Time-optimal control for formation reconfiguration of multiple unmanned aerial vehicles

For a team of unmanned aerial vehicles (UAVs) in leader-follower mode, the dynamic relative position relationships between follower vehicles and leader vehicle are described with elastic distance vector. The desired geometric shape in formation reconfiguration is constructed via the elastic coefficient matrix of distance. So the second-order kinematics model, follower vehicles' control equation is linearized with the elastic distance vector. Furthermore, the problem of formation flying reconfiguration is described as a time-optimal control problem with constrains. Pseudospectral Legendre method is proposed to find this time-optimal solution. Simulation results show that this control method can solve the formation flight reconfiguration effectively. Moreover, the elastic distance between two adjacent vehicles can adapt to the changes of the follower vehicles' velocities, so the tracking performance is improved greatly and become more secure.