A Guidance Law with Impact Time and Angle Constraints Under Nonlinear Varying Velocity Using Pseudospectral Online Planning

To address the challenge of precise impact time and angle control during the terminal phase of high-speed vehicle flight, this paper proposes a pseudospectral online planning terminal guidance law incorporating time and angle constraints. This approach effectively accounts for the nonlinear varying velocity characteristics under significant aerodynamic drag. Initially, an analytical expression for the optimal acceleration in angle control is derived based on a biased proportional guidance framework. Subsequently, a time control bias term is designed, building upon the analytical acceleration formula for angle control. To reduce computational complexity in numerical solutions, the time bias term is parameterized, and the deviation propagation equations are linearized. Then, utilizing Lagrange interpolation polynomials with Legendre-Gauss points as nodes, the state and control variables are discretized. Through pseudospectral approximation in the polynomial space, an analytical correction formula for time control is derived. Finally, numerical simulation results demonstrate that, compared to existing methods, the proposed algorithm offers superior control precision and computational efficiency, making it more suitable for the complex terminal flight environment of high-speed vehicles.