Optimal control of UAV elastic formation based on Legendre Pseudospectral Method

The UAV formation reconfiguration problem is described as an optimal control problem in this paper. UAV formation error dynamics are established according to elastic distance vector. The terminal state, control action energy constraints and the constraint of safe distance to avoid colliding are considered during formation reconfiguration. Satisfying all these constraints, the optimal control problem of continuous UAV formation reconfiguration is converted into a nonlinear programming problem. The optimal solution is obtained by Legendre Pseudospectral Method (LPM). The advantage of LPM is to obtain a higher accuracy with fewer nodes. Finally, a three-UAV formation reconfiguration is simulated. It is shown from the results that the ideal formation can be reached within the prescribed time, formation reconfiguration task can be completed and the control standard of minimal formation error and energy consumption can be achieved. The effectiveness and feasibility of the method is verified.