Abstract
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.
Highlights
The cooperative attack of a missile formation presents better performance than that of an individual missile in penetrating defense systems, detecting maneuvering targets, and surviving the threats [1]–[4], and the cooperative attack has become an attractive and active research topic
As the number of missiles participating in the optimization is gradually reduced with the evolution of iteration and the number of constraints considered is clearly decreased, the computational efficiency and the convergence property have been obviously improved for the cooperative trajectory optimization with the proposed Bil-sequential convex programming (SCP) method, which is beneficial to the expansion of the formation size
It may be noticed that both types of minimum distances are always above the lower bounds. These results demonstrate the effectiveness of the proposed bi-level SCP (Bil-SCP) method and the GPOPS in solving multimissile formation cooperative trajectory planning problems
Summary
The cooperative attack of a missile formation presents better performance than that of an individual missile in penetrating defense systems, detecting maneuvering targets, and surviving the threats [1]–[4], and the cooperative attack has become an attractive and active research topic. In the cooperative attack scenario, multiple missiles are required to attack the target simultaneously to utilize formation advantage with the purpose of striking the enemy defense system and the target [21], [22] To address this issue and to ensure the flight time consensus, Wang et al proposed a decoupled cooperative trajectory planning approach for UAV formation, in which the decoupled sub-problems of trajectory optimization considering the constraint on time consensus for each member was solved with SCP [23]. To address the aforementioned issues and improve the convergence property and computational efficiency, a bi-level SCP (Bil-SCP) method comprising both the system and the individual level, is developed to solve the cooperative trajectory optimization problem of missile formation considering multiple stages (i.e., formation aggregation, formation maintenance, formation penetration and cooperative attack).
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