Mode Formation Control of Nonlinear Multi-agent Systems with Local Lipschitz Continuous Dynamics

In this paper, the multi-agent formation problem of networked nonlinear multi-agent systems with local Lipschitz continuous dynamics under directed interaction topology, is investigated. Based on the nonlinear dynamics satisfying locally Lipschitz continuous conditions, three kinds of sliding mode controllers are proposed to solve the problem of multi-agent formation control. Using integral sliding mode controller in first-order system, formation shape is achieved within finite time. For second-order system, on the one hand, non-singular terminal sliding mode function is adopted to accomplish the system asymptotic convergence. Furthermore, super-twisting algorithm is proposed to make multi-agent achieve the desired formation within finite time. Lyapunov functions are applied in the whole paper to ensure the system stability. Numerical simulation examples are provided to demonstrate the effectiveness of the proposed sliding mode control methods.

Time-Varying Formation Tracking for UAV Swarm Systems With Switching Directed Topologies

Time-varying formation tracking (TVFT) control problems for a team of unmanned aerial vehicles (UAVs) with switching and directed interaction topologies are investigated, where the follower UAVs realize a given time-varying formation while tracking the leader UAV. A TVFT control protocol is firstly constructed utilizing local neighboring information, where the information of the leader UAV is only available to partial followers and the neighborhood can be switching. An algorithm composed of four steps is provided to design the TVFT protocol. It is proved that the UAV swarm system can realize the TVFT using the designed protocol if the dwell time for the switching directed topologies is larger than a fixed threshold and the TVFT feasibility condition is satisfied. Based on the ultrawideband positioning technology, a quadrotor UAV formation control platform with four quadrotor UAVs is given. The obtained theoretical results are applied to solve the target enclosing problems of the UAV swarm systems. A flying experiment for three follower quadrotor UAVs to enclose a leader quadrotor UAV is carried out to verify the effectiveness of the presented results.

Distributed output-feedback consensus control of multi-agent systems with dynamically changing directed interaction topologies

This paper considers the distributed output-feedback consensus control problem for a multi-agent system with higher order linear dynamics and subject to external disturbance, under dynamically changing directed topologies and weighting factors. An extended state observer (ESO) is first designed to estimate not only the unmeasurable agent states but also the external disturbance. Based on the output of the ESO, a novel distributed control protocol is proposed. We show that, with the application of the proposed control protocol, the consensus can be achieved asymptotically by the group of agents if the union of the directed interaction graphs contains a spanning tree frequently enough. A numerical example is given to verify the effectiveness of the theoretical results.

On the consensus tracking investigation for multi-agent systems on time scale via matrix-valued Lyapunov functions

This paper is devoted to the leader–follower consensus problem for high-order multi-agent systems with inherent nonlinear dynamics evolving on an arbitrary time domain. This problem is investigated using the time scale theory. Based on this theory, some sufficient conditions are derived to guarantee that the tracking errors exponentially converge to zero using the concept of matrix-valued Lyapunov functions when directed interaction topology is considered. An academic example is given to illustrate the pertinence and the feasibility of the theoretical results.

Adaptive cooperative formation control of autonomous surface vessels with uncertain dynamics and external disturbances

This paper investigates the leader-follower cooperative formation control problem of autonomous surface vessels (ASVs) with uncertain dynamics and external disturbances. Especially, ASVs can communicate with each other under a directed interaction topology. Based on directed graph theories, backstepping and the minimal learning parameter (MLP) algorithm, a novel distributed robust formation controller with two different adaptive laws is developed for each ASV. Dynamic surface control (DSC) is utilized to eliminate repeated derivative of virtual control laws, which is important to generate real-time control signals. Neural networks (NNs) approximation combined with an MLP-based adaptive law is incorporated into the proposed controller to enhance the robustness against model uncertainties. Then only one learning parameter instead of the enormous weights matrix is estimated for each ASV. An auxiliary adaptive law is designed to obtain a continuous controller when compensating approximation errors and disturbances. It is shown that desired formation shapes can be achieved with the proposed controller if the interaction topology has a directed spanning tree, and formation errors are guaranteed to be semi-global uniformly ultimately bounded (SGUUB). Simulations and comparison results are provided to illustrate the effectiveness of theoretical results.

