Formation Tracking Control Problem Research Articles

Theory and experiment on distributed output formation tracking of unmanned aerial and ground vehicle swarm systems over jointly connected digraphs

This paper studies the distributed output formation tracking control problem of the unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) swarm systems, where the UAV swarm cooperatively tracks the output trajectory of the UGV in a formation under directed jointly connected communication networks. A three-layer formation tracking protocol is proposed. Firstly, a novel distributed observer using neighbor interactions is designed for each UAV to estimate the states of the UGV with parameterized inputs over periodic jointly connected digraphs. Next, based on the observation result and output regulation theory, a virtual reference system that tracks the trajectory of the UGV in the desired formation is constructed to generate reference states for each UAV. Then based on the differential flatness of UAVs, a geometric controller is utilized for UAVs to track the reference states and form the formation. An algorithm to determine the gain matrices of the protocol is also presented while the convergence of the system is analyzed. Finally, an experiment platform with three quadrotor UAVs and one UGV is built. The effectiveness of the proposed protocol is validated both by the simulation and experiment.

Time‐varying group formation tracking control for multi‐agent systems using distributed multi‐sensor multi‐target filtering with intermittent observations

AbstractTime‐varying group formation tracking control problems for multi‐agent systems are investigated based on distributed multi‐sensor multi‐target filtering with intermittent observations. First, in order to estimate the states of multiple targets under the phenomenon of intermittent observations accurately, a distributed multi‐sensor multi‐target filtering algorithm is proposed based on cubature Kalman filtering. Second, a time‐varying group formation tracking protocol is designed for multi‐agent systems by using the state estimations obtained from the filtering algorithm and the neighboring interaction. The protocol enables multi‐agent systems to form time‐varying subformations and track multiple targets in the same subgroups, respectively. Third, the boundedness of the error covariance matrices is proved under the condition that the observation probability is higher than the minimum threshold. Then the estimation errors of the filtering algorithm are proved to be stochastically bounded by introducing a stochastic process. Furthermore, the boundedness of the group formation tracking errors is proved. Finally, a numerical example is used to verify the performance of the proposed algorithm and protocol.

Adaptive Formation Tracking Control of Multiple Vertical Takeoff and Landing UAVs With Bearing-Only Measurements.

This article studies the leader-following formation tracking control problem of multiple vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs) subject to uncertain parameters, in which the target formation configuration is defined by using the interneighbors' bearing vectors. An adaptive formation control algorithm with bearing-only measurements is proposed under a hierarchical control framework. More specifically, a saturated adaptive distributed control force is developed in the position loop with bearing-only measurements. Since the bearing vectors with respect to the neighbors can be directly measured by low-cost onboard cameras, the proposed formation algorithm can be implemented without interagent communication. Subsequently, in the attitude loop, an adaptive hybrid control scheme via two modified Rodrigues parameters (MRPs) sets is proposed, which achieves the command attitude tracking globally and also avoids the unwinding problem of MRPs. Based on the Lyapunov stability analysis and hybrid theory, we prove that the overall closed-loop error system is globally asymptotically stable. Finally, we provide a numerical example to demonstrate the effectiveness of the proposed control algorithm.

Fully Data-Driven Robust Output Formation Tracking Control for Heterogeneous Multiagent System With Multiple Leaders and Actuator Faults.

This article investigates a fully data-driven method to solve the robust output formation tracking control problem for the multiagent system (MAS) under actuator faults. The outputs of the followers are controlled to track those of multiple leaders with respect to a convex point while achieving an expected time-varying formation. To obviate the requirement of various system prior knowledge in typical MAS control, a hierarchical frame is developed with three learning and control stages using the online measured data. First, a distributed adaptive observer is designed to coordinate the state convex of multiple leaders while estimating unknown dynamics. The adaptive mechanism relaxes the demand for global topology. Second, by collecting and reusing the online system data, an off-policy reinforcement learning (RL) method is proposed in a continuous form to acquire nominal feedback gains from partial observations of the followers. Essential system models are learned along with the RL process, while solutions to the output regulation equations are implicitly obtained. Third, a comprehensive robust controller is further presented based on the previous learning results. To address the actuator faults with efficiency loss and bias, the adaptive neural networks and robust compensations are utilized in a model-free manner. The output formation tracking is achieved under a derived feasibility condition while stabilities of the learning and control methods are analyzed. Finally, simulation results demonstrate the validity of this fully data-driven control frame.

