Three-Dimensional Ascent Guidance Method for Two-Stage Solid Rocket Launch Vehicles under Multiple Constraints and Uncertainties

Abstract

This article proposes a new three-dimensional (3D) guidance algorithm for a two-stage solid rocket-powered launch vehicle in the ascent phase. The method consists of a longitudinal and lateral cooperative online trajectory generation method and a model predictive control (MPC) based tracking method. First, we introduced a new variable, named lateral displacement distance, to describe lateral motion. After decoupling the 3D dynamics into the longitudinal and lateral movements, the lateral distance was calculated by minimum order polynomials, as well as the altitude in the longitudinal plane. The multiple constraints were satisfied accordingly. This new representation transforms the online trajectory generation problem into a single-parameter root-finding problem, which is solved online by Newton’s method. Second, the traditional energy management method, which usually works in the last phase of multistage solid rockets, was extended to all stages. A proportion was put forward to allocate the energy management demand to the two stages of solid rockets. This strategy can enlarge the energy management capacity of solid rockets. Third, the MPC method was adopted to obtain the tracking guidance law to lessen the effect of uncertain parameters. The subsequent stability analysis shows that the MPC-based tracking controller is closed-loop stable and can handle the constraints and parameter uncertainties simultaneously. Finally, the effectiveness and robustness were verified by validating a two-stage solid rocket’s ascent phase flight under aerodynamic uncertainties and initial state deviations. In comparison to the existing energy management method, the incorporation of the sideslip angle design in this study renders solid rockets more capable at energy management. The proposed algorithm can accurately steer the rocket vehicle to the transition window.