In recent years, NASA has indicated a desire to return humans to the moon. With NASA planning manned missions within the next couple of decades, the concept development for these lunar vehicles has begun. The guidance, navigation, and control (GN&C) computer programs that will perform the function of safely landing a spacecraft on the moon are part of that development. The lunar descent guidance algorithm takes the horizontally oriented spacecraft from orbital speeds hundreds of kilometers from the desired landing point to the landing point at an almost vertical orientation and very low speed. Existing lunar descent GN&C algorithms date back to the Apollo era with little work available for implementation since then. Though these algorithms met the criteria of the 1960's, they are cumbersome today. At the basis of the lunar descent phase are two elements: the targeting, which generates a reference trajectory, and the real-time guidance, which forces the spacecraft to fly that trajectory. The Apollo algorithm utilizes a complex, iterative, numerical optimization scheme for developing the reference trajectory. The real-time guidance utilizes this reference trajectory in the form of a quartic rather than a more general format to force the real-time trajectory errors to converge to zero; however, there exist no guarantees under any conditions for this convergence. The proposed algorithm implements a purely analytical targeting algorithm used to generate two-dimensional trajectories "on-the-fly" or to retarget the spacecraft to another landing site altogether. It is based on the analytical solutions to the equations for speed, downrange, and altitude as a function of flight path angle and assumes two constant thrust acceleration curves. The proposed real-time guidance algorithm has at its basis the three-dimensional non-linear equations of motion and a control law that is proven to converge under certain conditions through Lyapunov analysis to a reference trajectory formatted as a function of downrange, altitude, speed, and flight path angle. The two elements of the guidance algorithm are joined in Monte Carlo analysis to prove their robustness to initial state dispersions and mass and thrust errors. The robustness of the retargeting algorithm is also demonstrated.

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Solving the optimal open-loop control problems for spacecraft large-angle attitude maneuvers generally requires the use of numerical techniques whose reliability is strongly case dependent. The primary goal of this dissertation is to increase the solution reliability of the associated nonlinear two-point boundary-value problems as derived from Pontryagin’s Principle. Major emphasis is placed upon the formulation of the best possible starting or nominal solution. Constraint relationships among the state and costate variables are utilized. A hybrid approach which begins with the direct gradient method and ends with the indirect method of particular solutions is proposed. Test case results which indicate improved reliability are presented. The nonlinear optimal control law derived from iterative procedures cannot adjust itself in accordance with state deviations measured during the control period. A real-time near-optimal guidance scheme which takes the perturbed states to the desired manifold by tracking a given optimal trajectory is also proposed. Numerical simulations are presented which show that highly accurate tracking results can be achieved. / Ph. D.

Current renewed interest in exploration of the moon, Mars, and other planetary objects is driving technology development in many fields of space system design. In particular, there is a desire to land both robotic and human missions on the moon and elsewhere. The core of a successful landing is a robust guidance, navigation, and control system (GN&C). In particular, the landing guidance system must be able to deliver the vehicle from an orbit above the planet to a desired soft landing, while meeting several constraints necessary for the safety of the vehicle. In addition, due to the performance limitations of current launch vehicles, it is desired to minimize the amount of propellant used during the landing. To make matters even more complicated, the landing site may change in real-time in order to avoid previously undetected hazards which become apparent during the landing maneuver. The Apollo program relied heavily on the eyes of the astronauts to avoid such hazards through manual control. However, for missions to the lunar polar regions, poor lighting conditions will make this much more difficult; for robotic missions, this is not an option. It is desired to find a solution to the landing problem such that the fuel used is minimized while meeting constraints on the initial state, final state, bounded thrust acceleration magnitude, and bounded pitch attitude. With the assumptions of constant gravity and negligible atmosphere, the form of the optimal steering law is found, and the equations of motion are integrated analytically, resulting in a system of five equations in five unknowns. When the pitch over constraint is ignored, it is shown that this system of equations can be reduced analytically to two equations in two unknowns. In addition, when an assumption of a constant thrust acceleration magnitude is made, this system can be reduced further to one equation in one unknown. It is shown that these unknowns can be bounded analytically. An algorithm is developed to quickly and reliably solve the resulting one-dimensional bounded search. The algorithm is used as a real-time guidance and is applied to lunar and Mars landing test cases. / text

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Thesis. 1978. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS. / Includes bibliographical references. / M.S.

Thesis. 1978. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS. / Includes bibliographical references. / M.S.

Thesis. 1976. M.S. cn--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO. / Includes bibliographical references. / M.S.cn

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