Optimal Rocket Landing Guidance Using Convex Optimization and Model Predictive Control

Abstract

In this paper, a novel guidance algorithm based on convex optimization, pseudospectral discretization, and a model predictive control (MPC) framework is proposed to solve the highly nonlinear and constrained fuel-optimal rocket landing problem. The main strategy is to solve the guidance problem by implementing online trajectory optimization in a receding-horizon manner and feeding the rocket with the most recently updated optimal control commands. A pseudospectral-improved successive convexification (PISC) algorithm is adopted to solve the trajectory optimization problem due to its high solution accuracy and computation speed. The PISC algorithm is then embedded in the MPC framework to construct the guidance algorithm. The recursive feasibility of the MPC-based guidance algorithm is guaranteed by executing the original and relaxed trajectory optimization algorithms in parallel. Additionally, the boundedness of the guidance error is proved. Therefore, the guidance algorithm is optimal, robust, and practically stable under constraints and disturbances. Numerical experiments are provided to demonstrate the effectiveness of the proposed algorithm.