Trajectory optimization for a fixed trim re-entry vehicle using direct collocation with nonlinear programming

Abstract

A procedure is developed to calculate locally optimal trajectories for a class of fixed-trim atmospheric re-entry vehicles. A four degree-of-freedom vehicle model is introduced and appropriate environmental models are chosen and implemented. Software is developed to discretize the optimal control problem using a direct collocation method. The resulting parameter optimization problem is solved using the MINOS non-linear programming software package. The resulting collocation guidance software is tested using data for the Kistler K-1 vehicle system and an existing vehicle simulation. Mass, wind, density, and entry angle dispersions are considered, as are various strategies for updating the trajectory during flight. The results demonstrate that the collocation method is a viable approach to the re-entry vehicle guidance problem. The collocation method integrates the vehicle equations of motion to a useful degree of accuracy using as few as 10 nodes, and the resulting control histories yield acceptably small final position errors.