Development of feasible G&C (guidance and control) methods for precision atmospheric re-entry has remained a challenge since pre-Apollo-era space exploration. The inherent difficulty arises from the governing hypersonic dynamics being significantly nonlinear, subject to parametric uncertainty, and limited with control authority. Vehicle safety requirements impose further constraints, and desired cost objectives complicate an already difficult G&C problem. The scope of this paper is to present a guidance algorithm for optimal trajectory generation based on a reduced-dimension reentry formulation. Preliminary simulations demonstrate the algorithm with feedback used to track the guidance trajectory in the presence of initial state uncertainty. The objective is to further this approach toward an onboard receding-horizon implementation