Time-varying formation dynamics modeling and constrained trajectory optimization of multi-quadrotor UAVs

The formation of multi-quadrotor UAVs (QUAVs) in long flights will encounter many constraints and obstacles in the flight process, so it is necessary to change the formation shape to avoid these constraints. When the flight path of QUAVs is individually optimized, multiple individual dynamic problems will be faced, making the solution complicated and spending a long time. In this paper, as a whole instead of individuals considering the QUAVs, the formation is regarded as a rigid body using the Voronoi graph theory method in the flight process. The constraints of the followed QUAVs are transformed into the constraints of leader QUAV. Therefore, the formation is transformed for different constraints by changing the virtual rigid body structure or shape. A time-varying model is established to facilitate the use of optimization. The energy consumption of the leader UAV within the specified time is minimized as the trajectory optimization objective. The optimization improvement of the end heading and height constraints is proposed. A trajectory optimization method for the leader QUAV based on Gauss pseudospectral method is proposed, transforming the original optimal control problem into the nonlinear programming one. The simulation results demonstrate and verify the proposed method.