An improved solution method via the pole-transformation process for the maximum-crossrange problem

The maximum-crossrange problem is difficult to solve rapidly and stably because of highly nonlinear dynamics and nonconvex constraints. In this paper, an improved successive second-cone programming method via the pole-transformation process is proposed. The main contribution of this work is twofold. Firstly, the pole-transformation coordinate frame is defined, and the original problem is reformulated by the pole-transformation process to avoid the linearization of downrange and crossrange angles. The terminal state constraint is relaxed to an inequality constraint, which improves the stability performance of the solution method. Secondly, an adaptively adjustment method of the trust-region contraction coefficient is proposed to improve the convergence performance of the solution method. The optimal solution of the original problem is obtained by the improved successive second-order cone programming method. The numerical experiments verify the effectiveness of the pole-transformation process, and the convergence and stability performances of the improved solution method proposed in this paper.