  The trajectory optimization of the atmospheric entry of a reusable launch
vehicle is studied. The objective is to maximize the crossrange of the vehicle
subject to two control-inequality path constraints, two state-inequality path
constraints, and one mixed state-and-control inequality path constraint. In
order to determine the complex switching structure in the activity of the path
constraints, a recently developed method for solving state-path constrained
optimal control problems is used. This recently developed method is designed to
algorithmically locate the points of activation and deactivation in the path
constraints and partition the domain of the independent variable into
subdomains based on these activation and deactivation points. Additionally, in
a domain where a state-inequality path constraint is found to be active, the
method algorithmically determines and enforces the additional necessary
conditions that apply on the constrained arc. A multiple-domain formulation of
Legendre-Gauss-Radau direct collocation is then employed to transcribe the
optimal control problem into a large sparse nonlinear programming problem. Two
studies are performed which analyze a variety of problem formulations of the
hypersonic reusable launch vehicle. Key features of the constrained
trajectories are presented, and the method used is shown to obtain highly
accurate solutions with minimal user intervention.