Distributed prescribed-time cooperative formation tracking control of networked unmanned surface vessels under directed graph

To investigate the formation tracking control problem of networked unmanned surface vessels (USVs) under a directed graph, this article provides a prescribed-time distributed cooperative formation tracking control scheme that specifies tracking error convergence time in advance. Firstly, aiming at the unknown state of the leading USV, a distributed prescribed-time state observer is designed for the following USVs, which can quickly and accurately estimate the position and speed of the leading USV in a prescribed time. Then, based on the state observer, the prescribed-time sliding surface is designed, and the prescribed-time cooperative formation tracking controller is constructed using the prescribed-time sliding mode surface. In addition, a fast adaptive compensation law is developed to mitigate the issue of input saturation. The analysis based on Lyapunov theory displays that the upper bounds of the convergence time of the observer, the sliding mode surface, and the controller proposed in this study explicitly exist in the controller parameters, so they can be easily adjusted in the control design process and are not restricted by the initial state. Finally, the simulation results demonstrate that the proposed approach exhibits high reliability and effectiveness.

Event‐triggered based bearing‐only formation control for nonlinear multi‐agent with unknown disturbance

AbstractThis article delves into the bearing‐only formation tracking control problem of nonlinear multi‐agent systems with unknown disturbances and unmodeled dynamics, wherein the distributed control solely utilizes the relative bearing information of its neighbors. Firstly, a disturbance observer combined with a neural network is proposed to eliminate the impact of unknown disturbances and unmodeled dynamics. Additionally, a pioneering event‐triggered based backstepping control approach is put forth for the formation tracking control problem of nonlinear multi‐agent systems, which economizes on communication bandwidth and computing resources by decreasing the update frequency of the controller. Finally, using the Lyapunov method, it is demonstrated that all signals of the control system are bounded, and the convergence errors are confined to a small neighborhood of the origin while excluding the “Zeno behavior” phenomenon through rigorous proof.

Finite-Time Anti-Saturated Formation Tracking Control of Multiple Unmanned Aerial Vehicles: A Performance Tuning Way

A highly effective control method is very important to guarantee the safety of the formation of flying missions for multiple unmanned aerial vehicles (UAVs), especially in the presence of complex flying environments and actuator constraints. In this regard, this paper investigates the formation tracking control problem of multiple UAVs in the presence of actuator saturation. Firstly, a brand-novel finite-time anti-saturated control scheme is proposed for multiple UAVs to track the desired position commands, wherein the tracking performance is tuned by introducing a logarithmic function-based state-mapping policy. Then, an adaptive scheme based on projection rules is devised to compensate for the negative effects brought by the actuator saturation. Based on the proposed formation tracking controller, the finite-time formation tracking performance tuning and control saturation problems can be addressed simultaneously with a comparatively allowable system robustness. Finally, three groups of illustrative examples are organized to verify the effectiveness of the proposed formation tracking control scheme.

