Distributed Time-Varying Formation Research Articles

Fixed-time event-triggered sliding mode time-varying formation control for multiple surface vessels with fast convergence

ABSTRACT This paper proposes a new fixed-time sliding mode time-varying formation control strategy for multiple surface vessels (MSVs) to improve control performance and ensure navigation safety. First, a fixed-time extended state observer (FxESO) is designed to provide estimations of velocities and lumped disturbances. Then, the event-triggered fixed-time distributed time-varying formation control law is designed based on prescribed performance function (PPF) and fixed-time nonsingular terminal sliding mode (FxNTSM) manifold. Finally, system stability is analyzed based on Lyapunov theory. The salient features of the proposed scheme are as follows. First, a novel hyperbolic cosecant PPF is incorporated into the control scheme to enhance control performance. Then, the proposed scheme is combined with relative threshold event-triggered strategy to reduce unnecessary updates of actuators. Finally, a uniform exact differentiator is introduced to avoid the formation control law including the acceleration of adjacent vessel. Comparative results are given to demonstrate the superiority of the proposed scheme.

Time-varying formation for MSVs with input and prescribed performance constraints by fixed-time event-triggered sliding mode control

This work develops a new fixed-time sliding mode time-varying formation control strategy for multiple surface vessels (MSVs) to improve the control performance, ensure the navigation safety and reduce the communication burden. At first, a fixed-time adaptive radial basis function neural network (FxRBFNN) observer is designed to provide the estimations for external environmental disturbances and model parameters uncertainties. Then, observer-based fixed-time distributed time-varying formation event-triggered control law is proposed based on the novel fixed-time auxiliary dynamic system (FxADS), the proposed prescribed performance function, the designed fixed-time nonsingular terminal sliding mode (FxNTSM) manifold and the proposed uniform exact differentiator. Finally, the system stability is proved by Lyapunov theory. The salient features as follows. First, to enhance the convergence performance for time-varying formation control method, a novel hyperbolic cosecant prescribed performance function (PPF) is introduced. Second, a novel FxADS is proposed to confront input constraints. Third, the proposed scheme is combined with a relative threshold event-triggered strategy to reduce the unnecessary updates of actuators under the premise of ensuring the control performance. Fourth, to avoid the proposed formation control law including adjacent vessel accelerations, this work proposed an improved uniform exact differentiator to identify them. Numerical simulations confirm that the proposed scheme has superior control performance.

Cooperative Time-Varying Formation Fuzzy Tracking Control of Multiple Heterogeneous Uncertain Marine Surface Vehicles With Actuator Failures.

This article addresses the cooperative time-varying formation fuzzy tracking control problem for a cluster of heterogeneous multiple marine surface vehicles subject to unknown nonlinearity and actuator failures. The proposed cooperative control scheme consists of two parts: 1) a distributed time-varying formation observer and 2) a decentralized adaptive fuzzy tracking controller. The distributed observer is designed to obtain a predefined time-varying formation pattern under a directed communication topology. Subsequently, based on the states of the distributed observer, a decentralized fuzzy tracking control law is developed using fuzzy-logic systems and the adaptive approach. Lyapunov functions are constructed to guarantee that the controlled marine vehicles attain the desired time-varying formation with asymptotical stability of tracking errors. Finally, simulation results are presented to validate the efficacy of the proposed control methodology.

Time-Varying Optimization-Based Approach for Distributed Formation of Uncertain Euler-Lagrange Systems.

We investigate a distributed time-varying formation control problem for an uncertain Euler-Lagrange system. A time-varying optimization-based approach is proposed. Based on this approach, the robots can achieve the expected formation configuration and meanwhile optimize a global objective function using only neighboring and local information. We consider the time-varying optimization where the objective functions can change in real time. In this case, the consensus-based formation tracking control issues and formation containment tracking control issues in the literature can be solved by the proposed approach. By a penalty-based method, the robots' states asymptotically converge to the estimated optimal solution to an equivalent time-varying optimization problem, whose optimal solution can achieve simultaneous formation and optimization. Furthermore, we consider two more general scenarios: 1) the local objective functions can have non-neighbor's information and 2) the optimization problems can have inequality constraints.

