Formation Control Problem Research Articles

Generalized Homogeneous Formation Control for Unicycle Multi-Agent Systems

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.

Distributed Adaptive Formation Control for Fractional-Order Multi-Agent Systems with Actuator Failures and Switching Topologies

In this paper, a class of distributed adaptive formation control problems are investigated for second-order nonlinear fractional-order multi-agent systems with actuator failures and switching topologies. To address these challenges, two adaptive coupling gains based on agents’ position and velocity are incorporated into the control protocol. Using the Lyapunov method along with graph theory and matrix analysis, sufficient conditions for system stability are derived in the presence of actuator failures and switching topologies. The effectiveness of the proposed control protocol is demonstrated through numerical simulations, which show its capability to maintain stable formation control under these challenging conditions.

Алгоритмы группового управления подводными подвижными объектами

The problem of formation control is relevant when searching for objects, surveying a given area, and group monitoring. In the underwater environment, this problem is complicated by restrictions on the frequency of receiving navigation data and the speed of information exchange between underwater robots. The purpose of this article is to develop and study group control algorithms that ensure the given formation and the maintenance of this formation during movement. The article provides an overview of the results in the field of group control of underwater vehicles, provides a mathematical model of the object, navigation system, underwater environment and communication system. The equations of kinematics and dynamics of a solid body in three-dimensional space, supplemented by equations of actuators, are used as a mathematical model. Algorithms for the distribution of moving objects in formation and nonlinear control algorithms for moving in a line are proposed. When constructing the devices, it is assumed that there is a group leader who transmits his coordinates to the rest of the underwater robots. Motion control is synthesized by the method of positional trajectory control in the form of a function of external coordinates. A study was carried out using numerical methods, during which the process of the formation and movement along the trajectory described by straight line segments was studied. The influence of errors in the navigation system and the frequency of data updates on the error of maintaining a given position by a separate underwater robot is investigated.

Reinforcement learning intermittent optimal formation control for multi-agent systems with disturbances

Abstract This paper investigates disturbance-resistant intermittent event-triggered optimal formation control problems of second-order multi-agent systems by using the reinforcement learning method, which takes into account the influence of network damage including denial-of-service (DoS) and deception attacks, stochastic noises, and unknown external disturbances. Firstly, we propose a novel disturbance observer based on adaptive control to estimate unknown external disturbances under an event-triggered mechanism. Secondly, by use of estimation of disturbances, an innovative intermittent event-triggered optimal formation algorithm is given. By applying theories such as Lyapunov stability and stochastic stability, sufficient conditions are derived to guarantee that all agents achieve the desired formation in mean square sense. Additionally, in the model-free case, the optimal controller is solved using the least squares method, which is computationally less complex than some existing approaches. Finally, the theoretical results are effectively validated through simulation examples.

Fault‐tolerant formation control of multi‐agent systems with multiple leaders based on intermediate variable estimator

AbstractThis article investigates the distributed fault‐tolerant formation control problem of a multi‐leader system with process faults and system uncertainties. This study guarantees all the followers to achieve a specified time‐varying formation and track the combination of multiple leaders. By treating faults as a special type of states, an enhanced system is constructed. Furthermore, an intermediate variable observer is designed, but the observer matching condition is not necessary. The observer is used to estimate faults and system uncertainties, for reconstructing the formation controller. The observer gains are determined by solving linear matrix inequalities. Subsequently, controller gains are designed based on Lyapunov theorem and adaptive techniques. Finally, the proposed method is verified through a simulation example.

Adaptive neural network based quadrotor UAV formation control under external disturbances

