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In this paper, we study the fixed-time formation (FixF) control problem for the nonlinear second-order multi-agent systems (MASs) with directed graph, where all agents are subject to communication disturbances. To overcome the bounded disturbance of communication and to guarantee the realization of predesignated formation within a fixed-time, a suitable FixF control protocol based on the backstepping method is proposed. Furthermore, to eliminate the dependence of the control parameters on global information, a new adaptive FixF control protocol is provided to combine with some mild conditions of control gain such that the formation with acceptable bounded error of MASs can be achieved within a fixed-time. Finally, the theoretical results are verified by two simulation examples, one of the simulation examples is that we set the desired formation as a regular octagon and the desired formation motion trajectory as a circle, the results show that all agents can form formation motion within a fixed-time. [ABSTRACT FROM AUTHOR]

Formation control is one of the most concerning topics within the realm of swarm intelligence. This paper presents a metaheuristic approach that leverages a natural co-evolutionary strategy to solve the formation control problem for a swarm of missiles. The missile swarm is modeled by a second-order system with a heterogeneous reference target, and the exponential of the resultant error is accumulated to be the objective function such that the swarm converges to optimal equilibrium states satisfying specific formation requirements. Focusing on the issue of the local optimum and unstable evolution, we incorporate a novel model-based policy constraint and a population adaptation strategy that significantly alleviates the performance degradation of the existing natural co-evolutionary strategy in terms of slow training and instability of convergence. With application of the Molloy–Reed criterion in the field of network communication, we developed an adaptive topology method that assures connectivity under node failure, and its effectiveness is validated theoretically and experimentally. The experimental results demonstrate that the accuracy of formation flight achieved by this method is competitive with that of conventional control methods and is much more adaptable. More significantly, we show that it is feasible to treat the generic formation control problem as an optimal control problem for finding a Nash equilibrium strategy and solving it through iterative learning. [ABSTRACT FROM AUTHOR]

The important practical problem of robust synchronization in distance and orientation for a class of differential-drive mobile robots is tackled in this work as an active disturbance rejection control (ADRC) problem. To solve it, a kinematic model of the governed system is first developed based on the distance and formation angle between the agents. Then, a special high-order extended state observer is designed to collectively estimate the perturbations (formed by longitudinal and lateral slipping parameters) that affect the kinematic model. Finally, a custom error-based ADRC approach is designed and applied assuming that the distance and orientation between the agents are the only available measurements. The proposed control strategy does not need time-derivatives of the reference trajectory, which increases the practical appeal of the proposed solution. The experimental results, obtained in laboratory conditions with a set of differential-drive mobile robots operating in a leader–follower configuration, show the effectiveness of the proposed governing scheme in terms of trajectory tracking and disturbance rejection. [ABSTRACT FROM AUTHOR]