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In the paper, the formation control problem in unknown environments for networked multi-unmanned aerial vehicle systems (UAVSs) is resolved under a nonlinear differential game (NL-DDG) framework. The main challenge of this framework is how to obtain feedback Nash strategies, which typically overly rely on global information and cannot ensure the existence of Nash strategies in unknown environments. Toward this goal, we initially design collision avoidance rules to ensure the safety of each UAV. Subsequently, we utilize an inverse optimal control method to construct the NL-DDG that incorporates both formation control and collision avoidance costs, enabling the derivation of analytical forms of Nash strategies relying solely on local information and minimizing performance metrics. In addition, the existence of feedback Nash strategy can be guaranteed with an undirected and connected information topology, which represents the optimality for the UAVSs. Moreover, we analyze the stability of the closed-loop system. Finally, the simulation results validate the effectiveness of the proposed scheme.

Designing cooperative multi-robot systems (MRS) requires expert knowledge both in control and artificial intelligence. Formation control is an important research within the research field of MRS. Since many researchers use different ways in approaching formation control, we try to give a taxonomy in order to help researchers design formation systems in a systematical way. We can analyze formation structures in two categories: control abstraction and robot distinguishability. The control abstraction can be divided into three layers: formation shape, reference type, and robotic control. Furthermore, robots can be classified as anonymous robots or identification robots depending on whether robots are distinguishable according to their inner states. We use this taxonomy to analyze some ground-based formation systems and to state current challenges of formation control. Such information becomes the design know-how in developing a formation system, and a case study of designing a multi-team formation system is introduced to demonstrate the usefulness of the taxonomy.

This paper investigates the formation control and obstacle avoidance problem for multi-agent systems (MASs), which aims to coordinate the pursuer agents to capture a mobile target. The target appears at a location randomly and its movement obeys Reactive Rabbit Model. The pursuers and the mobile target can be modeled as a Pursuit-Evasion Game (PEG). During the movement, not all of the pursuer agents can obtain the real-time information of the target. Moreover, the obstacle avoidance makes the formation of pursuer agents a big challenge to encircle the mobile target. In order to tackle these two problems, the formation control and obstacle avoidance algorithm is presented in this paper based on a novel virtual leader-follower strategy and potential functions. The obstacle avoidance problem can then be solved by constructing a velocity potential. The numerical analysis and simulation demonstrate the effectiveness of the proposed algorithm.

With the development of autonomous underwater vehicle (AUV) application techniques, formation control of multiple AUVs becomes a worldwide research focus. In this paper, first, formation control methods are summarized as: virtual structure method, behavior-based method, leader–follower method and artificial potential field method. Second, the peculiarities and difficulties of formation control especially for multi-AUV system are analyzed based on the research and development status in this area. The critical technical problems are summarized into three aspects: problem of AUV's dynamic complexity; problem of environmental complexity; problem of severe underwater communication constraints. Finally, the major development trends of multi-AUV system are discussed.

This paper presents a leader-follower type of fault-tolerant formation control (FTFC) methodology with application to multiple unmanned aerial vehicles (UAVs) in the presence of actuator failures and potential collisions. The proposed FTFC scheme consists of both outer-loop and inner-loop controllers. First, a leader-follower control scheme with integration of a collision avoidance mechanism is designed as the outer-loop controller for guaranteeing UAVs to keep the desired formation while avoiding the approaching obstacles. Then, an active fault-tolerant control (FTC) strategy for counteracting the actuator failures and also for preventing the healthy actuators from saturation is synthesized as the inner-loop controller. Finally, a group of numerical simulations are carried out to verify the effectiveness of the proposed approach.

Time-varying formation analysis and design problems for general linear multi-agent systems with switching interaction topologies and time-varying delays are studied. Firstly, a consensus-based formation control protocol is constructed using local information of the neighboring agents. An algorithm with three steps is presented to design the proposed formation control protocol. Then, based on linear matrix inequality technique and common Lyapunove–Krasovskii stability theory, sufficient conditions for general linear multi-agent systems with switching topologies and time-varying delays to achieve time-varying formation are given together with a time-varying formation feasibility condition. Finally, a numerical simulation is given to demonstrate the effectiveness of the obtained theoretical results.