Practical time‐varying formation tracking for multiple non‐holonomic mobile robot systems based on the distributed extended state observers

Practical time-varying formation tracking analysis and design problems for multiple non-holonomic mobile robot systems with directed interaction topologies are investigated by using the distributed extended state observers, where the practical time-varying formation tracking error is controlled within an arbitrary small bound. Different from the previous work, the dynamics of each robot is non-holonomic and the followers are required to form the practical time-varying formation with respect to the leader of unknown control inputs. Besides, the disturbances and the uncertainties are considered in the dynamic model of the follower. Distributed extended state observers are constructed by using only the neighbouring relative information to estimate both the state and the unknown control inputs of the leader simultaneously. A practical time-varying formation tracking protocol is presented based on the distributed extended state observers. The gain matrices of the observers in the practical time-varying formation tracking protocol can be obtained by solving three linear matrix inequalities. Moreover, the stability of the multiple non-holonomic mobile robot system under the proposed protocol is proved by using the properties of the Laplacian matrix and the Lyapunov stability theory. Finally, two numerical simulation examples are given to illustrate the effectiveness of the obtained theoretical results.

Formation Tracking Control of Second-Order Multi-Agent Systems With Time-Varying Delay

This paper considers the problem on formation tracking control of second-order multi-agent systems (MASs) with communication time-varying delay. Sufficient conditions on the directed interaction topology and existence of the feedback gains to ensure the desired control are presented. Through choosing two augmented Lyapunov–Krasovskii (L–K) functionals and using some novel Wirtinger-based integral inequalities, the previously ignored information can be reconsidered and the application area of derived results can be greatly extended. Moreover, a novel constructive technique is given to compute out the controller gain by resorting to solving the achieved linear matrix inequalities (LMIs). Finally, a numerical example with comparisons and simulations is provided to illustrate the obtained results.

Distributed Fault-Tolerant Time-Varying Formation Control for Second-Order Multi-Agent Systems With Actuator Failures and Directed Topologies

This brief investigates the distributed fault-tolerant time-varying formation control problems for second-order multi-agent systems with directed interaction topologies in the presence of both bias and loss of effectiveness actuator failures. Using the adaptive updating mechanism and the boundary layer theory, a continuous fault-tolerant formation control protocol is constructed to compensate for the actuator failures and the derivative of the time-varying formations. The proposed protocol is totally distributed without requiring any global knowledge about the interaction topologies or the bounds of the actuator failures. The formation feasible condition is provided, and it is proved that the formation errors are uniformly bounded and can converge to an adjustable small neighborhood of zero by the proposed continuous protocol under the influences of actuator failures.

Formation-containment control for multi-robot systems with two-layer leaders via hierarchical controller–estimator algorithms

This paper studies the formation-containment control for multi-robot systems with two-layer leaders in the presence of parametric uncertainties, input disturbances and directed interaction topologies. To cope with the aforementioned issues, we establish a novel formation-containment control framework, where the analysis of the systems is carried out step by step. A hierarchical controller–estimator (HCE) algorithm, containing distributed sliding-mode estimators in each sub-algorithm, is proposed for the two-layer leaders system. Moreover, by invoking finite-time stable and input-to-state stable theories, the sufficient conditions for convergence of the proposed HCE algorithm are presented. Finally, numerous simulations are performed to demonstrate the validity of the theoretical results.

Practical time‐varying formation tracking for high‐order nonlinear multiagent systems with multiple leaders based on the distributed disturbance observer

SummaryPractical time‐varying formation tracking analysis and design problems for high‐order nonlinear multiagent systems with directed interaction topologies are investigated by using the distributed disturbance observer, where the time‐varying formation tracking error can be controlled within an arbitrarily small bound. Different from the previous work, there exists a predefined time‐varying formation formed by the states of the followers and the formation tracks the convex combination of the states of the leaders with unknown control inputs. Besides, the leaders can be multiple, and the dynamics of each follower has heterogeneous nonlinearity and disturbance. First, a distributed disturbance observer‐based practical time‐varying formation tracking protocol is constructed using neighboring relative information, where only a part of the followers, which are named as well‐informed ones, are required to obtain the information of the multiple leaders. The proposed protocol can process the heterogeneous nonlinearity, the disturbance of each follower, and the unknown control inputs of the leaders simultaneously. Then, an algorithm with 2 steps is presented to design the practical time‐varying formation tracking protocol by solving an algebraic Riccati equation and an algebraic equation, where the time‐varying formation tracking feasibility condition is introduced. Moreover, the stability of the closed‐loop multiagent system under the proposed protocol is proved by using the properties of the Laplacian matrix and the Lyapunov stability theory. Finally, a numerical simulation example is provided to illustrate the effectiveness of the obtained theoretical results.