Fixed-time Formation Control Research Articles

Safety-Critical Fixed-Time Formation Control of Quadrotor UAVs with Disturbance Based on Robust Control Barrier Functions

This paper focuses on the safety-critical fixed-time formation control of quadrotor UAVs with disturbance and obstacle collision risk. The control scheme is organized in a distributed manner, with the leader’s position and velocity being estimated simultaneously by a fixed-time distributed observer. Meanwhile, a disturbance observer that combines fixed-time control theory and sliding mode control is designed to estimate the external disturbance. Based on these techniques, we design a nominal control law to drive UAVs to track the desired formation in a fixed time. Regarding obstacle avoidance, we first construct safety constraints using control barrier functions (CBFs). Then, obstacle avoidance can be achieved by solving an optimization problem with these safety constraints, thus minimally affecting tracking performance. The main contributions of this process are twofold. First, an exponential CBF is provided to deal with the UAV model with a high relative degree. Moreover, a robust exponential CBF is designed for UAVs with disturbance, which provides robust safety constraints to ensure obstacle avoidance despite disturbance. Finally, simulation results show the validity of the proposed method.

Event-Based Adaptive NN Fixed-Time Cooperative Formation for Multiagent Systems.

This article focuses on the fixed-time formation control problem for nonlinear multiagent systems (MASs) with dynamic uncertainties and limited communication resources. Under the framework of the backstepping method, a time-varying formation function is introduced in the controller design. To attain the prescribed transient and steady-state performance of MASs, a fixed-time prescribed performance function (FTPPF) is designed and the further coordinate transformation addressing the zero equilibrium point problem is removed. To achieve better approximating performance, a neural network (NN)-based composite dynamic surface control (CDSC) strategy is proposed, where the CDSC scheme is consisted of prediction errors and serial-parallel estimation models. According to the signals generated by the estimation models, disturbance observers are established to overcome the difficulty from approximating errors and mismatched disturbances. Moreover, an improved dynamic event-triggered mechanism and varying threshold parameters are constructed to reduce the signal transmission frequency. Via the Lyapunov stability theory, all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, the simulation results verify the effectiveness of the developed CDSC strategy.

Event-Triggered Distributed Adaptive Fixed-Time Formation Control of QUAVs With Input Constraints

Event-Triggered Distributed Adaptive Fixed-Time Formation Control of QUAVs With Input Constraints

Adaptive fuzzy fixed time formation control of state constrained nonlinear multi-agent systems against FDI attacks.

In this manuscript, based on nonlinear multi-agent systems (MASs) with full state constraints and considering security control problem under false data injection (FDI) attacks, the fixed-time formation control (FTFC) protocol was designed, which can ensure that all agents follow the required protocol within a fixed time. Fuzzy logic system (FLS) was used to compensate and approximate the uncertain function, which improved safety and robustness of the formation process. Finally, the fixed-time theory and Lyapunov stability theory were addressed to prove the effectiveness of the proposed method, and simulation examples verified the effectiveness of the theory.

Fixed-Time Formation Control of Multiple Wheeled Mobile Robots for Circumnavigating a Moving Target

Fixed-Time Formation Control of Multiple Wheeled Mobile Robots for Circumnavigating a Moving Target

Distributed fixed-time formation control for heavy haul trains based on sliding mode control

The problem of distributed fixed-time formation control for heavy haul trains is proposed in this paper. Firstly, a train-following model of multiple heavy haul trains with considering uncertain resistance and unknown disturbances is established, and the information transmission between heavy haul trains follows a predecessor-following topology. Then, based on fixed-time sliding mode control and adaptive control theories, a novel distributed fixed-time formation controller for heavy haul trains is designed. Finally, the control effects of the proposed controller are verified and analyzed by simulations. It is shown that the proposed fixed-time formation controller has more advantages in terms of convergence speed and convergence accuracy compared to the nonfinite-time formation controller. Besides, the convergence time is not affected by the initial state of the trains.

