Shuttle entry guidance revisited using nonlinear geometric methods

The entry guidance law for the Space Shuttle Orbiter is revisited using nonlinear geometric methods. The Shuttle guidance concept is to track a reference drag trajectory that has been designed to lead to a specified range and velocity. The current guidance law provides exponential tracking locally. We show that the approach taken in the original derivation of the Shuttle entry guidance has much in common with the more recently developed feedback linearization method of differential geometric control. Using the feedback linearization method, however, we are led to an alternative, potentially superior, guidance law. To compare the two guidance laws, stability and performance domains in state space are defined, taking into account the nonlinear dynamics, a state constraint, and a control constraint. The stability and performance domains for the Shuttle law and the alternative law are constructed numerically. The effects of increasing the control capability and changing a parameter in the guidance laws are illustrated. The alternative guidance law achieves the desired performance over a larger domain of the state space; the stability domains for the two laws are similar. For the current operating domain of the Shuttle, the performance improvement offered by the alternative guidance law is probably not significant. With a larger operating domain for the Shuttle or some other entry vehicle, the alternative guidance law should be considered. A more comprehensive comparison taking into account important factors not considered here, such as robustness, would be necessary to decide whether or not the alternative guidance law is superior.