Entry trajectory tracking law via feedback linearization

As a step toward extending the two-dimensional (longitudinal) entry predictive/tracking guidance scheme used by the U.S. Space Shuttle Orbiter to three dimensions, a control law for tracking a three dimensional entry trajectory is designed. The tracking law commands the angles of attack and of bank that are required to follow a ground track specified as a function of energy. Feedback linearization is used to design the tracking law. Some extensions to the existing theory are required to accommodate features of the entry tracking problem. Downrange and crossrange angles serve as output variables for the feedback linearization and lead to state and control transformations that convert the entry dynamics to an equivalent linear system in an approximate sense, which is defined. A feedback tracking law is then designed, taking advantage of the linear structure of the system dynamics in the transformed variables. This tracking law is shown to achieve bounded tracking of the output variables. Simulation results indicate the effectiveness of the tracking law in compensating for initial offsets from a reference trajectory.