Real-time Multi-Constrained Polynomial Guidance Based on Analytical Gradient Derivation

The fast generation of optimal trajectories for long-range aircraft, while considering multiple path and terminal constraints, has remained a persistent challenge because of its purely numerical solution process. In this study, to meet the challenge mentioned above, a real-time multi-constrained polynomial guidance method is proposed based on the analytical derivation of gradients for to-be-determined parameters with respect to the optimization objective. Firstly, we formulate the original multi-constrained trajectory optimization problem as a polynomial coefficient determination problem, wherein all parameters except one can be determined analytically. Secondly, we discretize the problem and drive the analytical gradient of the performance indicators with respect to the last parameter. As a result, the last parameter can be quickly determined using a gradient descent iteration method. Thirdly, a closed-loop guidance system is developed based on the fast generation of polynomial trajectory, wherein multiple path and terminal constraints are considered. By these three steps, the original multi-constrained trajectory optimization problem can be partially analyzed (performance index gradient can be calculated analytically), thereby greatly improving the solution speed and enabling the algorithm to be used for on-board close-loop optimization guidance. Simulations in the last section are given to validate the effectiveness of the proposed techniques and verify the advantages of the algorithm on rapidity and constraint satisfaction.