Investigation of Waypoint Characteristics for ZEM/ZEV Method for Moon Landing Problem

Abstract

The focus of this research is to assess the use of waypoints and their effects on spacecraft guidance for a lunar landing scenario, using the Zero-Effort Miss/Zero-Effort Velocity (ZEM/ZEV) method. The lunar landing scenario simplifies equations and places the focus on the waypoint’s effects. The goal of investigating using waypoints and how to evaluate them is to eventually provide the spacecraft guidance with a closed-loop solution that reduces computational demands in-flight and allow a spacecraft to compute an optimal path in-flight. By computing a path in-flight, mission fuel requirements related to path planning can be decreased, leading to significant savings across the industry. Other research in this area has not fully identified what parameters constitute a desirable waypoint and have typically chosen waypoints through a more brute force method. The solution to assess waypoint characteristics is to compute a path using the ZEM/ZEV method without a waypoint and then compare the path to a path with a single waypoint. When adding a single waypoint, characteristics are changed to see how much impact those characteristics have on the optimality of the path. Through these comparisons, it is found that the optimal path is not equivalent to a path with a waypoint inserted, regardless of what characteristic is changed. This shows that the ZEM/ZEV approach violates Bellman’s principle of optimality because when the path is calculated from the waypoint to the final target, it does not result in the same trajectory for the remaining time. This suggests that the ZEM/ZEV approach, despite being proven as the optimal control law that satisfies the problem, may not have an optimal substructure. It is also found that gravity has a significant effect on the outcome of an optimal path and that when gravity is removed, the path with a waypoint is much closer to the optimal path.