A pseudospectral-convex optimization algorithm for rocket landing guidance

This paper presents an online trajectory optimization algorithm for the rocket landing guidance problem. By combining pseudospectral discretization and an improved successive convexification method, the precision and rapidness of the algorithm are considered simultaneously. To address precision, the pseudospectral discretization method with so-called “spectral accuracy” is adopted, and according to the characteristics of rocket powered landing flight, the unique feature of pseudospectral method can be utilized to build a more accurate optimization model. From the aspect of rapidness, the discrete optimization problem is transformed into a series of convex subproblems via lossless and successive convexification. The successive convexification algorithm is improved by using a dynamic trust-region updating strategy, thereby improving the convergence performance. Convergence analysis is presented to prove that any accumulation point generated by the improved successive convexification algorithm is a stationary point of the original problem. The effectiveness of the proposed algorithm is demonstrated by numerical experiments. With the high-precision optimized trajectory and fast computing speed, the algorithm has the potential to be implemented onboard for real-time applications.