Low-thrust, high-accuracy trajectory optimization

Multirevolution, very low-thrust trajectory optimization problems have long been considered difficult problems due to their large time scales and high-frequency responses. By relating this difficulty to the well-known problem of aliasing in information theory, an antialiasing trajectory optimization method is developed. The method is based on Bellman's principle of optimality and is extremely simple to implement. Appropriate technical conditions are derived for generating candidate optimal solutions to a high accuracy. The proposed method is capable of detecting suboptimality by way of three simple tests. These tests are used for verifying the optimality of a candidate solution without the need for computing costates or other covectors that are necessary in the Pontryagin framework. The tests are universal in the sense that they can be used in conjunction with any numerical method whether or not antialiasing is sought. Several low-thrust example problems are solved to illustrate the proposed ideas. It is shown that the antialiased solutions are, in fact, closed-loop solutions; hence, optimal feedback controls are obtained without recourse to the complexities of the Hamilton-Jacobi theory. Because the proposed method is easy to implement, it can be coded on an onboard computer for practical space guidance.