A comparison of Newtonian, Kustaamheimo/Stiefel, and Sperling/Burdet solutions to optimal trajectory problems
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Detailed documentation of the HILTOP and ASTOP computer programs is presented along with results of the analyses of the possible extension of the HILTOP program and results of an extra-ecliptic mission study performed with HILTOP.
For abstract, see N75-28084.
Altitude potential of an off-the-shelf F4-C aircraft is examined. It is shown that the standard F4-C has a maximum altitude capability in the region from 85000 to 95000 ft, depending on the minimum dynamic pressures deemed acceptable for adequate flight control. By using engine overspeed capability and by making use of prevailing winds in the stratosphere, it is suggested that the maximum altitude achievable by an F4-C should be in the vicinity of 95000 ft for routine flight operation. This altitude is well in excess of the minimum altitudes which must be achieved for monitoring the possible growth of suspected aerosol contaminants.
Atmospheric sampling has been carried out by flights using an available high-performance supersonic aircraft. Altitude potential of an off-the-shelf F-15 aircraft is examined. It is shown that the standard F-15 has a maximum altitude capability in excess of 100,000 feet for routine flight operation by NASA personnel. This altitude is well in excess of the minimum altitudes which must be achieved for monitoring the possible growth of suspected aerosol contaminants.
The singular perturbation theory (SPT) approximation of optimal feedback control laws is presented and methods for on-line application of these approximations are discussed. It is demonstrated that SPT control laws break down when the current state is near the terminal target state. The use of continuation methods to improve the accuracy of the SPT approximation and to obtain global solutions of two-point boundary value problems is also discussed. As an illustration, consideration is given to the minimum-time control of a supersonic aircraft for a three-dimensional intercept problem.
Equations of motion were derived for the three dimensional flight of a lifting vehicles, taking into consideration all the main effects of different forces acting on a vehicle at orbital speeds. A set of equations was formulated which are valid for both the flight with lift modulation inside a planetary atmosphere and the Keplerian motion in the vacuum. The equations are independent of the physical characteristics of the vehicle. The only parameters involved are the maximum lift to drag ratio of the vehicle and a constant characterizing the atmosphere. The results obtained can be applied without modifications to any future reentry vehicle, regardless of its size, shape, and mass.
A practical scheme is presented for generating fixed range, minimum fuel vertical flight profiles that also satisfy time-of-arrival constraints. The resulting algorithm is suitable for incorporation into an on-board flight management system. Example results show that such a capability can save up to 6% of fuel burned in flights subject to delays because of terminal area congestion.
Rising fuel costs combined with other economic pressures have resulted in industry requirements for more efficient air traffic control and airborne operations. NASA has responded with an on-going research program to investigate the requirements and benefits of using new airborne guidance and pilot procedures that are compatible with advanced air traffic control systems and that will result in more fuel efficient flight. The results of flight testing an airborne computer algorithm designed to provide either open-loop or closed-loop guidance for fuel efficient descents while satisfying time constraints imposed by the air traffic control system is summarized. Some of the potential cost and fuel savings that are obtained with sophisticated vertical path optimization capabilities are described.
Previously cited in issue 07, p. 975, Accession no. A82-20296
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The work completed to date is comprised of the following: a simple vehicle model representative of the aerospace plane concept in the hypersonic flight regime, fuel-optimal climb profiles for the unconstrained and dynamic pressure constrained cases generated using a reduced order dynamic model, an analytic switching condition for transition to rocket powered flight as orbital velocity is approached, simple feedback guidance laws for both the unconstrained and dynamic pressure constrained cases derived via singular perturbation theory and a nonlinear transformation technique, and numerical simulation results for ascent to orbit in the dynamic pressure constrained case.
Two velocity optimization schemes for resolving redundant joint configurations are compared. The Extended Moore-Penrose Technique minimizes the joint velocities and avoids obstacles indirectly by adjoining a cost gradient to the solution. A new method can incorporate inequality constraints directly to avoid obstacles and singularities in the workspace. A four-link arm example is used to illustrate singularity avoidance while tracking desired end-effector paths.
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A method for generating finite-dimensional approximations to the solutions of optimal control problems is introduced. By employing a description of the dynamical system in terms of its attainable sets in favor of using differential equations, the controls are completely eliminated from the system model. Besides reducing the dimensionality of the discretized problem compared to state-of-the-art collocation methods, this approach also alleviates the search for initial guesses from where standard gradient search methods are able to converge. The mechanics of the new method are illustrated on a simple double integrator problem. The performance of the new algorithm is demonstrated on a 1-D rocket ascent problem ('Goddard Problem') in presence of a dynamic pressure constraint.
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A method for generating finite-dimensional approximations to the solutions of optimal control problems is introduced. By employing a description of the dynamical system in terms of its attainable sets in favor of using differential equations, the controls are completely eliminated from the system model. Besides reducing the dimensionality of the discretized problem compared to state-of-the-art collocation methods, this approach also alleviates the search for initial guesses from where standard gradient search methods are able to converge. The mechanics of the new method are illustrated on a simple double integrator problem. The performance of the new algorithm is demonstrated on a I-D rocket ascent problem ('Goddard Problem') in presence of a dynamic pressure constraint.