Energy Based Suboptimal Reentry Guidance of a Reusable Launch Vehicle Using Model Predictive Static Programming

Abstract

Using the recently-developed computationally efficient model pred ictive static programming (MPSP) and three-dimensional nonlinear vehicle dynamics with spherical and rotating earth, an energy based suboptimal reentry guidance technique is presented in this paper for a reusable launch vehicle (RLV). This guidance essentially shapes the trajectory of the RLV by predicting the necessary angle of attack and bank angle that the vehicle should execute. The path constraints (imposed as ‘soft constraints’) are in the form of structural load and thermal load constraint as well as bounds on angle of attack and bank angle. The terminal constraints (imposed as ‘hard constraints’), on the other hand, are are in th e form of three-dimensional position and velocity vector components at the end of the reentry. Whereas the angle of attack solution comes out of the MPSP guidance directly, the bank angle command generation is done in two steps. First, the required heading angle is considered as an intermediate control variable to steer the vehicle towards the desired final coordinates. Next, the required bank angle is computed through a dynamic inversion loop considering the heading angle dynamics. Such a two-loop synthesis leads to smoothness as well as reversals in the bank angle at appropriate points in the trajectory within the specified bounds. The computationally e fficient MPSP guidance law is primarily based on nonlinear optimal control theory and hence embeds effective trajectory optimization concepts into the guidance law. In addition to the promising results for the nominal case, it has also been demonstrated that the proposed guidance has sufficient robustness for perturbat ions in the states, which may possibly arise from noise input.