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This paper presents a distributed planar leader-follower formation maneuver control strategy for multi-agent systems with different agent dynamic models. This method is based on the barycentric coordinate-based (BCB) control, which can be performed in the local coordinate frame of each agent with required local measurements. By exploring the properties of BCB Laplacians, a time-varying target formation can be BCB localizable by a sufficient number of leaders uniquely, and this formation is converted from a given nominal formation with geometrical similarity transformation. The proposed control laws can continuously maneuver collective single- and double-integrator agents to achieve a translation, scale, rotation, or even their compositions in various directions. For the formation shape control problem of multi-car systems with/without saturation constraints, the obtained control performance can preserve good robustness. Global stability is also proven by mathematical derivations and verified by numerical simulations. [ABSTRACT FROM AUTHOR]

In order that the flight vehicle group could form the expected formation, the “leader-follower” formation control law is investigated. First, the distributed extended state observer (DESO) is designed such that the followers could estimate the virtual leader’s position and velocity. Then, the expected positions of the followers are calculated based on the observer outputs and the nominal formation configuration. A dynamic surface control-based position tracking control law is designed for the followers to track the expected positions. Based on the Lyapunov theory, the stability of the proposed method is proved, while numerical simulations validate the effectiveness. The DESO could estimate both the virtual leader’s position and velocity via only the position observations. The method proposed guarantees that the orientation of the formation is consistent with the direction of the virtual leader’s velocity.

The practical fixed-time affine formation (PFAF) control problem for multi-agent systems is studied in this brief. The tasks of formation assembly, transformation and time-varying maneuver are able to be completed by affine formation control technique based on stress matrix flexibly and conveniently. Based on time-based generators (TBG) techniques, two fixed-time control laws are designed for leaderless and leader-follower affine formation control problems, respectively. Compared with the existing finite-time affine formation control laws, the convergence times of the proposed control laws in this brief are independent of the system’s initial states. Finally, numerical simulation results are presented to demonstrate the effectiveness of the proposed control laws. [ABSTRACT FROM AUTHOR]

This paper considers an affine maneuver tracking control problem for leader-follower type second-order multi-agent systems in the presence of time-varying delays, where the interaction topology is directed. Using the property of the affine transformation, this paper gives the sufficient and necessary conditions of achieving the affine localizability and extends it to the second-order condition. Under the (n + 1)-reachable condition of the given n-dimensional nominal formation with n + 1 leaders, a formation of agents can be reshaped in arbitrary dimension by only controlling these leaders. When the neighboring positions and velocities are available, a formation maneuver tracking control protocol with time-varying delays is constructed with the form of linear systems, where the tracking errors of the followers can be specified. Based on Lyapunov-Krasovskii stability theory, sufficient conditions to realize affine maneuvers are proposed and proved, and the unknown control gain matrix can be solved only by four linear matrix inequalities independent of the number of agents. Finally, corresponding simulations are carried out to verify the theoretical results, which show that these followers can track the time-varying references accurately and continuously. [ABSTRACT FROM AUTHOR]

The affine formation maneuver (AFM) control problem using the zero-sum differential game is studied for a second-order multi-agent system (MAS) against cyber-injection attacks on the actuators. First and foremost, the distributed control signals and the cyber-injected attack signals are viewed as two competing teams. Then, the leader-follower tracking error system is established where the followers aim to track the AFMs of the leaders. The leader-follower distributed optimal control policies and the cyber-attack attenuation policies are derived from the Nash equilibrium solution of the Hamilton-Jacobi-Isaac (HJI) equation. The solution of the HJI equation is estimated with the aid of the critic neural network. The weights of the critic system are learned online based on the adaptive dynamic programming (ADP) scheme. The uniformly ultimately bounded stability of the closed-loop system under the formulated zero-sum differential game control strategy has been proven by the Lyapunov stability theorem. A simulation example illustrates that the presented control method can attenuate cyber-injection attacks on the actuators and maintain the AFMs of the agents. [ABSTRACT FROM AUTHOR]

