Feeley, Timothy S. | Search NASA

NASA NTRS1991

Techniques for developing approximate optimal advanced launch system guidance

An extension to the authors' previous technique used to develop a real-time guidance scheme for the Advanced Launch System is presented. The approach is to construct an optimal guidance law based upon an asymptotic expansion associated with small physical parameters, epsilon. The trajectory of a rocket modeled as a point mass is considered with the flight restricted to an equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of this problem can be separated into primary effects due to thrust and gravitational forces, and perturbation effects which include the aerodynamic forces and the remaining inertial forces. An analytic solution to the reduced-order problem represented by the primary dynamics is possible. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form.

Feeley, Timothy S.↗

NASA NTRS1990

A real-time approximate optimal guidance law for flight in a plane

A real-time guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higher-order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that real-time approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in three-dimensions is made apparent from the solution presented.

Feeley, Timothy S.↗