Optimal formation tracking control based on reinforcement learning for multi-UAV systems

This paper investigates the problem of optimal formation tracking control for multi-UAV systems with model uncertainty and external disturbances. Firstly, by combining the sliding mode method and a neural network, an adaptive sliding mode controller is derived that counteracts the effects of modeling uncertainty and external disturbance. Subsequently, the optimal formation tracking control problem of the original system is then converted to the optimal control problem of a nominal system, and an actor–critic reinforcement learning framework is built using adaptive neural network identifiers to recursively approximate the total optimal policy and cost function. The Lyapunov analysis method shows that the stability of the closed-loop system and the convergence of the estimation weights for the actor–critic network are guaranteed. Additionally, a formation tracking using virtual experiment platform for multi-UAV systems are constructed based on the Robot Operating System (ROS) and Gazebo simulator. Finally, virtual-reality experiments is performed to demonstrate the effectiveness of the proposed control scheme.

Game-based distributed optimal formation tracking control of underactuated AUVs based on reinforcement learning

This paper investigates game-based distributed optimal time-varying formation tracking control problem based on backstepping technique and reinforcement learning (RL) for autonomous underwater vehicles (AUVs) with time-varying disturbances and input saturation. The proposed method enables the multi-AUV to track a desired trajectory while holding the time-varying formation. To accomplish this, we adopt a game between leader and followers to enhance robustness of the system to time-varying disturbances. The approximate optimal solution of the established Hamilton–Jacobi–Isaacs (HJI) equation is obtained by RL which performs online via the single critic Neural Network (SCNN). Hence, the optimal solution corresponds to the saddle point equilibrium of the tracking game. In addition, the command filter is used to construct the unknown hydrodynamic parameter and time-varying disturbances. Furthermore, we introduce a quasi-norm to confront input saturation. The effectiveness of the proposed approach is verified by the simulation results provided.

Distributed Robust Formation Tracking Control for Quadrotor UAVs with Unknown Parameters and Uncertain Disturbances

In this paper, the distributed formation tracking control problem of quadrotor unmanned aerial vehicles is considered. Adaptive backstepping inherently accommodates model uncertainties and external disturbances, making it a robust choice for the dynamic and unpredictable environments in which unmanned aerial vehicles operate. This paper designs a formation flight control scheme for quadrotor unmanned aerial vehicles based on adaptive backstepping technology. The proposed control scheme is divided into two parts. For the position subsystem, a distributed robust formation tracking control scheme is developed to achieve formation flight of quadrotor unmanned aerial vehicles and track the desired flight trajectory. For the attitude subsystem, an adaptive disturbance rejection control scheme is proposed to achieve attitude stabilization during unmanned aerial vehicle flight under uncertain disturbances. Compared to existing results, the novelty of this paper lies in presenting a disturbance rejection flight control scheme for actual quadrotor unmanned aerial vehicle formations, without the need to know the model parameters of each unmanned aerial vehicle. Finally, a quadrotor unmanned aerial vehicle swarm system is used to verify the effectiveness of the proposed control scheme.

Adaptive fuzzy finite‐time formation asymptotic tracking control for nonholonomic multirobot systems with inputs quantization

SummaryThis paper investigates the finite‐time formation tracking control problem for nonholonomic multirobot systems with inputs quantization. The fuzzy logic systems (FLSs) and adaptive method are introduced to approximate unknown nonlinear functions and parameters. Multirobot needs to keep safe and effective communicating range, the barrier function and prescribed performance method are employed to ensure collision avoidance and connectivity maintenance. Then, in order to make each robot more precisely and quickly track referenced leader's trajectory and consider the finite channel bandwidth in practical applications, the travel range of robots can be maintained at more secure region and formation can operate normally within the given bandwidth. By combining the command filter and finite‐time theory, a novel decentralized finite‐time formation asymptotic tracking (FTFAT) control strategy is further proposed based on inputs quantization technology, it guarantees that all signals are bounded and the formation tracking errors asymptotically converge to zero in finite‐time. Finally, the practicability of FTFAT strategy is demonstrated absolutely for nonholonomic multirobot systems.

