Formation Control Problem Research Articles

Cooperative group formation control for multiple quadrotors system with finite- and fixed-time convergence

A multitude of quadrotors cooperatively executing complicated tasks in predefined geometric configurations has attracted arising attention. Accurate and effective formation control laws are essential for completing missions. Finite- and fixed-time group formation control problems for multiple quadrotors are researched in this paper. The quadrotors are first divided into M distinct and non-overlapping subgroups. In each subgroup, quadrotors are driven to form the predefined configuration, with the whole achieving M-group formation meanwhile. Two distributed algorithms for multiple quadrotors system are then designed to realize finite- and fixed-time group formation. Detailed and theoretical analysis of finite- and fixed-time group formation formability is conducted. Sufficient conditions are provided by utilizing the Lyapunov stability and bi-limit homogeneity theory. Two simulations are carried out to verify the effectiveness of proposed algorithms.

Formation control of discrete-time nonlinear multi-glider systems for both leader–follower and no-leader scenarios under switching topology: Cases for a fleet consisting of a wave glider and multiple underwater gliders

The formation control of multiple underwater gliders has been incredibly helpful in ocean research and inspection. However, it can be substantially challenging due to its underactuation, nonlinear dynamics, weak mobility, vulnerability to the ocean current, and long communication interval. Based on a fleet with a wave glider and multiple underwater gliders, this study introduces a formation control strategy suitable for leader–follower and no-leader scenarios under switching communication topology. The underwater gliders in the fleet are linearized by feedback linearization and the mathematical model is described in discrete time. The formation control protocol is established by combining the consensus of speed control in the forward direction with the path following control in the lateral direction and applying partial state information of the leader and followers under the randomly switching topology. By performing state transformation and analyzing matrix properties, sufficient conditions are obtained for the discrete-time glider systems under randomly switching topology to achieve the desired formation. Also, convergence results are derived whether the formation feasibility conditions are satisfied or not. Two cases for a fleet consisting of a wave glider and multiple underwater gliders are given in the numerical simulation and sea trials, including the leader–follower scenario for formation control during cruising, and the no-leader scenario for the coordination of underwater gliders in depth direction. The results of simulation and sea trials show that the theoretical results can be used to deal with the formation control problem for multi-glider systems.

Finite-time velocity-free adaptive neural constrained cooperative control of Euler–Lagrange systems

This paper addresses a new constrained control design problem to develop the trajectory-tracking specifications of the cooperative control of Euler–Lagrange systems with respect to the convergence rate and steady-state errors by constraining the limited bounds on the trajectory-tracking errors in the leader–follower formation control problem. A control design based on an asymmetric barrier Lyapunov function is proposed for the leader–follower formation control of Euler–Lagrange systems in the presence of unknown parameters and unmodeled dynamics that progresses to the infinity when its arguments attain to the predefined bounds. These constrained output states are considered in the leader–follower formation control problem to cope with the system restrictions such as limited sensing ranges. The Lyapunov stability is pursued to assure that all the signals of the closed-loop system are bounded and the leader–follower formation errors are finite-time semi-globally uniformly ultimately bounded. Finally, computer simulation results represent the impression of the newly proposed constrained leader–follower formation control for the Euler–Lagrange systems.

Leader–follower formation control of four-legged robots with discrete-valued inputs

This paper addresses a leader–follower formation control problem for four-legged robots under discrete-valued input constraints. Four-legged robots are more suitable for rough terrain missions than wheeled robots because the tip positions of their legs can be changed depending on the terrain. However, it is difficult to control these robots through continuous-valued inputs because they are steered by switching between specific movements (i.e., discrete-valued signals). Motivated by this fact, we have proposed controllers that achieve fixed formations of four-legged robots using discrete-valued inputs, but moving formations, which are necessary for some applications, have not been considered yet. Herein, we present a solution to the above leader–follower formation control problem based on the combination of PD-like formation controllers and dynamic quantization. We further introduce a performance index to evaluate the difference between two systems whose inputs are quantized and unquantized and analyze the index for the feedback system with the presented controllers. As a result, an upper bound of the performance index is derived as a function of the system parameters. This is useful to evaluate the impact of the quantization on the behavior of the feedback system and to provide a theoretical guarantee of the stability of the system.

