Optimal control of formation reconfiguration for multiple UAVs based on Legendre Pseudospectral Method

The formation reconfiguration problem of the multiple unmanned aerial vehicles (Multi-UAVs) is described as an optimal control problem in this paper. Firstly, the control model of formation flight is constructed with the three-dimensional elastic distance vector, which describes the relationship between the speed and distance of adjacent UAVs in the leader-follower type. Furthermore, the constraints of communication distance and the security anti-collision distance are taken into account, and the formation is modeled to a fuel optimal problem with terminal state restrictions. Then, the optimal control problem of UAV formation flight is transformed into a nonlinear programming problem based on Legendre Pseudospectrum Method. The advantage of LPM is to obtain a higher accuracy with fewer nodes in the process of discretization. Finally, the formation with three UAVs is simulated in Matlab and solved by Tomlab toolkit. The simulation results show that the formation can be well achieved the desired new shape with minor position error and optimal fuel. The effectiveness and feasibility of the method is verified.