Distributed formation tracking control of underactuated surface vehicles based on event-trigged control

In this paper, a distributed formation tracking control problem is investigated for underactuated surface vessels (USVs). The uncertainties induced by model uncertainties and external disturbances are assumed to be unknown. An event-trigged disturbance observer (ETDO) is proposed to provide the estimations of the uncertainties, and an event-triggered mechanism is used to determine when measured velocity information must be sent to the observer. An event-trigged controller (ETC) is designed based on a backstepping technique, dynamic surface control, and the observer. Stability analysis of distributed formation control system is given to prove all signals are bounded. Simulations demonstrate the proposed control strategy.

Bearing-Based Formation Tracking Control With Time-Varying Velocity Estimation.

This article studies the bearing-based formation tracking control problem of multiple double-integrator agents. A leader-following structure, where the leader moves with the reference dynamics, is adopted. Different from the existing methods, which require complete information of the time-varying reference velocity, in this article, only the time-varying reference orientation information is known by part of the followers and the amplitude of the reference velocity is unknown. To solve the problem, this article proposes a velocity-estimation-based control scheme, which consists of an estimator for estimating the varying rate of the reference orientation, an adaptation law for estimating the amplitude of the reference velocity, and bearing-based control inputs for tracking the leader and achieving the bearing-based formation based on the estimations. Moreover, the scaling formation maneuver can be achieved by using an auxiliary distance measurement. It shows that both the estimation errors and control errors converge to zero under the connectivity of the topology and properties of bearing rigidity. The closed-loop system is analyzed to be semiglobally uniformly asymptotically stable based on the cascaded system theory. Numerical simulations are presented to demonstrate the effectiveness of our method.

Distributed Fault-Tolerant Formation Tracking Control for Multiagent Systems With Multiple Leaders and Constrained Actuators.

The distributed formation tracking control problem with multiple leaders under actuator faults and constraints is investigated in this article. All followers in the multiagent system should achieve a desired time-varying formation and track the convex combination of multiple leaders. To accomplish the control task, an active reconfigurable control scheme is proposed using the local information between agents, as well as the fault values of individuals provided by fault estimation observers. Combining with the Lyapunov stability theorem and the property of the Laplacian matrix, the control gains are calculated using the adaptive technique with a formation tracking feasibility condition. The original reconfigurable protocol is modified by utilizing anti-windup compensators to against saturation phenomenons (both magnitude and rate) in actuators. The simulation results validate that the presented scheme can address the faults as well as the actuator saturation.

Fixed-time formation fault tolerant control for unmanned surface vehicle systems with intermittent actuator faults

This article studies the fixed-time fuzzy formation tracking control problem for multiple unmanned surface vehicle (USV) systems with intermittent actuator faults. Since each USV is subject to unknown motion dynamics and the external disturbances. The fuzzy state observers are developed to estimate the positions and velocity in multiple USV systems, and disturbance observers are developed to estimate the external disturbances, and fuzzy logic systems are utilized to identify the unknown motion dynamics. Then, to compensate for the influence of intermittent actuator faults, the novel fixed-time adaptive output-feedback formation fault-tolerant controllers are constructed by constructing the integral type Lyapunov function and co-designing the last virtual controller. The presented formation control method can guarantee all the signals in multiple USV systems are bounded in fixed-time. Finally, simulation results and comprehensive comparisons are provided to verify the effectiveness of the presented formation control method.

Distributed optimal formation tracking control based on reinforcement learning for underactuated AUVs with asymmetric constraints

This paper investigates the distributed optimal formation tracking control problem based on backstepping technique and reinforcement learning for multiple underactuated autonomous underwater vehicles (AUVs). Based on the graph theory, we propose a virtual distributed formation tracking controller in the kinematics model while the barrier Lyapunov function is utilized to make sure the connectivity preservation and the collision avoidance. An optimal controller based on the reinforcement learning(RL) is designed to minimize a cost function in the dynamic motion, and critic–actor neural networks (NNs) are further applied for online implementation of the reinforcement learning algorithm. As a result, the optimal control design for the underactuated AUVs with the uncertain Hydrodynamic can be online realized. The command filter is adopted to solve the issue of the explosion of complexity. The simulation results are given to confirm the validity of the proposed method.