Distributed dynamic obstacle avoidance design to connectivity-preserving formation control of uncertain underactuated surface vehicles under a directed network

This paper presents a Lyapunov-based recursive design approach for unifying distributed connectivity-preserving formation control and dynamic obstacle avoidance problems of uncertain multiple underactuated surface vehicles (USVs) with heterogeneous range constraints. Compared with related works, the main contribution of this study is to develop a novel control design for preserving network connectivity under dynamic obstacle avoidance in the distributed formation tracking framework. Because of the limited communication ranges, it is difficult to maintain the network interactions among USVs during dynamic obstacle avoidance. To deal with this problem, a collision-avoiding function is defined as a local error surface for the recursive control design, and a distributed complementary signal vector is introduced in the connectivity-preserving formation error surface. The complementary signals are designed to prevent network disconnections when the formation error is increased by the avoidance action and to ensure the stability of the collision-avoiding error dynamics, which eventually lead to preventing network disconnections during dynamic obstacle avoidance. An adaptive formation tracking scheme is designed via the neural networks-based command-filtered backstepping. The stability of the overall closed-loop system with preserved network connectivity and obstacle avoidance is proved based on the Lyapunov stability theorem. Finally, the theoretical approach is demonstrated through simulations.

Distributed Bearing-Only Formation Control for UAV-UWSV Heterogeneous System

This paper investigates the bearing-only formation control problem of a heterogeneous multi-vehicle system, which includes unmanned aerial vehicles (UAVs) and unmanned surface vehicles (UWSVs). The interactions among vehicles are described by a particular class of directed and acyclic graphs, namely heterogeneous leader-first follower (HLFF) graphs. Under the HLFF structure, a UAV is selected as the leader, moving with the reference dynamics, while the followers, including both UAVs and UWSVs, are responsible for controlling the position with regard to the neighbors in the formation. To solve the problem, we propose a velocity-estimation-based control scheme, which consists of a distributed observer for estimating the reference velocity of each vehicle and a distributed formation control law for achieving the desired formation based on the estimations and bearing measurements. Moreover, it is shown that the translation and scale of the formation can be uniquely determined by the leader UAV. The theoretical analysis demonstrated the finite-time convergence of the velocity estimation and the asymptotic convergence of the formation tracking. Comparative simulation results are provided to substantiate the effectiveness of the proposed method.

Fixed-time leader-follower formation control of underactuated unmanned surface vehicles with unknown dynamics and ocean disturbances

This paper investigates the formation control problem of underactuated unmanned surface vehicles with unknown dynamics and ocean disturbances. To tackle the leader-follower configuration, an improved fixed-time velocity controller is proposed for the virtual vehicle to guide the followers efficiently. For the tracking control of the follower vehicles, a concise controller is designed by borrowing on backstepping and nonsingular sliding mode control techniques. A novel adaptive filter is developed to address the so called “explosion of complexity” problem in the traditional backstepping framework, which could simplify the control structure and facilitate the implementation of the proposed controller in practical engineering. Furthermore, the radial basis function neural network is employed to identify the unknown dynamics of the vehicle model. A bounded-feedback adaptive law is developed to estimate the upper bound of the ocean disturbances. That could greatly enhance the robustness and accuracy of the controller. Finally, a rigorous proof has been given to guarantee the practical fixed-time stability of the closed-loop system. Two examples are provided to demonstrate the effectiveness and superiority of the theoretical results.