Fixed-time velocity-free safe formation control of AUVs with actuator saturation and unknown disturbances

This paper designs a fixed-time formation control law for multiple autonomous underwater vehicle (AUV) system (MAS) subjected to unmeasurable velocities, actuator saturation and time-varying disturbances. To address these challenges, the actuator saturation and time-varying disturbances are initially integrated into lumped disturbances, the initial step is to integrate actuator saturation and time-varying disturbances into lumped disturbances, followed by designing a fixed-time extended state observer (FTESO) to estimate the unavailable velocities and the lumped disturbances in fixed time. Moreover, a nonlinear filter is also utilized to eliminate the problem of computational explosion that arises due to derivatives in the controller design process. Additionally, a tan-type barrier Lyapunov function (TT-BLF) is presented to constrain the tracking errors within a predetermined time-varying constraint function. Then, a novel fixed-time formation control algorithm based on FTESO and TT-BLF is further designed to ensure that the formation tracking errors converge to a small neighborhood near origin in fixed time, and the fast formation task can be completed within a fixed time. Finally, the simulation experiments verify the effectiveness of the proposed controller.

Cross-Domain Fixed-Time Formation Control for an Air-Sea Heterogeneous Unmanned System with Disturbances

This paper studied the cross-domain fixed-time formation control problem of an air-sea heterogeneous unmanned system (ASHS). Taking advantage of individual characteristics of unmanned aerial vehicles (UAVs), unmanned surface vehicles (USVs), and unmanned underwater vehicles (UUVs), the ASHS was introduced to accomplish the ocean stereoscopic observation mission, which was transformed into the formation control problem. Due to the difference of dimension and the communication constraint between UAV, USV, and UUV, a cross-domain communication protocol was proposed to achieve the state information flow between heterogeneous unmanned vehicles with different dimensions rather than construct the identical low-dimensional output. The high-dimensional unmanned vehicle can receive full state information from low-dimensional neighbors, while the low-dimensional follower can only receive partial state information from high-dimensional neighbors. Moreover, by means of fixed-time control theory and the backstepping control technique, the distributed fixed-time observer and controller were designed to solve the formation control problem for the ASHS with disturbances. Simulation results show that the ASHS can achieve fixed-time formation control with the proposed coordinated control protocols. Meanwhile, the convergence time of the proposed fixed-time formation control protocols is independent of the initial state.

Continuous fixed-time formation control for AUVs using only position measurements

Continuous fixed-time formation control for AUVs using only position measurements

Fixed-time formation control for AUVs with unknown actuator faults based on lumped disturbance observer

Fixed-time formation control for AUVs with unknown actuator faults based on lumped disturbance observer

Fast fixed-time nonsingular terminal sliding-mode formation control for autonomous underwater vehicles based on a disturbance observer

In this paper, a novel disturbance observer-based fixed-time formation control method is proposed for autonomous underwater vehicles with actuator faults, model uncertainties and unknown disturbances. Firstly, a fast fixed-time stable system is improved, which has a faster convergence rate than existing stable system. Then, the leader-follower formation control strategy is combined with the path planning strategy based on the artificial potential field to obtain a collision-free formation configuration. Besides, a fast fixed-time disturbance observer is designed to compensate for unknown composite disturbances, which enhances the robustness of the system. Further, based on the disturbance estimation information and the improved nonsingular fast fixed-time terminal sliding-mode surface, a robust fast fixed-time formation control method is presented, which achieves the desired formation configuration. Finally, simulation and comparison results show the effectiveness of the proposed control strategy.

Fixed-Time Fault-Tolerant Formation Control for a Cooperative Heterogeneous Multiagent System With Prescribed Performance

This article investigates the fixed-time fault-tolerant formation control problem of a leader–follower heterogeneous multiagent system (HMAS), including multiple unmanned aerial vehicles (UAVs) and multiple unmanned ground vehicles (UGVs) under loss of effectiveness actuator faults and disturbances. Different from the existing fixed-time formation results, to realize the special application, a finite-time performance function (FTPF) is considered, which can guarantee that formation error converges to a prescribed arbitrarily small region within a known time. Then, based on sliding mode control and bi-limit homogeneity, distributed and decentralized fixed-time formation control algorithms are constructed for the HMAS in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$y$ </tex-math></inline-formula> axis and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z$ </tex-math></inline-formula> axis, respectively, which can steer the whole system achieving target formation configuration within a scheduled time. In addition, based on local state information, adaptive online updating strategies for unknown actuator efficiency factors and lumped uncertainties are proposed. Then, under the online updating parameters, two novel distributed and decentralized adaptive fault-tolerant formation control laws are presented using practical fixed-time stability theory, which not only achieves stable formation tracking with finite-time prescribed behavioral metrics but also ensures that the formation errors are uniformly bounded within a settling time. Finally, the effectiveness of the developed control schemes is verified by simulation examples.