Time-varying formation control of multiple unmanned surface vessels with heterogeneous hydrodynamics subject to actuator attacks

This paper studies the time-varying formation for multiple unmanned surface vessels (USVs) with heterogeneous hydrodynamics under actuator attacks. Firstly, the distributed time-varying formation is achieved under a formation feasibility condition. Secondly, an extended state observer (ESO) is devised to estimate the heterogeneous hydrodynamics and the external time-varying disturbance of multiple USVs, as well as the unknown control input of the leader USV simultaneously based on the neighbor USVs’ relative information; Thirdly, a distributed security controller is jointly designed based on the relative information of neighbors with the presence of an additive adaptive correction term to suppress the effects of actuator attacks instead of redesigning the nominal controller; Finally, the effectiveness of the derived theoretical method is demonstrated by simulation results.

Completely Distributed Time-Varying Formation Target Tracking for Quadrotor Team via Image-Based Visual Servoing

In this article, the completely distributed adaptive time-varying formation target tracking control problem for quadrotor team via image-based visual servoing is addressed. An adaptive cascade formation controller is proposed, which consists of a trajectory tracking controller, an attitude controller, and an image-based visual servoing controller. All the controllers consist of a nominal part to achieve the desired performance and a robust part to retrain the influence of parameter uncertainties and external disturbance. The robust properties of the closed-loop control system are proven via the theoretical analysis. Moreover, the simulation results validate the effectiveness of the proposed formation tracking control protocol in this paper.

Collision Avoidance and Connectivity Preservation for Time-Varying Formation of Second-Order Multi-Agent Systems With a Dynamic Leader

In this paper, the problem of time-varying formation tracking control, with collision avoidance (CA) and connectivity preservation (CP), is studied for second-order multi-agent systems. Consider the unknown control input of virtual leader, an estimator is introduced to design a distributed time-varying formation tracking control protocol, while relaxing the condition the leader’s velocity is constant. Different from some existing results, relative velocity-based action function is designed such that both CA and CP with small negative effects on formation are achieved, and a simpler method is proposed to eliminate the large jump and discontinuity of potential field force. Furthermore, the Lyapunov-like approach is used for the stability analysis and the theoretical results are derived. Accordingly, it is demonstrated that velocity tracking errors can asymptotically converge to 0, and steady-state position tracking errors are bounded and related to initial state. Finally, two simulation examples verify the effectiveness of theoretical results.

Fully Distributed Time-Varying Formation Control for Multiple Uncertain Missiles

The article addresses the fully distributed time-varying formation control problem for multiple missiles involving uncertainties. An adaptive control protocol is developed for the missiles, which includes uncertainties in the flight dynamics, while the adaptive control protocol does not require global information of the network missile system. Global formation flight stability is proven via the Lyapunov theory. Simulation tests are performed to validate the effectiveness of the developed protocol as applied to the network system.

Distributed Time-Varying Formation Control for Linear Swarm Systems With Switching Topologies Using an Adaptive Output-Feedback Approach

Fully distributed time-varying formation (TVF) control problems are addressed in this paper using an adaptive output-feedback approach for general linear swarm systems with fixed and switching topologies. In contrast to the earlier results on formation control problems, the general linear swarm system can achieve the predefined TVF using only local output information and independent of the Laplacian matrix associated with the communication topologies. The implementation cost of calculating the global information and requiring full state information is avoided when achieving the desired TVF. First, a node-based TVF control protocol is constructed via dynamic output feedback for the case with fixed communication topology, where adaptive-based coupling weights are introduced to eliminate the dependence on the global information about the topology. Then an algorithm is presented to determine the gain matrices in the node-based adaptive TVF control protocol, and a feasible formation constraint is provided. The stability of the algorithm is proved based on the Lyapunov theory. Furthermore, under the case of switching communication topologies, an edge-based TVF control protocol is constructed with dynamic output feedback and an adaptive law for adjusting the coupling weights among agents. A sufficient condition is derived using the common Lyapunov theory for general linear swarm systems to achieve the predefined TVF satisfying the feasible formation constraint. Two numerical examples are presented to illustrate the theoretical results.