The formation control of a team comprised of multiple quadrotor Unmanned Aerial Vehicles (UAVs) may severely be affected by the unknown external disturbances. The external disturbances are caused by wind forces to create aero-dynamical disturbances. This article addresses the robust formation control problem of multiple UAVs system despite the effect of external disturbances that allow sustaining a stable network connection among the UAVs and maintaining different formations assigned to them. First, a Radial Basis Function Neural Network (RBFNN) based model is developed to reciprocate the external disturbances along the positional and the attitude subsystems. Then incorporating the estimated disturbance values a distributed adaptive formation controller is devised using the Lyapunov theory. It consists of a positional and an attitude controller associated with the translational and the rotational movements of the UAVs. The stability is validated by satisfying the criteria of the Lyapunov stability function. The UAVs are connected through variable adjacency matrix based directed network topology and the network connectivity is established through the properties of the Laplacian Matrix. The robustness of the designed controller is justified via rigorous simulation studies for different sets of desired formations such as triangular, squared, tetrahedron, octahedron and cube shaped. The reference trajectories are considered as spiral, straight line and circular shaped. The time varying external disturbances are considered of sinusoidal waveform of different magnitudes. The simulation results signifies that the proposed RBFNN based formation controller reciprocate different sinusoidal waveforms to achieve the desired formations successfully. Extensive comparative studies demonstrate the efficacy of the proposed adaptive formation controller over the existing controllers presented in the literature for different shapes of trajectories and desired formations.

Formation Control with Feedback Nash Strategy for Multiple Unmanned Aerial Vehicles in Unknown Environments

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.

A Bio-Inspired Sliding Mode Method for Autonomous Cooperative Formation Control of Underactuated USVs with Ocean Environment Disturbances

In this paper, a bio-inspired sliding mode control (bio-SMC) and minimal learning parameter (MLP) are proposed to achieve the cooperative formation control of underactuated unmanned surface vehicles (USVs) with external environmental disturbances and model uncertainties. Firstly, the desired trajectory of the follower USV is generated by the leader USV’s position information based on the leader–follower framework, and the problem of cooperative formation control is transformed into a trajectory tracking error stabilization problem. Besides, the USV position errors are stabilized by a backstepping approach, then the virtual longitudinal and virtual lateral velocities can be designed. To alleviate the system oscillation and reduce the computational complexity of the controller, a sliding mode control with a bio-inspired model is designed to avoid the problem of differential explosion caused by repeated derivation. A radial basis function neural network (RBFNN) is adopted for estimating and compensating for the environmental disturbances and model uncertainties, where the MLP algorithm is utilized to substitute for online weight learning in a single-parameter form. Finally, the proposed method is proved to be uniformly and ultimately bounded through the Lyapunov stability theory, and the validity of the method is also verified by simulation experiments.

Formation control and lag formation control for human–machine interaction second-order multiagent systems

In this paper, the formation control and lag formation control problems for second-order multiagent systems (MASs) with and without nonlinear intrinsic dynamics are discussed, in which a fraction of agents are controlled by humans and the others are free from human intervention. By selecting suitable control protocol and Lyapunov functional, a formation criterion for the second-order nonlinear MAS is derived. Furthermore, considering that time delay always exists between agent and virtual leader due to finite transmission speed, a lag formation criterion for the second-order nonlinear MAS is also obtained by selecting appropriate control strategy. In addition, the above obtained results are further extend to the double-integrator MAS. Finally, the devised control strategies are verified by exploiting two numerical examples.

Output-feedback formation tracking control of autonomous surface vessels with collision avoidance

In this paper, a formation control problem with collision avoidance is investigated for underactuated surface vessels with position–heading measurements. Each vessels is subject to actuator magnitude and rate saturations. At first, an anti-saturation nonlinear extended state observer is developed to recover the linear velocity and yaw rate as well as unknown uncertainty and disturbances. Then, observer-based formation control laws are designed based on an artificial potential functions, obstacle avoidance yaw references and a backstepping technique. The stability of closed-loop formation control system is proved. The salient features of this paper are as follows. First, formation control with the capability of collision avoidance is achieved by using artificial potential functions and obstacle avoidance yaw references, which is more aggressive. Second, the proposed controller is able to deal with the magnitude and rate constraints of the actuator. Third, the proposed anti-saturation nonlinear extended state observer can achieve better estimation results for rapidly changing signals. Simulation results are given to substantiate the proposed formation control laws.

A generalized homogeneity-based formation control for perturbed unicycle multi-agent systems

In this paper, the formation control problem is considered for unicycle multi-agent systems whose kinematic models contain some external perturbations. The approach to addressing the problem involves the development of a homogeneity-based leader–follower formation control protocol, which takes into account bounded perturbations. It is shown that such a control protocol can be obtained if there is an external supervisor monitoring the group and broadcasting a limited amount of data to followers. Simulations as well as experimental results are performed to illustrate the effectiveness of the proposed control protocol using the QBot2 unicycle mobile robot.