This paper studies the distributed formation tracking control problem of heterogeneous multi-agent systems where the multiple targets have unknown inputs with finite dimensional Fourier decompositions and each target’s measurement output is just available to partial agents. A distributed observer-based formation tracking control algorithm is proposed. The distributed observers are based on the consensus protocol and designed to estimate the inputs and states of all targets from the available measurement outputs and neighbor information. The tracking controller is a state feedback based on the estimated state center of the targets. It is proved that the estimation errors of all agents converge to zero, if and only if each target node in the extended topology is reachable from each agent node and the consensus gain is larger than certain value. It is further proved that under the formation tracking control algorithm, the agents can asymptotically achieve predesigned formation and encircle the targets. A numerical simulation example is given to verify the validity of the algorithm.

This paper presents novel affine formation algorithms and implementations in different scenarios for the coordination of multi-agent systems with triple-integrator agent dynamics for both sampled-data and continuous-time settings. The agents in affine maneuver control are to be capable of producing required geometric shapes and simultaneously accomplishing desired maneuvers such as shearing, rotation, translation and scaling. From existing work, these tasks can be accomplished for systems whose agent dynamics are described using double-integrators and the agents communicate continuously in time. In some practical situations, however, the inter-agent communication may be limited to periodic intervals of time. Furthermore, a wide range of systems is governed by complex dynamics described with higher-orders. This paper presents two novel algorithms based on triple-integrator agent dynamics. Four implementation cases comprising of two scenarios each studied in both continuous-time and sampled-data cases are considered. Under the proposed algorithms, the collection of agents are capable of tracking time-varying targets which are affine transforms of the reference formation, if the leaders have knowledge of the required formation maneuvers. Detailed implementation results are presented to demonstrate the efficacy of the proposed algorithms.

The formation control problem in multi-quadrotor systems is studied in this paper. Each quadrotor has limited access to its neighbors’ information due to communication constraint. First, the dynamics model of the quadrotor is linearized using Newton–Euler method. The distributed formation control law is then designed and the stability analysis is provided. An experimental platform is built with three Parrot Bebop drones and an indoor motion capture system. Numerical and experimental results are provided to show the effectiveness of the proposed algorithms.

Multi-agent formation control is an important part of distributed perception and cooperation, which is convenient to complete various complex tasks and would be a key research direction in the future. This paper reviews the corresponding problems of formation control and the existing centralized and distributed formation control strategies. In particular, we discuss four types of distributed formation control methods based on position and displacement in the global coordinate system and distance and bearing in the nonglobal coordinate system, respectively. Moreover, this paper analyzes affine formation which does not require the global coordinate system. Combined with the current practical applications of multi-agent systems, the latest research for the formation control of the unmanned aerial vehicle (UAV), unmanned ground vehicle (UGV), unmanned surface vehicle (USV) and autonomous underwater vehicle (AUV) is given. Finally, the challenges and opportunities in this burgeoning field are discussed.

This paper investigates the coordinated motion control problem of autonomous underwater vehicles (AUVs), and an adaptive cooperative formation control method based on event-triggered mechanism is designed. In the estimation of external disturbance and model uncertainty, adaptive parameters are adopted to represent the upper bound of the learning weight matrix, which reduces the computational pressure of the system. It is proved theoretically that the signals in the system are semi-global uniformly ultimately bounded and independent of the initial state of the system. An event-triggered control mechanism is introduced, and the system updates the control law only when the event is triggered. Simulation results show that the controller can achieve the expected formation shape and save the communication resources of the system.

This paper proposes an efficient fast-optimal balanced differential game (DG) approach to address the formation control problem in dynamic environments for networked multi-agent systems (MASs). Compared to existing receding horizon distributed differential game (RH-DDG) approaches, the proposed approach employs a two-layer game structure to balance optimality and real-time performance, with a focus on formation control, collision avoidance and obstacle avoidance. In the offline layer, the problem is converted into a distributed differential game (DDG) where each agent computes strategies using distributed information from locally neighboring agents. The strategy of each agent self-enforces a unique global Nash equilibrium (G-NE) with a strongly connected communication topology, providing an optimal reference trajectory for the online game. In the online layer, a receding horizon differential game with an event-trigger mechanism (RH-DGET) is presented to track the G-NE trajectory. Ego players are triggered to update online Nash strategies only when the event-triggering condition is satisfied, ensuring the real-time safety certificate. Rigorous proofs demonstrate that the online Nash strategies converge to the offline G-NE until the trigger ends, and a certain dwell time condition is given to prevent the Zeno behavior. Simulation results validate the effectiveness of the proposed approach.

