Generalized-α-projection Method For Multi-agent Formation Contro

With the rapid development of modern society,formation control of multi-agent system has shown broad application prospects in military,aerospace and other fields,and has gradually become a research hotspot in the field of automatic control.The coordination and formation control of common multi-agent systems,such as mechanical systems,ships,aircraft,unmanned aerial vehicles,spacecraft,etc.,has become the research object of increasing concern.However,with the deepening of the multi-agent related research,the complexity of the single agent equation increases and the number of agents increases,which puts forward higher requirements for the stability of the numerical algorithm.The generalized-α method is a fast and efficient method for solving differential equations.The generalized-α projection method combined with the constrained projection method can solve the differential equations stably when the step size is large,and the computational efficiency is high.In this paper,a multi-agent formation control dynamic model is established to study the control effect and numerical stability of the generalized-α projection method.In this paper,a multi-agent formation control dynamic model described by Lagrange equations is established.The force generated by the virtual constraints is applied to the system through the actuator as a controlling force,so that the system can keep the constraints of the control target.The Lagrange multiplicator method is used to design the formation control law,and the differential equation describing the motion in the dynamics model is transformed into the differential algebraic equation with virtual constraints.The generalized-α projection method is given to solve the multi-agent formation control problem,and compared with R-K method and Baumgarte method,the application of numerical stability method in the multi-agent field is studied.Then,for two typical multi-agent formation control problems,the low-speed supply formation problem of ocean surface ships and the formation maintenance control problem of formation satellites,the generalized-α projection method is applied to solve the problem,and is compared with the fourth-order Runge-Kutta method,Baumgarte method and other stability methods.The experimental results show that the generalized-αprojection method can accurately control the formation of multi-agent,solve the problem efficiently and quickly when the initial value has interference,and avoid the difficulty of parameter selection in Baumgarte method.Extending the generalized-α projection method to multi-agent formation control is helpful to the development of multi-agent control science.