Online trajectory optimization and guidance algorithm for space interceptors with nonlinear terminal constraints via convex programming

Abstract

Purpose In this paper, an online convex optimization method for the exoatmospheric ascent trajectory of space interceptors is proposed. The purpose of this paper is to transform the original trajectory optimization problem into a sequence of convex optimization subproblems. Design/methodology/approach For convenience in calculating accuracy and efficiency, the complex nonlinear terminal orbital elements constraints are converted into several quadratic equality constraints, which can be better computed by a two-step correction method during the iteration. First, the nonconvex thrust magnitude constraint is convexified by the lossless convexification technique. Then, discretization and successive linearization are introduced to transform the original problem into a sequence of one convex optimization subproblem, considering different flight phases. Parameters of trust-region and penalty are also applied to improve the computation performance. To correct the deviation in real time, the iterative guidance method is applied before orbit injection. Findings Numerical experiments show that the algorithm proposed in this paper has good convergence and accuracy. The successive progress can converge in a few steps and 3–4 s of CPU time. Even under engine failure or mission change, the algorithm can yield satisfactory results. Practical implications The convex optimization method presented in this paper is expected to generate a reliable optimal trajectory rapidly in different situations and has great potential for onboard applications of space interceptors. Originality/value The originality of this paper lies in the proposed online trajectory optimization method and guidance algorithm of the space inceptors, especially for onboard applications in emergency situations.

Correction Strategy of Online Midcourse Guidance for High-Speed Gliding Target Interceptor

“…Compared with the methods of regenerating optimal trajectories based on the target's maneuver in documents [6][7][8][9][10][11][12][13][14][15][16][17], the method in this paper does not need to regenerate the optimal trajectory based on the updated PIP of the target, which avoids the huge computational cost brought by re-optimization. In addition, compared with the methods in documents [18][19][20][21][22][23][24][25][26][27], the correction algorithm in this paper is not limited to the original trajectory. If the trajectory needs to be changed, the engine start direction can be determined by the required speed, which is more suitable for the application scenario where PIP updates occur in a wide space and for intercepting high-speed gliding targets.…”

“…However, due to the optimization near the nominal trajectory, it cannot cope with the situation that the terminal constraint update range is large and the updated law is uncertain. Some references attempted to introduce the rolling time domain control method [24], the model predictive static programming method [25], and the iterative guidance method [26,27] to continuously and iteratively correct the trajectory, but they could not effectively solve the problem of the PIP random update in a wide range.…”