American Institute of Aeronautics and Astronautics 1 Optimal Online Path Planning for Approach and Landing Guidance Ali Heydari 1 and S. N. Balakrishnan 2 Missouri University of Science & Technology, Rolla, Missouri, 65409 A method for solving finite-horizon optimal control of nonlinear systems has been developed in this paper and used for an online path planning problem. The new controller synthesis is motivated by the state-dependent Riccati equation (SDRE) technique that was developed for solving regulator and tracking problems. However, finite-time problems need to meet specified boundary conditions for the associated Riccati equations. A closed form solution, called the Finite-SDRE, is obtained for the time-varying Riccati equations by using certain approximations. The application in this paper is the closed loop guidance of a reusable launch vehicle (RLV) during its approach and landing (A&L) phase in such a way to land the RLV at a fixed downrange with the least possible vertical velocity and flight path angle. Simulation studies show that the controller provides an excellent performance in terms of meeting the objectives and is quite robust to initial conditions. Nomenclature ܥ ஽ = drag coefficient ܥ ஽ బ = zero-lift drag coefficient ܥ ௅ = lift coefficient ܥ ௅ ଴ = zero-angle-of-attack lift coefficient ܦ= drag force,   = Earth’s gravitational acceleration, 32.174 ݏ/ݐ ଶ ܪ= scale height, 8.5  ℎ = altitude,  ݐ ܭ ூ = lift-induced drag coefficient parameter ܮ= lift force,   = reusable launch vehicle mass, ݏݑ ݏ ݍത = dynamic pressure / ݐ ଶ  = state penalizing matrix  = control penalizing matrix  = final state penalizing matrix  ௔ = aerodynamic reference area  ݐ ଶ ݐ= time, ݏ ݑ= control vector  = velocity magnitude, ݏ/ݐ ݔ= state vector  = downrange,  ݐ  ௙ = fixed final downrange,  ݐ ߙ= angle of attack,  ߛ= flight-path angle,  ߩ= air density, ݏݑݏ/ ݐ ଷ ߩ ଴ = sea-level air density, 0.0027 ݏݑݏ/ ݐ ଷ 1 Ph.D. Student, Dept. of Mechanical and Aerospace Eng., 400 W. 13th St. Rolla, MO 65409, ali.heydari@mail.mst.edu, AIAA Student Member. 2 Professor, Dept. of Mechanical and Aerospace Eng., 400 W. 13th St. Rolla, MO 65409, bala@mst.edu, AIAA Associate Fellow. AIAA Atmospheric Flight Mechanics Conference 08 - 11 August 2011, Portland, Oregon AIAA 2011-6641 Copyright © 2011 by A. Heydari & S.N. Balakrishnan. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.