High-Accuracy Rocket Landing via Lossless Convexification

With the development of rocket technology, achieving high-precision landing has become a key technical challenge in the field of aerospace. To cope with this challenge, we propose a lossless convexification algorithm based on the integral pseudospectral method in this paper. Firstly, for the fuel optimization problem, the continuous dynamic equations and constraints are discretized with high accuracy using an integral-type pseudospectral method. By constructing a global integration matrix at Legendre–Gauss nodes, the original complex continuous problem is effectively transformed into a discrete form that is more tractable for numerical optimization. Secondly, the non-convex constraints are transformed using the lossless convexification technique, thereby reformulating the original problem as a second-order cone programming (SOCP) problem. The effectiveness of the proposed algorithm is validated through numerical simulations, which demonstrate high landing accuracy, robustness, and fuel efficiency. These results highlight the algorithm’s high performance and strong potential for practical application in space missions.