Displacement-based formation control with predefined attitude over time-varying topologies

This paper explores a displacement-based formation control problem in the presence of misaligned orientations among different body coordinate frames. When agents sense and adjust their relative positions, these misalignments suggest the attitudes of the agents in the absence of an agreement, thereby distorting collective behavior. To mitigate this distortion, an angular velocity control protocol is provided and embedded into a positively invariant set, aiming to establish a predefined attitude agreement. Based on this agreement, a formation control protocol is then to achieve the desired formation shape. Unlike the original alignment case, not only the dynamics of the agents among different coordinate frames are considered, but also the connectivity on the underlying topologies is relaxed. It should be pointed out that constructing a common Lyapunov function for these systems is challenging, since typical conditions for its existence and solvability, e.g., the double stochasticity condition or the non-trivial eigenvalue assignment, may not be satisfied. To address these challenges, a geometric analysis framework, derived as several polytopes and associated properties, is extended to handle these systems without the requirement for such conditions. By utilizing these properties, the control objectives of attitude and formation control are achieved, indicating that the desired formation shape is guaranteed through the implementation procedure of the attitude consensus. Finally, an example is conducted to verify the main results.

A Robust Hybrid Iterative Learning Formation Strategy for Multi-Unmanned Aerial Vehicle Systems with Multi-Operating Modes

This paper investigates the formation control problem of multi-unmanned aerial vehicle (UAV) systems with multi-operating modes. While mode switching enhances the flexibility of multi-UAV systems, it also introduces dynamic model switching behaviors in UAVs. Moreover, obtaining an accurate dynamic model for a multi-UAV system is challenging in practice. In addition, communication link failures and time-varying unknown disturbances are inevitable in multi-UAV systems. Hence, to overcome the adverse effects of the above challenges, a hybrid iterative learning formation control strategy is proposed in this paper. The proposed controller does not rely on precise modeling and exhibits its learning ability by utilizing historical input–output data to update the current control input. Furthermore, two convergence theorems are proven to guarantee the convergence of state, disturbance estimation, and formation tracking errors. Finally, three simulation examples are conducted for a multi-UAV system consisting of four quadrotor UAVs under multi-operating modes, switching topologies, and external disturbances. The results of the simulations show the strategy’s effectiveness and superiority in achieving the desired formation control objectives.

Dynamic event-triggered time-varying formation control for heterogeneous unmanned swarm systems with scaling attacks

This paper addresses the problem of time-varying formation control for heterogeneous unmanned swarm systems (USSs) consisting of multiple unmanned aerial vehicles (UASs) and unmanned surface vehicles (USVs) based on a directional switching topology. Firstly, a novel USSs model is established, involving the effect of multiple network attacks, network bandwidth constraints and input saturation. In particular, a scaling attack model is proposed to account for denial-of-service (DoS) and deception attacks. Secondly, a distributed controller based on a dynamic event triggering mechanism is designed to reduce the communication load by adjusting the communication frequency between individuals, and the Zeno phenomenon is effectively avoided. Finally, the Lyapunov function is used to obtain sufficient conditions for system stability and bounds on the frequency and duration of network attacks. The experiments and comparison results verify the proposed strategy's effectiveness and superiority.

Convergence analysis of state estimation for UAV formation under GPS‐denied environments

AbstractIn this article, we focus on the state estimation and formation control problem for a multi‐UAV system, where only parts of UAVs have GPS measurements, that is, the anchors, and the other UAVs measure their relative positions with anchors. With a second‐order discrete‐time model of each UAV in the formation, we analyze the convergence of state estimation (including its expectation and covariance) for commonly used consensus‐based formation control protocols, under the effect of control and measurement noise. More specifically, based on the discrete‐time stability analysis, we obtain the sufficient and necessary conditions for the expectation stability of the formation control. Using the fixed point theorem in positive symmetric matrix subspace and observability analysis, we rigorously prove that the covariance of estimation is bounded if and only if the anchor node set is globally reachable. Based on our analysis, the formation control parameters and system topology can be designed to satisfy sufficient conditions, such that the desired formation pattern can be achieved for the multi‐UAV dynamic system under GPS‐denied environments. Simulation results corroborate the effectiveness of our theoretical results.

