Rocket Landing Guidance Based on Linearization-Free Convexification

The landing problem of a reusable rocket is generally a highly constrained and nonconvex optimization problem. In this paper, we will convexify the problem without relying on any linearization. Specifically, we propose to quickly determine some of the state variables in advance so that the nonlinearity of the dynamics is greatly reduced, and then we accurately convexify the problem by change of variables and transformation of the optimization objective. This convexification process enables us to design an iterative algorithm that can converge very reliably, and the convergence does not rely on any trust region constraint. It should be highlighted that the algorithm is very efficient, generally taking just milliseconds to converge on a personal computer. Furthermore, by ensuring the recursive feasibility of calling the iterative algorithm in each guidance cycle, we can design a landing guidance algorithm that is able to achieve precise landing under various uncertainties and disturbances. Numerical examples are provided to demonstrate the high performance of the iterative algorithm and the landing guidance algorithm.