Trajectory Optimization Method of Interceptor for High-Speed Gliding Target via Hp-Adaptive Radau Pseudo-Spectral Method

The high speed gliding aircraft has fast flight speed, posing high interception difficulty. This paper proposes a multi-stage interception scheme and presents a trajectory optimization method based on the hp adaptive Radau pseudospectral method (hp-ARPM) for interceptors. This method can effectively meet various constraints such as heat flux density and dynamic pressure, effectively solving the trajectory optimization problem of interceptors. Firstly, the flight process of interceptors is divided into initial boost stage, midcourse guidance stage, and terminal guidance stage to meet the requirements for long range interception of high-speed gliding aircraft. Taking into account that the initial boost stage is strongly affected by aerodynamic forces while the midcourse guidance stage is weakly affected, separated motion models are established for the initial boost stage and the midcourse guidance stage to more precisely describe the flight behavior of interceptors. Secondly, a multi-stage, multi-constraint nonlinear trajectory optimization model for interceptors is constructed, with connection constraints, process constraints, and optimization performance indicators established for different flight stages. Then, by using the hp-ARPM to transform the optimal control problem into a nonlinear programming problem (NLP), the optimal control solutions for the boost stage and midcourse guidance stage of interceptors are directly obtained by solving the NLP problem. The hp-ARPM method can adaptively adjust the number of nodes, improving optimization accuracy and computational efficiency. Simulation comparison experiments demonstrate that the multi-stage interception scheme proposed in this paper is feasible, and the hp-ARPM shows superior performance indicators compared to the Gauss pseudo-spectral method (GPM).