Event-Triggered formation control for time-delayed discrete-Time multi-Agent system applied to multi-UAV formation flying

This paper studies the formation control for a time-delayed discrete-time multi-agent system (MAS). An event-triggered controller is proposed to reduce the communication load of the system. Based on the designed event-triggered condition and properties of Schur stable matrix, the stability of formation for discrete-time MAS is proved. Utilizing the virtual simulation platform integrated Robot Operating System (ROS) and Gazebo, a virtual scene with unmanned aerial vehicles (UAVs) models is built and the verification for the theoretical algorithm is completed. Finally, an experimental platform with four practical UAVs is constructed and the result shows that the expected formation is achieved and controller proposed can solve the formation control problem for time-delayed discrete-time MASs. Besides, the effectiveness of the event-triggered mechanism on reducing communication frequency is comfirmed in practical scenarios.

Nonlinear Extended State Observer-Based Distributed Formation Control of Multiple Vessels with Finite-Time Prescribed Performance

In the presence of unmeasurable velocities and system uncertainties, the distributed formation control problem is investigated in this paper for multiple vessels. A robust formation controller is proposed by incorporating an extended state observer (ESO) and finite-time prescribed performance function (FTPPF). Firstly, a nonlinear ESO is designed to estimate the unmeasurable velocities and system uncertainties. Subsequently, a novel FTPPF is designed to improve the dynamic performance of multi-vessel formation systems, where the upper bound of the convergence time and the constraint bounds can be set in advance based on the actual circumstances. Then, the proposed ESO and FTPPF are applied to the distributed formation controller design for multiple vessels. The proposed formation control scheme can maintain the multiple vessels in an expected formation with high tracking accuracy, a faster convergence speed, and smaller fluctuations. Finally, the performance of the proposed control method is verified by theory analysis and simulations.

Formation Control for Second-Order Multi-Agent Systems with Collision Avoidance

This paper deals with the formation control problem without collisions for second-order multi-agent systems. We propose a control strategy which consists of a bounded attractive component to ensure convergence to a specific geometrical pattern and a complementary repulsive component to guarantee collision-free rearrangement. For convergence purposes, it is assumed that the communication graph contains at least a directed spanning tree. The avoidance complementary component is formed by applying repulsive vector fields with unstable focus structure. Using the well-known input-to-state stability property a control law for second-order agents is derived in a constructive manner starting from the first-order case. We consider that every agent is able to detect the presence of any other agent in the surrounding area and also can measure and share both position and velocity with his predefined set of neighbours. The resulting control law ensures the convergence to the desired geometrical pattern without collisions during the transient behaviour, as well as bounded velocities and accelerations. Numerical simulations are provided to show the performance and effectiveness of the proposed strategy.

Cost-effective distributed FTFC for uncertain nonholonomic mobile robot fleet with collision avoidance and connectivity preservation

In this paper, the fault-tolerant formation control (FTFC) problem is investigated for a group of uncertain nonholonomic mobile robots with limited communication ranges and unpredicted actuator faults, where the communication between the robots is in a directed one-to-one way. In order to guarantee the connectivity preservation and collision avoidance among the robots, some properly chosen performance functions are incorporated into the controller to per-assign the asymmetrical bounds for relative distance and bearing angle between each pair of adjacent mobile robots. Particularly, the resultant control scheme remains at a cost-effective level because its design does not use any velocity information from neighbors, any prior knowledge of system nonlinearities or any nonlinear approximator to account for them despite the presence of modeling uncertainties, unknown external disturbances, and unexpected actuator faults. Meanwhile, each follower is derived to track the leader with the tracking errors regarding relative distance and bearing angle subject to prescribed transient and steady-state performance guarantees, respectively. Moreover, all the closed-loop signals are ensured to be ultimately uniformly bounded. Finally, a numerical example is simulated to verify the effectiveness of this methodology.

