Tracking Law for A New Entry Guidance Concept

Introduction A new entry guidance concept is developed for an unpowered lifting vehicle. The two-dimensional longitudinal plane entry guidance scheme used by the U.S. Space Shuttle Orbiter is extended to a threedimensional entry guidance scheme. The guidance task is posed as planning and tracking a reference trajectory. This paper concerns the design and analysis of the tracking law. In the new guidance scheme, the complete ground-track is planned as a function of energy and tracked by commanding both the angle of attack and angle of bank. This extension to the Shuttle entry guidance scheme is carried out within the theoretical framework of differential flatness and feedback linearization. Approximately flat outputs for the system dynamics are identified which are then used to construct a state-variable transformation which together with a static state feedback control transformation renders the system approximately input-output, as well as input-state linear. In the transformed state and control variables, the system dynamics can be represented by two approximately decoupled linear systems. A feedback tracking law is then designed by taking advantage of the linear structure of the system dynamics in the transformed coordinates. This tracking law is shown to achieve bounded tracking of the flat outputs. Simulation results indicate that, if provided with an appropriate reference trajectory, the tracking law guides the vehicle to within one nautical mile of the target in downrange and cross-range during the hypersonic entry phase. 'Graduate Student, Student Member AIAA. t Research Assistant, AIAA member, presently at The Aerospace Corporation, 2350 E. El Segundo Blvd., El Segundo, CA 90245. ^Associate Professor, Associate Fellow AIAA. § Copyright ©by Kenneth D. Mease, Published by AIAA with permission Current efforts to develop a reusable launch vehicle (RLV) and a space station crew return vehicle provide particular motivation for improving the entry guidance capability for a lifting unpowered vehicle. In this paper we develop a natural extension to the longitudinal entry guidance scheme used by the U.S. Space Shuttle Orbiter. The new entry guidance scheme follows from the property of differential flatness of a system." A controlled system is differentially flat if there exist output functions, termed flat outputs, equal in number to the control inputs, such that all the state and control functions can be determined from the output functions and their derivatives through purely algebraic relations. A differentially flat system offers the possibility of reduced-order trajectory planning in terms of the flat outputs. Moreover, the flat outputs often permit feedback linearization of the controlled system dynamics, i.e., they lead to state and control transformations that globally linearize the dynamics. Thus guidance law design and analysis may become greatly simplified for a differentially flat system. Following this paradigm, the guidance task is divided naturally into a trajectory planning subtask of determining the reference output functions consistent with a trajectory that meets all the guidance objectives, and a trajectory tracking subtask of determining the control commands to track the reference output functions. The longitudinal-plane entry guidance logic used for the Shuttle can be viewed as a product of the approach just described. Drag is the flat output used in trajectory planning and the magnitude of the bank angle is commanded to track the reference drag trajectory. The reference drag trajectory is planned as a function of velocity such that it achieves the desired down-range and satisfies the vehicle thermal, normal load and dynamic pressure constraints, as well as the controllability constraint imposed by the