Regulation About Time-Varying Trajectories: Precision Entry Guidance Illustrated

Abstract

Anewmethodforregulating nonlineardynamicsystemsabouttime-varying referencetrajectoriesisintroduced. The control law is a closed-form approximate receding-horizon control law based on the linearized time-varying dynamics. No on-line integration or explicit gain scheduling is required for implementation. Closed-loop stability canalwaysbeachievedwithsuchacontrollaw.TheapplicationofthismethodinentryguidancefortheX-33vehicle leads to very accurately controlled e ight in all the state variables in simulations, which was dife cult to achieve previously. This application demonstrates the potential of this approach as a powerful guidance and trajectory control method in cases for which high precision is required. I. Introduction T HE trajectory control problem for dynamic systems is often addressed in two steps: off-line trajectory planning and on-line trajectory tracking. It is the case for many robot control problems. Inaerospaceengineering,entryguidanceofa spacecraftis currently performed this way. Off-line trajectory planning allows careful design of the trajectory to satisfy all the constraints, optimize performance,andbalancethecone icting requirementsarising fromdifferent aspects of the mission. In the on-line implementation, however, some judicious choices in deciding how to accomplish the control objectives may have to be made because of the limited number of controlsand nonlineardynamics.Forinstance,intheentry guidance problem, the primary means for trajectory control is through modulation of the bank angle. Current nonlinear control methodology