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. • The underactuated AUVs are considered in this paper. • Graph rigidity and backstepping techniques are employed to achieve formation control. • Affine transformation technique is used to realize formation reconfiguration. • The Lyapunov based stability analysis shows that the proposed controller is stable. • Experimental results demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Formation path planning is a significant cornerstone for unmanned aerial vehicle (UAV) swarm intelligence. Previous methods were not suitable for large-scale UAV formation, which suffered from poor formation maintenance and low planning efficiency. To this end, this paper proposes a novel millisecond-level path planning method appropriate for large-scale fixed-wing UAV formation, which consists of two parts. Instead of directly planning paths independently for each UAV in the formation, the proposed method first introduces a formation control strategy. It controls the chaotic UAV swarm to move as a single rigid body, so that only one planning can obtain the feasible path of the entire formation. Then, a computationally lightweight Dubins path generation method with a closed-form expression is employed to plan feasible paths for the formation. During flight, the aforementioned formation control strategy maintains the geometric features of the formation and avoids internal collisions within the formation. Finally, the effectiveness of the proposed framework is exemplified through several simulations. The results show that the proposed method can not only achieve millisecond-level path planning for the entire formation but also excellently maintain formation during the flight. Furthermore, simple formation obstacle avoidance in a special case also highlights the application potential of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the formation control problem for a multi-agent system is studied. Two new robust control algorithms for serial and parallel formations respectively are proposed, which take the constraints of limited field of view into consideration. Without the need for any global information, the only relative information required is distance and bearing angle, thus is easy to implement with onboard directional sensors. It is then demonstrated how complex formations can be realized by combining the proposed basic controllers. Finally, effectiveness of the proposed algorithms is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

To drive a group of agents to maneuver continuously with the desired collective forms, this paper addresses a distributed formation maneuver control problem of directed networked high-order multi-agent systems in arbitrary dimensions. Unlike the conventional methods where the target formation is time invariant, we propose an affine formation method based on the properties of affine transformation, in which the target formation can be time-varying and affinely transformed from the given nominal formation. This paper provides and proves a sufficient and necessary condition of achieving the directed graphical affine localizability, and it only needs that the leaders have a generic configuration and the followers are accessible to the subset of leaders. To achieve the whole formation maneuvers, assume that the leaders decide the whole formation's maneuver actions, then the control algorithms of the arbitrary-order integrator followers are proposed to track the time-varying target formation and the global convergence of tracking errors is also proved. Furthermore, this paper studies the practical problems of formation maneuvers when existing non-uniform time delays. Finally, both two-dimensional and three-dimensional simulation examples are given to demonstrate the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the trajectory tracking by multiple agents in formation. Each agent is modeled as a double-integrator system. The proposed algorithm works on a connected graph instead of a fully connected graph that requires lesser communication and computation. The three aspects of the control scheme—connectivity assurance, collision avoidance, and formation have been ensured by the design of the novel control law consisting of four terms. A novel bounded potential function has been introduced that ensures interagent collision avoidance through the innovative design of critical parameters associated with this potential function. Another novel bounded potential function has been designed to ensure the connectivity in the group. The concept of consensus has been used to acquire and maintain the desired formation pattern with velocity agreement among agents. The proposed control scheme is further extended to the problem of trajectory tracking while achieving other control objectives. Both the schemes have been shown to be convergent using Barbalat's Lemma. Detailed theoretical analysis of the algorithms has been carried out including boundedness of the control actions. The performance of proposed algorithms has been demonstrated through extensive simulations in 2-D and 3-D environments using 6 and 60 agents, respectively. [ABSTRACT FROM AUTHOR]

The paper outlines orbit and formation control of a long-distance (>100 km) two-satellite formation for the monitoring of the Earth gravity. Orbit control applies to a single satellite and performs altitude control. Here, formation control is formulated as a control capable of altitude and distance control at the same time. The satellites being placed in a low Earth orbit, orbit, and formation control employ the measurements of a global navigation system. Formation control is imposed by long-distance laser interferometry, which is the key instrument for gravity measurement. Orbit and formation control are low-frequency control systems in charge of canceling bias and drift of the residual drag-free accelerations. Drag-free control is the core of the orbit/formation control since it allows the formation to fly drag-free only subject to gravity. Drag-free control being required to have a bandwidth close to 1 Hz, is designed as the inner loop of the formation control. In turn, formation control must not destroy drag-free performance, in which objective demands that formation control be effective only below the 0.2 mHz orbital frequency. Control design is based on a new orbit and formation dynamics, which are compared with the classical Hill–Clohessy–Wiltshire equations. The new dynamic equations are the first step in building the embedded model, which is the core of the control unit. Embedded model derivation is explained only for the orbit control, and briefly mentioned for the formation control. Simulated results are provided. Drag-free results are compared with GOCE experimental data. [ABSTRACT FROM PUBLISHER]