This paper addresses two substantial aspects in the field of robotics: trajectory planning and trajectory tracking for multi-robot systems. The collective movement of the multi-wheeled mobile robots is based on a formation control with a leader–follower strategy. To ensure safe navigation toward the destination within a workspace containing multiple obstacles, we skillfully combine the Modified Artificial Potential Field (MAPF) method and the Improved Particle Swarm Optimization (IPSO) algorithm for a group of nonholonomic mobile robots. A global planner based on IPSO algorithm is assigned to the leader robot, to find the optimal collision-free path. Compared to recent nature-inspired methodologies, the improvement suggested enhance the search capabilities of the algorithm, resulting in a 2% reduction in path length and a 29% decrease in computation time. Simultaneously, the follower robot has the ability to employ either a formation policy or a local planner using MAPF. The proposed modifications address the primary limitations of the conventional method, notably the susceptibility to local minima and the challenge of reaching goals near obstacles. Furthermore, this local planner is adept at evading both static and dynamic obstacles. Extensive real hardware experiments are conducted within multiple scenarios using the mobile robot Qbot-2e to corroborate the obtained simulation results and validate the effectiveness of the proposed approaches both in tracking the desired trajectories, finding the optimal feasible collision-free path and avoiding static and dynamic obstacles for multi-robot systems.

In this paper, a novel formation control strategy is proposed to address the target tracking and circumnavigating problem of multi-UAV formation. First, two sets of definitions, space angle definition and space vector definition, are presented in order to describe the flight state and construct the desired relative velocity. Then, the relative kinematic model between the UAV and the moving target is established. The distributed control law is constructed by using dynamic feedback linearization so as to realize the tracking and circumnavigating control with the desired velocity, circling radius and relative angular spacing. Next, the exponential stability of the closed-loop system is further guaranteed by properly choosing some corresponding parameters based on the Lyapunov method. Finally, the numerical simulation is carried out to verify the effectiveness of the proposed control method.

This paper presents a novel multiple unmanned aerial vehicle (UAV) swarm controller based on the fractional calculus theory. This controller is designed based on fractional order Darwinian pigeon-inspired optimization (FODPIO) and PID algorithm. Several comparative simulations are conducted in the paper. The simulation results reveal that FODPIObased multi-UAV formation controller is superior to the basic PIO and differential evolution (DE) method. The fractional coeffcient in FODPIO algorithm makes it effective optimization with fast convergence rate, small overshoot, and better stability. Therefore, the controller proposed in this paper is feasible and robust.

Inspired by the pigeon behavior pattern, this paper proposes an Unmanned Aerial Vehicle (UAV) swarm control scheme based on hybrid bionic swarm intelligence, which can realize multi-UAV obstacle avoidance during formation control. First, the leadership mechanism of pigeon flock is mapped to UAV swarm, and the virtual leaders are introduced to solve the unfixed relative position of level-1 leader problem. Second, the control law for UAV swarm formation is designed based on artificial potential field theory and analysis of the bionic mechanism. To avoid local minima, a guidance phase is added to the UAV formation process. By analyzing the flocking algorithm, a cooperative interaction control model of UAV swarm is established. Third, the cooperative interactive control law for UAV swarm obstacle avoidance is proposed based on improved artificial potential field function. Then the two bionic swarm control models are combined to realize the formation and obstacle avoidance of UAV swarm based on mixed bionic swarm intelligence. Finally, a series of simulations are conducted to demonstrate the proposed hybrid UAV swarm control algorithm.

In this paper, the formation control problem for unicycle multi-agent systems is considered. The design of a generalized homogeneous leader–follower formation control protocol is studied which shows that such a control protocol can be obtained by “upgrading” from the classical linear control. With this proposed control protocol, a finite-time stability of the formation error is ensured if the acceleration of the leader is bounded by some known value. In addition, if the leader acceleration is unknown but bounded, the robust formation is achieved by ensuring the formation error’s input-to-state stability. Simulations are carried out to verify the effectiveness of the proposed control protocol.

In this paper we give an analytic study to construct a command for a group of vehicles to reach a target in an hostile environment. A consensus be-tween different agents is established. This work is an extension to a previous one^{El Kamel et al.(2009)} to the case of multi-vehicle. The vector which contains all the velocity fields is considered as a feedback control law. We developed a new technique which decompose the vector of velocities to a sum of two parts; an attractive part that guarantees the convergence toward the target and a re-pulsive part that ensures obstacle avoiding. Our approach is based on LaSalle's theorem. The feedback control law ensures also that each vehicle/agent choose the optimal trajectory in front of the obstacle without neither switching control nor tracking trajectory. We introduce the consensus algorithm with a constant reference state using graph theoretical tools to create an hierarchical forma-tion. The stability of the formation is realized when all agents converge to the desired configuration in neighborhood of the target.