Formation Tracking Control Based On Coordinated Flowfield Estimation

The formation tracking control system has received widespread attention because of the extensive application in ocean information acquisition and space exploration.Previous works ignored influence of the flowfield in external environment for moving multi-agent.In fact,flowfields will not only drive agents to deviate from their trajectories but also destroy the group formation.Therefore,the study of formation tracking control problem in flowfield have great theoretical and practical value.The robust formation tracking control problem based on consistency and adaptive backstepping design method in the two-dimensional Euler flowfield is researched in this paper.Then the design method is expanded to deal with formation tracking control problem on spheres in the three-dimensional parametric flowfield.Finally,the estimation method is further expanded to solve formation tracking control problem for a moving target with unknown speed.The main contents are as follows:Firstly,formation tracking control problem in two-dimensional space based on estimation for an Euler flowfield is studied in this paper.The velocity direction of the flowfield is known but the size is unknown.The update rate of the Euler flowfield's speed is proposed based on adaptive design and consistency method.By geometric expansion method and backstepping design method,virtual control laws of velocity in normal and tangent directions for agents are designed to reach formation tracking,then acceleration inputs in normal and tangent directions are designed to make the errors between the actual speed and the virtual control converge to zero.Conditions for stability of the system are given by LaSalle-Yoshizawa theorem.Validity of the algorithm is proved by simulation results.Secondly,formation tracking control problem on spheres in three-dimensional space based on the estimation for parameterized flowfield is studied in this paper.The basis vectors of the flowfield are known but coefficients are unknown.Based on adaptive estimation for unknown parameters of the flowfield,spherical geometric extension method and Lyapunov method are used to design control input in normal direction of sphere,tangent direction of sphere and tangent direction of the orbit to track the given orbit and form the desired formation.Conditions for stability of the system are given by LaSalle-Yoshizawa theorem.Correctness of the result is proved by numerical simulation results.Finally,formation tracking control problem for the moving target is researched in this paper,when the moving direction of the target is known but velocity is unknown.Consistency method and adaptive design method are applied to estimate velocity of the target.By adaptive backstepping design method,the acceleration components in normal and tangent directions of the orbit is designed based on relative position information to achieve formation tracking for the moving target.Finally,stability of the system is proved by LaSalle-Yoshizawa theorem and simulation results are given by Matlab and Webots.