Distributed adaptive fixed-time formation control for UAV-USV heterogeneous multi-agent systems

This paper investigates formation trajectory tracking control for heterogeneous multi-agent systems with external disturbances, model uncertainties and input saturation. The system that is considered comprises one unmanned aerial vehicle (UAV) and multiple unmanned surface vessels (USVs). First, based on directed graph theory, a distributed formation control protocol is proposed for the UAV-USV heterogeneous multi-agent system. Second, combining the advantages of the adaptive technique and radial basis function (RBF) neural networks, a global fixed-time adaptive neural network nonsingular fast terminal sliding formation control protocol is designed to ensure tracking of the desired trajectory and form the predetermined formation configuration within a fixed time in the presence of various uncertainties. Through the proposed adaptive neural network (NN) control technology, the lumped uncertainty can be estimated, and the number of update parameters can be reduced, thereby relieving the calculation burden of the controllers. In addition, a dynamic event-triggered mechanism is incorporated into the controllers, which can reduce the update frequency of controllers, thereby decreasing the communication number of controllers. A saturation function is introduced simultaneously to solve the problem of input saturation. Finally, the simulation results are given to indicate the feasibility of the proposed formation control protocol.

Formation Control of Unmanned Surface Vehicles Using Fixed-Time Non-Singular Terminal Sliding Mode Strategy

Unmanned surface vehicles (USVs) have been widely applied in the fields of marine hydrological exploration, marine resource exploration, area search, target detection, and military operations. In order to meet the demand of a complex ocean environment, USVs are frequently grouped together to improve the reliability of mission accomplishment. In this paper, a fixed-time control strategy, combined with a non-singular terminal sliding mode, is proposed for the formation control of USVs under complex external disturbances and system uncertainties. The main contributions of this paper are: (1) the leader–follower formation control framework is divided into a tracking control subsystem and a formation control subsystem. A new fixed-time non-singular terminal sliding mode (FTNTSM) strategy is developed for the tracking control subsystem, which dramatically increases the convergence rate and ensures closed-loop fixed-time stability; (2) a finite-time uncertain observer (FUO) is designed to observe lumped uncertainty items, which greatly increase the stability and robustness of the formation system; (3) the FUO-based fixed-time formation control (FUOFT-FC) strategy is designed for the formation control subsystem, which ensures the fast and stable formation of USVs. Fixed-time convergence of the formation system is established by Lyapunov stability analysis. Rigorous simulation and comparative studies demonstrate that the proposed method is superior to the state-of-the-art methods.

Fixed-Time Formation Control for Unmanned Surface Vehicles with Parametric Uncertainties and Complex Disturbance

In this paper, under parametric uncertainties and complex disturbances, a leader–follower formation control strategy based on accurate disturbance observer (ADO) and a novel fixed-time fast terminal sliding mode (FTFTSM) control for unmanned surface vehicles (USVs) is proposed. The main contributions of this paper are: (1) A novel fixed-time fast terminal sliding mode tracking control (FTFTSM-TC) strategy is designed for the tracking control subsystem, which greatly improves the convergence rate of the leader USV in trajectory tracking. (2) An ADO is designed to observe lumped disturbances with the smallest approximation error. The ADO greatly reduces the interference of disturbances and improves the performance of the formation system. (3) An ADO-based fixed-time formation control (ADO-FTFC) strategy is developed for the formation control subsystem to maintain the desired formation. Stability of the formation control system is established by the Lyapunov theory. Simulation results show that the proposed control strategy is superior for the USVs formation control.