Path-guided time-varying formation control with collision avoidance and connectivity preservation of under-actuated autonomous surface vehicles subject to unknown input gains

This paper investigates the distributed time-varying formation control for a swarm of under-actuated autonomous surface vehicles subject to unknown input gains, in addition to model uncertainties and ocean disturbances. The fleet is required to follow a parameterized path with a time-varying formation while avoiding collisions and maintaining connectivity at a complex sea environment. At the kinematic level, a distributed guidance control law is proposed based on a consensus approach, a path-following design, artificial potential functions, and an auxiliary variable approach. At the kinetic level, an adaptive kinetic control law is designed based on an indirect model reference adaptive control approach where a neural estimator is developed for identifying unknown input gains, model uncertainties and ocean disturbances. The stability of the closed-loop system is proven via cascade stability analysis. The advantage of the proposed method is three-folds. First, the developed time-varying formation controller is able to achieve various coordinated behaviors such as cooperative target tracking and target enclosing. Second, the proposed time-varying formation controller is robust against model uncertainties, ocean disturbances and unknown input gains. Third, the proposed distributed controller holds the capability of collision avoidance and connectivity preservation. Simulation results substantiate the effectiveness of the proposed path-guided time-varying formation controllers.

Distributed Time-Varying Formation Control for Multiagent Systems With Directed Topology Using an Adaptive Output-Feedback Approach

This paper addresses fully distributed formation control problems for high-order linear multiagent systems (MASs) with directed communication topology. In order to overcome the shortcomings of designing time-varying formation (TVF) protocols via the global information of the communication network and the full states of all the agents in existing formation results, a novel adaptive TVF protocol is developed. First, dynamic output feedback information and sequential observers are used to construct the adaptive TVF protocol. Then, a distributed algorithm which includes a TVF feasibility constraint is proposed. Only local outputs of neighboring agents are used in the algorithm. Moreover, applying the proposed approach and the Lyapunov stability theory, it is found that the fully distributed TVF can be achieved. Finally, numerical simulations are given to demonstrate the theoretical results.

Distributed Time-Varying Formation Robust Tracking for General Linear Multiagent Systems With Parameter Uncertainties and External Disturbances.

This paper investigates the time-varying formation robust tracking problems for high-order linear multiagent systems with a leader of unknown control input in the presence of heterogeneous parameter uncertainties and external disturbances. The followers need to accomplish an expected time-varying formation in the state space and track the state trajectory produced by the leader simultaneously. First, a time-varying formation robust tracking protocol with a totally distributed form is proposed utilizing the neighborhood state information. With the adaptive updating mechanism, neither any global knowledge about the communication topology nor the upper bounds of the parameter uncertainties, external disturbances and leader's unknown input are required in the proposed protocol. Then, in order to determine the control parameters, an algorithm with four steps is presented, where feasible conditions for the followers to accomplish the expected time-varying formation tracking are provided. Furthermore, based on the Lyapunov-like analysis theory, it is proved that the formation tracking error can converge to zero asymptotically. Finally, the effectiveness of the theoretical results is verified by simulation examples.

Distributed Time-Varying Formation Tracking Analysis and Design for Second-Order Multi-Agent Systems

Distributed time-varying formation tracking analysis and design problems for second-order multi-agent systems with one leader are studied respectively, where the states of followers form a predefined time-varying formation while tracking the state of the leader. Different from the previous results on formation tracking control, the formation for the followers can be described by specified time-varying vectors and the trajectory of the leader can also be time-varying. A distributed formation tracking protocol is constructed using only neighboring relative information. Necessary and sufficient conditions for second-order multi-agent systems with one leader to achieve time-varying formation tracking are proposed by utilizing the properties of the Laplacian matrix, where the formation tracking feasibility constraint is also given. An approach to design the formation tracking protocol is proposed by solving an algebraic Riccati equation. The presented results can be applied to deal with the target enclosing problems and consensus tracking problems for second-order multi-agent systems with one target/leader. An application in the target enclosing of multiple vehicles is provided to demonstrate the effectiveness of the theoretical results.

Time-varying formation control for second-order swarm systems with switching directed topologies

Formation control problems for second-order swarm systems with general directed topologies are addressed in this paper, where the desired formation can be time-varying and the directed topology can be switching. Firstly, a distributed time-varying formation control policy using local neighboring state information is proposed. Then an algorithm to design the policy with switching directed topologies is presented. Sufficient conditions for second-order swarm systems to achieve the predefined time-varying formation under the designed policy are derived based on the piecewise Lyapunov function theory, where the formation feasibility constraint and the threshold for the dwell time are proposed, respectively. Moreover, an explicit expression of the formation reference function is obtained to describe the macroscopic trajectory of the whole time-varying formation under the influence of the switching directed topologies. Finally, a numerical simulation is provided to demonstrate the effectiveness of the obtained results.