Distributed Framework Matching

This article studies the problem of distributed framework matching (FM), which originates from the assignment task in multirobot coordination and the matching task in pattern recognition. The objective of distributed FM is to distributively seek a correspondence which minimizes some metrics describing the disagreement between two frameworks (i.e., graphs and their embeddings). In view of the type of the underlying graph in the framework, two formulations, undirected framework matching (UFM) and directed framework matching (DFM), and their convex relaxations, relaxed UFM (RUFM), and relaxed DFM (RDFM), are presented. UFM is converted into a graph matching (GM) problem with the adjacency matrix being replaced by a matrix constructed from the undirected framework under certain graphical conditions, and can be solved distributively. Sufficient conditions for the equivalence between UFM and RUFM, and the perturbation admitting exact recovery of correspondence are established. On the other hand, DFM embeds the configuration of the directed framework via another type of matrix, whose computation is distributed, and can deal with the case of two frameworks with different sizes of node sets. A distributed optimization algorithm for solving RDFM is proposed and its convergence results are established which allows DFM to be solved in a fully distributed manner. Simulation examples on both synthetic data and real world datasets demonstrate the applicability and efficacy of our theoretical results in formation control and object matching problems.

Leader-Follower Formation Learning Control of Discrete-Time Nonlinear Multiagent Systems.

This article investigates the leader-follower formation learning control (FLC) problem for discrete-time strict-feedback multiagent systems (MASs). The objective is to acquire the experience knowledge from the stable leader-follower adaptive formation control process and improve the control performance by reusing the experiential knowledge. First, a two-layer control scheme is proposed to solve the leader-follower formation control problem. In the first layer, by combining adaptive distributed observers and constructed in -step predictors, the leader's future state is predicted by the followers in a distributed manner. In the second layer, the adaptive neural network (NN) controllers are constructed for the followers to ensure that all the followers track the predicted output of the leader. In the stable formation control process, the NN weights are verified to exponentially converge to their optimal values by developing an extended stability corollary of linear time-varying (LTV) system. Second, by constructing some specific "learning rules," the NN weights with convergent sequences are synthetically acquired and stored in the followers as experience knowledge. Then, the stored knowledge is reused to construct the FLC. The proposed FLC method not only solves the leader-follower formation problem but also improves the transient control performance. Finally, the validity of the presented FLC scheme is illustrated by simulations.

Vortex Formation Control for Linear Multiagent Systems With Unknown Leader Input and External Disturbances

This brief investigates vortex formation control problem for linear multiagent systems with unknown leader input and external disturbances. This brief proposes a distributed control protocol with antisymmetric matrix which can adjust the interaction between agents to realize the vortex formation of multiagent system. Each agent only communicates with their neighbor agents through the communication topology without requiring the whole system to be fully connected, which makes the control protocol more suitable for large-scale systems. The unknown bounded external disturbance and the input information of leader that may be encountered in practical application are considered in the protocol design. A control term related to the symbolic function is introduced to deal with bounded external disturbances and unknown leader input signal, which can deal with more complex external environment and uncooperative leader in practical applications. Finally, a numerical example is presented to verify the proposed protocol.

Straight-Path Following and Formation Control of USVs Using Distributed Deep Reinforcement Learning and Adaptive Neural Network

Dear Editor, This letter presents a distributed deep reinforcement learning (DRL) based approach to deal with the path following and formation control problems for underactuated unmanned surface vehicles (USVs). By constructing two independent actor-critic architectures, the deep deterministic policy gradient (DDPG) method is proposed to determine the desired heading and speed command for each USV. We consider the realistic dynamical model and the input saturation problem. The radial basis function neural networks (RBF NNs) are employed to approximate the hydrodynamics and unknown external disturbances of USVs. Simulation results show that our proposed method can achieve high-level tracking control accuracy while keeping a desired stable formation.

Secure Control Design for Networked Control Systems With Nonlinear Dynamics Under Time-Delay-Switch Attacks

A continuous controller is developed for a centralized network control system (NCS), which is composed of agents with nonlinear dynamics subject to a time-delay-switch (TDS) attack and additive disturbances. Since the state tracking error is unmeasurable during TDS attacks, controllers cannot use the state tracking error to coordinate the NCS. Therefore, a novel error signal is designed to address this unique challenge and enable the NCS to achieve a formation control objective. Furthermore, a TDS attack mitigation strategy is developed, which uses both learning- and model-based approaches to estimate an agent’s state for TDS attack detection and compensation. Lyapunov–Krasovskii functionals are used in the stability analysis to prove that the tracking errors converge to a steady-state residual, which is a function of the system uncertainty and TDS attack properties. The leader–follower formation control problem for unmanned aerial vehicles based on a pure pursuit guidance law is selected for a simulation study to validate the performance of the proposed method.