Cloud-based time-varying formation active fault-tolerant predictive control of networked multi-agent systems with actuator and sensor faults

This paper addresses the time-varying formation control problem of second-order networked multi-agent systems consisting of a virtual leader and multiple followers, where random communication constraints in the forward and feedback channels as well as actuator and sensor faults are considered. A state observer is designed to estimate the system state and the potential faults, based on which a time-varying formation active fault-tolerant predictive control scheme is proposed. Then, a necessary and sufficient condition is derived to guarantee the stability of the closed-loop system and to achieve the time-varying formation, which is independent of random communication constraints as well as actuator and sensor faults. Finally, simulation results of three contrastive cases are presented to verify the effectiveness of the proposed control scheme.

Position constrained adaptive time-varying formation control of autonomous surface vessels with uncertain dynamics

This paper investigates the adaptive time-varying formation control problem of autonomous surface vessels (ASVs) with position constraints, uncertain dynamics and external disturbances under directed communication topology. Different from the existing studies, the nonlinear error transformation function is combined with formation control to achieve position constraints of ASVs. Based on dynamic surface control and backstepping method, a virtual control law is designed for each vessel. Radial basis function neural networks are employed to approximate the unknown nonlinear continuous function caused by ASVs’ model uncertainties, and the minimum learning parameter (MLP) method is applied to reduce computational complexity. Then, a time-varying formation position constrained controller and an adaptive law are proposed for each ASV. By using the Lyapunov stability theory, it is proved that all signals of the closed-loop ASV system are semi-global uniformly ultimately bounded and the position constrained objective can be achieved. Finally, simulation analyses are given to verify the effectiveness of theoretical results.

Safety-critical formation control of switching uncertain Euler-Lagrange systems with control barrier functions

This paper investigates the safety-critical formation control problem with disturbance rejection for switching uncertain EL MASs in the presence of multiple stationary/moving obstacles. A safety-critical control method is proposed for achieving a collision-free formation for a group of EL systems subject to safety constraints, model uncertainties, and external disturbances. Specifically, a distributed adaptive nominal control law is designed to accomplish the formation control task. Then, based on ISSf-CBF derived safety constraints, a distributed quadratic programming problem is established for computing the optimal control input subject to safety constraints. The safety and stability of the closed-loop control system have been demonstrated. Finally, one exemplary application to safety-critical formation control of some practical multiple mechanical systems is provided to illustrate the effectiveness of the main result.

Safe affine formation using terminal sliding mode control with input constraints

AbstractFormation control is a fundamental task in the realm of autonomous multiagent systems. To drive a group of agents to maneuver continuously with the desired formation, this paper studies the finite‐time affine formation control problem with disturbances, input constraints and safety guarantee. A non‐singular terminal sliding mode control (NTSMC) is implemented to achieve finite‐time convergence of all followers to their desired positions. Additionally, an auxiliary system is deployed to address input constraints resulting from the physical properties of the affine formation system. To mitigate the impact of lumped disturbances, a finite‐time disturbance observer (FTDO) is employed to estimate the disturbances and compensate for their effects. Based on FTDO, the auxiliary system and the above NTSMC, a finite‐time robust controller is developed as the nominal controller. By modifying the nominal controllers to comply with safety constraints, control barrier functions are employed to ensure the safety of the formation system in obstacle‐filled environment. Finally, the effectiveness and feasibility of this method are validated through simulations and real‐world experiments.

Optimal distributed time-varying formation control for second-order multiagent systems: LQR-based method

The optimal leaderless and leader-following time-varying formation (TVF) control problems for second-order multiagent systems (MASs) are investigated, where two optimal TVF control protocols are proposed to achieve the desired formations as well as minimize the comprehensive optimization function that contain the cooperative performance index and the control energy index. For leaderless case, the optimal formation control problem is reformulated as an infinite-time state regulator problem by employing the state space decomposition method, which is subject to specified constraints on energy and performance indices, and the analytic criterion for optimal TVF achievability is subsequently proposed. Then, the results of optimal leaderless TVF control are extended to the leader-following case with switching topologies, where the main challenge is changed to find the optimal controller rather than the optimal gain matrix, and the optimal value of the comprehensive index is accurately determined. Finally, two simulation cases are proposed to validate the effectiveness of the theoretical results, and comparisons with previous works are presented to expound the optimality of the proposed formation control method.