Multistage cooperative trajectory planning for multimissile formation via Bi-level sequential convex programming

Owing to the highly nonlinear dynamics and high number of nonlinear constraints, it is exceedingly difficult and computationally expensive to solve the cooperative trajectory planning problem of multimissile formation using existing approaches. To address this issue and improve the convergence property and computational efficiency, a bi-level sequential convex programming (SCP) method consisting of a system coordination level and an individual optimization level is proposed to solve the cooperative trajectory planning of missile formation. At the system level, the time consensus constraints are determined, the cooperative constraints that should be considered in the next iteration of the individual trajectory optimization level are identified, and the members that have converged are removed from the optimization sequence. As the number of members in the optimization sequence and the number of cooperative constraints considered in the individual SCP are clearly decreased, the convergence property and the computational efficiency of cooperative trajectory planning are evidently improved. At the individual level, the proposed method creatively proposes the innovative idea: based on the updated information of the system level, each member solves its individual trajectory optimization sub-problem independently and sequentially by gradually adding and tightening the cooperative constraints with the evolution of optimization iteration of SCP, which can further enhance the convergence property. Numerical simulations show that the proposed bi-level SCP method can effectively solve the multistage cooperative trajectory planning of multimissile formation with good convergence property, exhibiting the excellent scalability to the number of members and higher effectiveness. The comparison with the generation optimal control software (GPOPS) method further demonstrates the high efficiency of the proposed method.