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.

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

For the past four decades, Mars missions have relied on Viking heritage technology for supersonic descent. Extending the use of propulsion, which is required for Mars subsonic deceleration, into the supersonic regime allows the ability to land larger payload masses. Wind tunnel and computational experiments on subscale supersonic retropropulsion models have shown a complex aerodynamic flow field characterized by the interaction of underexpanded jet plumes exhausting from nozzles on the vehicle with the supersonic freestream. Understanding the impact of vehicle and nozzle configuration on this interaction is critical for analyzing the performance of a supersonic retropropulsion system, as deceleration will have components provided by both the aerodynamic drag of the vehicle and thrust from the nozzles. This investigation focuses on the validity of steady state computational approaches to analyze supersonic retropropulsion flowfield structures and their effect on vehicle aerodynamics. Wind tunnel data for a single nozzle and a multiple nozzle configuration are used to validate a steady state, turbulent computational fluid dynamics approach to modeling supersonic retropropulsion. An analytic approximation to determine plume and bow shock structure in the flow field is also developed, enabling rapid assessment of flowfield structure for use in improved grid generation and as a configuration screening tool. Results for both the computational fluid dynamics and analytic approaches show good agreement with the experimental datasets. Potential limitations of the two methods are identified based on the comparisons with available data. Six additional geometries are defined to investigate the extensibility of the analytical model and determine the variation of supersonic retropropulsion performance with configuration. These validation geometries are split into two categories: three geometries with nozzles located on the vehicle forebody at varying nozzle cant angles, and three geometries with nozzles located on the vehicle aftbody at varying nozzle cant angles and number of nozzles. The forebody nozzle configurations show that nozzle cant angle is a significant driver in performance of a vehicle employing supersonic retropropulsion. Aerodynamic drag preservation for a given thrust level increases with increasing cant angle. However, increasing the cant angle reduces the contribution of thrust to deceleration. The tradeoff between these two contributions to the deceleration force is examined, noting that performance improvements are possible with modest nozzle cant angles. Static pitch stability characteristics are investigated for the lowest and highest cant angle configurations. The aftbody nozzle configuration results show that removing the plume flow from the region forward of the vehicle results in less interaction with the bow shock structure. This impacts aerodynamic performance, as the surface pressure remains relatively undisturbed for all thrust values examined. Static pitch stability characteristics for each of the aftbody nozzle configurations are investigated; noting that supersonic retropropulsion for these configurations exhibits a transition point from static stability to instability as a function of this center of mass location along the axis.