Fixed-time formation-containment control for uncertain multi-agent systems with varying gain extended state observer

In this article, the fixed-time formation-containment control is investigated for multi-agent systems with model uncertainties and external disturbances. First, a novel fixed-time varying gain extended state observer is developed to observe the states and the total disturbance of each formation-leader and follower. Then a fixed-time formation control protocol for each formation-leader is constructed to realize formation tracking. The desired trajectory for the formation-leader is generated by a fixed-time formation distributed observer. It can estimate the information of the tracking-leader within fixed time. Furthermore, a fixed-time containment distributed observer is put forward for each follower to estimate the convex hull spanned by the states of the formation-leaders, which can generate the reference signal for each follower and thus a fixed-time containment control protocol can be developed. Finally, the proposed strategy is successfully applied to the wheeled mobile robots. Experimental results confirm the validity of the proposed approach.

Fixed-Time Formation Control for Second-Order Disturbed Multi-Agent Systems under Directed Graph

This paper investigates the fixed-time formation (FixF) control problem for second-order multi-agent systems (MASs), where each agent is subject to disturbance and the communication network is general directed. First, a FixF protocol is presented based on the backstepping technique, where the distributed cooperative variable structure control method is utilized to handle the bounded disturbances. Then, to remove the dependence of control gains on the global information, a practical adaptive FixF control is presented, where the MASs can achieve formation with a bounded error within fixed time. Finally, a numerical example is presented to validate the theoretical result.

Fixed-time formation control for spacecraft with prescribed performance guarantee under input saturation

This paper investigates the fixed-time stability of spacecraft formation flying by considering input saturation and prescribed performance constraints, including the safe distance constraint between members and control accuracy. By analyzing the relationship between the positional tracking error and the minimum safe distance between spacecrafts, a new form of the prescribed performance function with fixed-time convergence is developed to constrain the overshoot and accuracy of the tracking error. A nonsingular saturated terminal sliding-mode surface is developed to stabilize the system states in fixed time. A fixed-time coordinated tracking controller with input and rate saturation is finally developed by combining sliding-mode control, the back-stepping method, fixed-time observers, an anti-windup saturation compensator, and an auxiliary system. The stability of the closed-loop system is validated by Lyapunov stability theory. The results of simulation verified the effectiveness of the proposed control algorithm.

Robust fixed-time formation control for quadrotor unmanned aerial vehicles with directed topology

Formation control is one of the key technologies for multiple unmanned aerial vehicles (UAVs). Compared with asymptotic or finite-time controllers, fixed-time controller can provide a guaranteed settling time, which does not depend on initial conditions and is an appealing property for controller design. Thus, robust fixed-time formation controller design for quadrotor UAVs under external disturbance and directed topology is investigated in this paper. A multi-variable super-twisting like integral sliding mode surface and a disturbance observer are respectively designed for position and attitude loops to guarantee robustness. Bi-limit homogeneity is utilized to design the whole closed-loop fixed-time controllers. By skillfully using bi-limit homogeneity technique and Lyapunov theory, the comprehensive stability of position and attitude loops is addressed. Finally, the multiple UAVs are utilized to track a pre-planned trajectory in 3D space and simulation results illustrate that the settling time can be reduced about 40% compared with finite-time controllers.

Predictor-based practical fixed-time adaptive sliding mode formation control of a time-varying delayed uncertain fully-actuated surface vessel using RBFNN

This paper focuses on fixed-time formation control (FTFC) of a fully-actuated surface vessel (FASV) considering complex unknowns, including fully unknown dynamics and disturbances, input saturation and time-varying delays. First, using prediction idea to address time delay, a novel state predictor (SP) strategy combining with state transformation (ST) technique is devised for each FASV to predict the evolution of system states such that fixed-time stability can be ensured while solving the delay problem. Besides, the uncertainties in the transformed system are attentively considered. In addition, aiming to distinctly identify complex unknowns, predictor-based neural network is injected into the foregoing delay processing method. Finally, using time base generator (TBG), a new adaptive terminal sliding mode (ATSM) is incorporated into FTFC strategy which in turn contributes to decreasing control inputs and acquiring smooth convergence process. Simulation results and comparisons are thoroughly provided to testify the effectiveness and superiority of the designed FTFC scheme.