Towards end-to-end formation control for robotic fish via deep reinforcement learning with non-expert imitation

Collaboration of multiple robotic fish can accomplish various underwater tasks effectively. However, controlling robotic fish to maintain a specific formation remains a huge challenge, especially in complex and changing flow fields. This paper presents an end-to-end formation control approach in the leader–follower topology by combining deep reinforcement learning and imitation learning. First, we build a high-fidelity environment based on computational fluid dynamics (CFD) to generate samples for training the formation controller. In this environment, we maneuver the robotic fish by adjusting the maximum swing of its tail. Then, we model the formation control problem as a Markov decision process (MDP), where a compound reward function is tailored to guide the training. To improve the learning efficiency of the deep reinforcement learning (DRL) based controller, we propose a novel DRL algorithm on the top of deep Q-networks (DQN) and behavior cloning, which we call dueling double DQN (D3QN) with imitation. Combining with the designed imitation-based action selection strategy, this algorithm significantly reduce the blindness of agent exploration at the beginning of training. A series of experiments demonstrate the advantages of the proposed algorithm in terms of control accuracy, training efficiency, as well as generalization ability for different formation configurations.

Distributed adaptive formation control of multi-agent systems with measurement noises

In this paper, we investigate the distributed adaptive formation control problem of leader-following multi-agent systems where the measurements are subject to noises. A distributed LMS-like algorithm is proposed to estimate the relative position between the followers and the leader. By employing the “certainty equivalence” principle, an adaptive motion controller is designed to achieve the desired formation under dynamically changing interaction topologies. The incompatibility in simultaneously satisfying the persistent excitation condition required by localization estimators and accomplishing the control tasks makes the theoretical analysis challenging. In order to deal with this issue, an excited noise signal is embedded into the control law. We give the upper bounds of both the estimation errors and formation error of the closed-loop multi-agent system under the distributed adaptive control law. Finally, the numerical simulations are provided to demonstrate the effectiveness of our theoretical results.

Event-based formation control for multiple unmanned aerial vehicles under directed topology

This paper focuses on the problem of formation control for multiple unmanned aerial vehicles (UAV) subject to cyber attacks by a novel event-triggered communication scheme. An average method is introduced to design the triggering condition of this communication scheme, by which the amount of wrong triggering events caused by the sudden change of system states is greatly decreased, thereby saving a great deal of network bandwidth and reducing network congestion. Considering cyber attacks, a new event-based formation control strategy is developed for multi-UAV systems under directed topology by utilizing a control compensation approach. Sufficient conditions for the multi-UAV system to achieve the desired formation are acquired. Finally, a simulation example is undertaken to demonstrate the effectiveness of the theoretical results.

The multi-AUV time-varying formation reconfiguration control based on rigid-graph theory and affine transformation

This paper studies the time-varying formation reconfiguration control for multiple underactuated autonomous underwater vehicles (AUVs) with an Euler–Lagrange-like model. The goal is to control a fleet of AUVs to achieve any desired formation shape using a distance-based graph rigidity and affine transformation (GR-AT) algorithm. Firstly, the distance-based graph rigidity with backstepping technology is utilized to solve the formation controlproblem, and we acquire the initial nominal formation. In the sequel, we transform the nominal formation into any desired formation shape using the properties of the affine transformation (including translation, scaling, rotation, shearing, or a combination of them). Even the geometric shapes formed can be constantly changed. The Lyapunov stability theory can ensure the uniform ultimate boundedness of whole distance errors. Finally, several simulation examples with formation reconfiguration are given to validate the efficacy of the designed control methods. Moreover, some experimental results are presented to confirm the validity and applicability of the scheme with four real bionic robot fish.