Observer-based time-varying group formation tracking for one-sided Lipschitz nonlinear second-order multi-agent systems

This paper discusses the observer-based time-varying group formation tracking (TVGFT) control problem for one-sided Lipschitz nonlinear second-order multi-agent systems (MASs). The followers in the MASs are divided into multiple groups, where only one follower in each group knows the leaders information, and a control protocol is designed through the interactions among the followers. Based on the one-sided Lipschitz definition and the properties of Laplacian matrices, sufficient conditions are provided to achieve the TVGFT for one-sided Lipschitz nonlinear MASs. By solving the linear matrix inequality (LMI), sufficient criteria for achieving TVGFT can be obtained. Finally, it is demonstrated from simulations that the designed control protocol can achieve TVGFT effectively.

Extended Kalman Filter Based Resilient Formation Tracking Control of Multiple Unmanned Vehicles via Game-Theoretical Reinforcement Learning

In this paper, we discuss the resilient formation tracking control problem of multiple unmanned vehicles (MUV). A dynamic leader-follower distributed control structure is utilized to optimize the performance of the formation tracking. For the follower of the MUV, the leader is a cooperative unmanned vehicle, and the target of formation tracking is a non-cooperative unmanned vehicle with a nonlinear trajectory. Therefore, an extended Kalman filter (EKF) observer is designed to estimate the state of the target. Then the leader of the MUV is adjusted dynamically according to the state of the target. In order to describe the interactions between the follower and dynamic leader, a Stackelberg game model is constructed to handle the hierarchical decision problems. At the lower layer, each follower responds by observing the leader's strategy, and the potential game is used to prove a Nash equilibrium among all followers. At the upper layer, the dynamic leader makes decisions depending on the response of all followers to reaching the Stackelberg equilibrium. Moreover, the Stackelberg-Nash equilibrium of the designed game theoretical model is proven. A novel reinforcement learning-based algorithm is designed to achieve the Stackelberg-Nash equilibrium of the game. Finally, the effectiveness of the method is verified by a variety of formation tracking simulation experiments.

Spherical Formation Tracking Control of Non-Holonomic UAVs with State Constraints and Time Delays

This paper addresses a novel spherical formation tracking control problem of multiple UAVs with time-varying delays in the directed communication network, where the dynamics of each UAV is non-holonomic and in the presence of spatiotemporal flowfields. The state constraints (that is, position and velocity constraints) are derived from our previous differential geometry method and the F–S formulas. The state constraints and time delays in the directed communication network bring many difficulties to controller design. To this end, a virtual-structure-like design is given to achieve a formation with delayed information by using Lyapunov–Krasovskii functionals, and then proposing a barrier Lyapunov function for the satisfaction of state constraints to design a novel spherical formation tracking algorithm. The general assumption of the rate of change of time-varying delays, and a certain initial position and velocity adjustment range are given. Simulation results show the feasibility and effectiveness of the proposed algorithm.

Event-Triggered Formation Tracking Control With Application to Multiple Mobile Robots

In this article, we address the distributed event-triggered leader–follower formation tracking control problem of general linear multiagent systems with a dynamic leader in sampled-data settings. A novel locally computable state-estimate-based event generator is established for each follower agent to regulate the interagent communication at each sampling instant. Then, we propose a distributed formation tracking protocol based on the triggered sampled information such that the formation tracking control problem can be formulated as a stability-analysis problem of the closed-loop formation error dynamics. The event generator and formation tracking controller gains can then be co-designed using the feasible linear matrix inequality conditions that are derived from Lyapunov-based stability-analysis methods that guarantee the ultimate boundedness of the closed-loop formation error dynamics. Finally, numerical simulations along with experiment implementations were conducted for a group of linearized unicycle-type mobile robots to demonstrate the effectiveness and advantages of the proposed method.