Fast Trajectory Optimization for the Time Delay Effect on Supercavitating Flight

Utilizing supercavitation to achieve drag reduction, a supercavitating vehicle (SV) could travel 3 similar to 5 times faster than conventional underwater vehicles. Aiming at pursuing high stability and better performance for the SV, research on trajectory optimization for the SV in vertical plane was carried out. The principle of independence of cavity section expansion was applied for modelling of the time delay supercavity. Dynamic equations incorporated with complex force models of SVs were analyzed in detail, on the basis of which a mathematical model of the optimal diving trajectory was established. Subsequently, the Time Delay Gauss Pseudospectral Method (TDGPM) was developed to achieve fast optimization. The solving process was significantly accelerated by converting the optimal control problem into nonlinear programming (NLP) problem. The time delay effect of supercavitating flight was taken into account by interpolation of variables on all discretized nodes. Numerical solutions for different optimal diving trajectories and corresponding manoeuvres were obtained based on the proposed method using 20 Gauss-Legendre discretization nodes. Results of rapid optimization of the supercavitating trajectories indicate the feasibility and fast convergence of TDGPM.