Optimal Guidance for Quasi-Planar Lunar Ascent Based on Local Degradation

The problem of guiding a constant thrust vehicle to achieve lunar orbit with optimal fuel consumption is the focus of this article. The computational cost of the optimal guidance law remains a challenge for onboard computers for traditional indirect optimal methods, primarily due to the numerical iteration required to solve nonlinear equations within small guidance cycles. To address this, an algorithm based on the fast local iteration (FLI) is presented in this article. First, a scaling factor <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> is introduced into the guidance law, which is recalculated in each guidance cycle, making the complete guidance law degenerate into a zeroth-order problem that can be solved analytically within each cycle. Second, the FLI algorithm is developed to solve for appropriate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> iteratively to find the best matching problem for cycles, and detailed theoretical reasoning is conducted. Finally, the algorithm is tested across three simulation scenarios. In comparison with the results of the pseudospectrum method, the proposed algorithm demonstrated commendable speed, versatility in initial state selection, and adaptability to gravitational field functions, respectively, all while maintaining good fuel consumption performance.